Wikipedia talk:WikiProject Mathematics/Archive/2024

Jan 2024

Undue weight (Lambert function)

Looking at a recent edit in it.wiki, I noticed that the Lambert function page (as well as some related one) is full of references to the work of T.C. Scott and his collaborators always added by the same user (TonyMath), which I presume is Scott himself. The same applies to en.wikipedia (although here it is less obvious because the relevant pages are longer) and in many other languages. I cannot immediately judge all his additions, but my guess is that his work is being given undue weight, given all the scientific literature that is being published nowadays. For sure, the very recent work related to the Riemann hypothesis that he just linked seems not nearly notable enough to be referenced on Wikipedia. There are many many criterions for the Riemann hypothesis, only a few of which are notable, and the fact that an obscure one can be expressed by using also a generalization of the Lambert function (which is a very natural/simple function to come up in all sort of problems) is not very relevant at all. It would be helpful if someone could give a look to his edits to see if his works should be referenced or not. --Sandrobt (talk) 10:03, 2 January 2024 (UTC)

Yes, that paper from less than a month ago is not due mention in that context. XOR'easter (talk) 15:30, 2 January 2024 (UTC)

For clarification, I was given the green light to include the section on the Generalized Lambert W function by a Wikipedia editor. This Generalized Lambert W function has a number of successful applications in Physics and Applied Mathematics. The talk section for the Lambert W function will confirm that. I was told to be bold and make the changes myself. Since then I have taken it upon myself to make the updates in good faith. There is a considerable and noteworthy body of work associated with the Generalized W function. FYI, that work by Ross McPhedran on the Keiper-Li Criterion for the Riemann Hypothesis is notable. It might not be maybe ready to be cited on the Wiki page for the Riemann Hypothesis but IMHO, it is worthy of the Wiki page for the Lambert W function itself (which is always looking for applications). Having said all this, I will adhere to this change of policy. TonyMath (talk) 03:13, 3 January 2024 (UTC)

There's been no change in policy; WP:SECONDARY, WP:DUE and WP:COI have been the "law of the land" (as it were) for a long time. XOR'easter (talk) 04:24, 3 January 2024 (UTC)

Rest assured, I am not asking you to overturn your decisions. I am aware of these policies which is why I pleaded my case on the talk page for the Lambert W function. Robinh read my papers, deemed them worthy and gave me the green light and told me be bold and make the changes myself. TonyMath (talk) 04:45, 3 January 2024 (UTC)

Li's criterion is indeed notable as it attracted quite some interest at the time (I didn't realize you were referring to it since you used the non-standard name Keiper-Li). However your work on the criterion is clearly not sufficiently relevant to be mentioned in Wikipedia. And as far as I'm concerned a clean up should not be limited to that paper. Of all the generlizations of Lambert's function only yours are relevant? It's a function that has appear countless many times. I doubt the literature on its generalization reduces to your works only.--Sandrobt (talk) 20:48, 4 January 2024 (UTC)

The reason why the Wiki section cites my work is because this generalization of the Lambert W function is largely my invention albeit worked out with collaborators in different fields. It has indeed many applications in fundamental Physics including relativity and quantum mechanics. As I mentioned before, I was given the green light as I mentioned earlier. There is also the work of Mező István which is similar but his generalization is a special case of my own. He is also cited in Wikipedia. Apart from that, I am not aware of any other generalizations of the Lambert W function that are useful and have so many applications with all due respect. However, if you are aware of any of them, you are welcome to add to the Wiki site. FYI, my generalization is the only one mentioned at NIST (National Institute of Standards and Technology). See [1]. TonyMath (talk) 00:13, 5 January 2024 (UTC)

I have no particular insight about this topic, but note that "given the green light" is not really how Wikipedia works. Anyone (including you) is welcome to "boldly" create/edit articles here, but then other editors are likewise welcome to dispute or modify those edits, and the final content/form of articles is decided by consensus. Nobody here is accusing you of doing anything inappropriate, but the decision about how the article should finally look doesn't really depend on any permission granted beforehand. –jacobolus (t) 01:23, 5 January 2024 (UTC)

I fully appreciate what you are saying and I have tried to address this issue of consensus within the talk pages as best I could over the years. I should explain my motivations behind all this. The Lambert W function was one of those relativity obscure functions, invented by Lambert in the 18th century and "reinvented" every decade or so, ever since. Mathematicians and Physicists would stumble upon it without realizing it was Lambert's function. It wasn't until the 1990s, that the team of Mathematicians and Mathematical Physicists (including myself) involved with the Maple system that the ubiquitous nature of this function was realized. Applications grew in number and when the standard function was insufficient, generalizations were made to accommodate an even greater range of applications. Unlike other special functions, the Lambert W function was not developed in a holistic way. Rather we stumbled unto it by necessity. This is where the use of systems like Maple and Mathematica and awareness by e.g. Wikipedia and other online sites are very helpful. This helps avoid re-inventing the wheel. By now, there is definitely a body of work out there where some consensus has been achieved by users and researchers (although apparently, that consensus might not have been achieved w.r.t. Wikipedia). Please consider this before any further changes to the Wiki site. If I may (and at the risk of offending you), I cannot help but sense that part of the problem is that the Physics aspect might not be fully appreciated here. Let me point out that Lambert made contributions to Mathematics and Physics/Engineering. This work has always been inter-disciplinary. TonyMath (talk) 02:33, 5 January 2024 (UTC)

Like many Wikipedia articles about mathematical functions (including some I have contributed to), this article is unfortunately currently substantially a compendium of loosely organized data, heavy on numbers and formulas (and in this case also gratuitous distracting proofs about indefinite integrals) and light on explanation, with poor narrative flow. What prose it does have assumes an extreme level of background and is all but illegible to most readers, densely full of undefined jargon. If anyone wants to best improve the article, in my opinion the most valuable contribution would be to add to/clarify the prose, and possibly get a bit choosier about the more obscure formulas. I don't know enough about this topic to help with that though. –jacobolus (t) 04:13, 5 January 2024 (UTC)

I agree! The development of the Lambert W function over the years according to the historical dynamic I described has indeed lead to a somewhat chaotic and chunky site. IMHO, the Wiki page for the Lambert W function needs to be streamlined. A possibility would be to compartmentalize the Wiki site into at least two sites: one page for the main overall description and thrust of the function and the other with various identities and details i.e. a much needed overhaul. TonyMath (talk) 04:53, 5 January 2024 (UTC)

Concerning the work on the Keiper-Li criteria, this is largely the work of Ross McPhedran. You insist that the paper is unworthy of mention. McPhedran is a mathematical Physicist of considerable renown. You can look him up in Google scholar. Have you even read the paper? IMHO, it's a considerable achievement and worthy of mention albeit not on the site of the Riemann hypothesis itself. TonyMath (talk) 00:34, 5 January 2024 (UTC)

McPhedran appears to have published four works on the Li criterion (arXiv:1801.07415, 2003.14241, 2311.06294, and ACM CCA), with a grand total of two citations on Google Scholar. There is no evidence that these works have had any impact whatsoever. He is indeed a notable physicist, but not notable for this. —David Eppstein (talk) 00:46, 5 January 2024 (UTC)

Fine. Concerning McPhedran's work, clearly this has to be given time. At any rate, I am not asking to overturn the actions made so far. I was only answering the messages by @Sandrobt. TonyMath (talk) 01:08, 5 January 2024 (UTC)

For further clarification on the issue of why there aren't more generalizations reported in Wikipedia, when it comes to developing the Lambert W function, there are really only two main groups. There is the group of Robert Corless, David Jeffrey and co-workers including the canonical publication with the famous Computer Scientist Donald Knuth and my group with its collaborators including the great British physicist Alexander Dalgarno. There are a few other players, most of which I know or the group Corless et al. know. I wish there were more groups. On this issue of "consensus', from time to time, there have been individuals that have tried to contribute to the Wiki page only to be rejected. On the whole, I'd say Wikipedia editors have done their necessary filtering and supervision over the years. TonyMath (talk) 03:51, 5 January 2024 (UTC)

Bernoulli polynomials and Euler polynomials

The article Bernoulli polynomials is almost as much about the Euler polynomials as it is about the Bernoulli polynomials. Would it be a good idea to rename the article to "Bernoulli polynomials and Euler polynomials"?  --Lambiam 19:08, 21 December 2023 (UTC)

See also Talk:Bernoulli polynomials § Requested move 24 December 2023.  --Lambiam 09:34, 5 January 2024 (UTC)

Derivative#Total derivative, total differential and Jacobian matrix

The Derivative article looks pretty fair overall until towards the end, particularly § Total derivative, total differential and Jacobian matrix. It could use attention. I'm not convinced that it's adequately cited or that the {{citation needed}} tags are in the right places; the text seems overly detailed in places. XOR'easter (talk) 15:44, 2 January 2024 (UTC)

The article is about a special case, so I've uptated the {{about}} to reflect that and to provide more links. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:04, 2 January 2024 (UTC)

That's an awful lot of links. Would anyone really expect to find pushforward (differential) when they click on a link for Derivative? XOR'easter (talk) 17:07, 2 January 2024 (UTC)

My guess is that this article should be focused on the derivative concept, with some types and generalizations; that section is overly detailed IMO, and it could probably be removed and written on its own article, Total derivative. Hopefully, someone can give an alternative opinion. Dedhert.Jr (talk) 06:16, 6 January 2024 (UTC)

I was just thinking that the material that really gets into the weeds could be moved over to total derivative. I'm reluctant to abandon it entirely, because it at least tried to explain motivations, but it needed work and probably did not belong in the same article that covers how to differentiate $x^{2}$. XOR'easter (talk) 14:43, 6 January 2024 (UTC)

I already hide them for temporarily. It is almost complete, just only referencing problems in some sections. One citation needed tag appears in the definition by using the limit. The history of continuity and differentiable still needs more sources, especially for the claim that most of the functions are differentiable at all or almost every point. The directional derivative is a similar problem with the overly detailed total derivative; I guess this redundant point could be removed, but keep the last paragraphs and find some sources. The rest is the verifiability of the sources in some sections that I have to check and then find more sources again. Dedhert.Jr (talk) 14:51, 6 January 2024 (UTC)

Sums of three cubes, and sums of four cubes

We have a page on the sum of four cubes problem, as well as the sums of three cubes problem. The two problems have significant overlap. The four cubes problem is definitively known for numbers not congruent to 4 or 5 mod 9 and is suspected true for numbers satisfying that congruence, while the three cubes problem is only suspected true for numbers not congruent to 4 or 5 mod 9 and definitively false for numbers satisfying that congruence. Also, naturally, if one were to prove the three cubes problem, then adding 1 or -1 would solve the four cubes problem too. Given the similarity, and the relative lack of content on the four cubes problem, is it worth keeping the two pages separate? GalacticShoe (talk) 22:00, 5 January 2024 (UTC)

I think they are both distinct from each other in flavor, and long enough that a merger is not called for and would be unhelpful to readers seeking information on either one. —David Eppstein (talk) 23:42, 5 January 2024 (UTC)

Fair enough. Would it be useful for each article to include at least a short section on the other problem? As it stands, I feel like the two problems are connected enough to merit more than an inconspicuous listing in their See alsos. GalacticShoe (talk) 17:26, 6 January 2024 (UTC)

E (mathematical constant)#Alternative characterizations

I'm vaguely dissatisfied with e § Alternative characterizations. When I came across it, it was an uncited grab-bag of unmotivated properties without motivations or relations. I've tried to flesh it out, but I'm still not convinced this is the right way to present the material. XOR'easter (talk) 21:03, 1 January 2024 (UTC)

I don't like the numbered list. I'd prefer just paragraphs of prose. –jacobolus (t) 17:03, 2 January 2024 (UTC)

I've prosified that passage now and rearranged things somewhat. XOR'easter (talk) 17:37, 2 January 2024 (UTC)

After looking at this again, the whole section seems pretty redundant (there's also a "Representations" further down). It could possibly be just eliminated. –jacobolus (t) 18:29, 2 January 2024 (UTC)

That's a good point; however, I tend to feel that there's a difference between what is presented as a definition of e and a formula that eventually works out to e. People define e by saying that it's the sum of an infinite series or that it's the number which satisfies some nice calculus property, not that it is the result of a Wallis-like infinite product. I've edited the beginning of "Representations" to make it less redundant. XOR'easter (talk) 19:00, 2 January 2024 (UTC)

While we're here, what major things about $e$ is the article missing? XOR'easter (talk) 00:39, 7 January 2024 (UTC)

Requested move at Talk:Information processing (psychology)#Requested move 7 January 2024

There is a requested move discussion at Talk:Information processing (psychology)#Requested move 7 January 2024 that may be of interest to members of this WikiProject. Vanderwaalforces (talk) 19:13, 7 January 2024 (UTC)

Diagonal and co-diagonal

Since there was no source for the diagonal morphism, I added references to the article and then I realized that some of those references also explain the co-diagonal morphisim. So, I thought I'd add the definition of co-diagonal morphism to the Diagonal morphism. Is this notion in the correct place? If it is a correct, I'm thinking of renaming the article to the "Diagonal and co-diagonal" and create a redirect co-diagonal morphism. Also, which is better, codiagonal or co-diagonal? --SilverMatsu (talk) 00:00, 1 January 2024 (UTC)

I added a figure. But, rather than adding a thumbnail to the top of the article, it may be better to split the figure into two and insert it into the body of the article. --SilverMatsu (talk) 00:17, 8 January 2024 (UTC)

Proposed new project topic: Mathematics Didactics

Wikipedia is an educational platform in itself and this project, in particular, focuses on mathematics. Therefore, I believe it is essential to present the topic of ‘Research in Mathematics Didactics’. This field of study is crucial for improving the teaching and learning of mathematics, and I hope that by making it known, we can contribute to its development. Lucas Varela Correa (talk) 16:30, 7 January 2024 (UTC)

See existing article at Mathematics education and especially its extensive subsection Mathematics education § Research. —David Eppstein (talk) 17:38, 7 January 2024 (UTC)

I don't understand what you are proposing specifically. Please feel free to contribute to Wikipedia articles about math education per se and also include material about math education where it is relevant to other articles.

Many of the Wikipedia articles about basic mathematical topics (at the primary/secondary school level) are incomplete or mediocre, and can definitely use help. If you give some idea of your expertise / interests, maybe someone can recommend a place to start. –jacobolus (t) 19:18, 7 January 2024 (UTC)

I think the topic is research in mathematics education, rather than the practice of mathematics education or the subjects typically taught in the practice of mathematics education. My impression is that when people call it "didactics" they tend to mean a greater focus on the philosophy of the topic and less focus on how to actually go about doing it, but that may be an inaccurate opinion based on unfamiliarity. Regardless, see the link for our existing coverage of this topic. —David Eppstein (talk) 19:54, 7 January 2024 (UTC)

The section Mathematics education § Research is IMO not very good. It's a grab bag of miscellaneous topics at different levels of abstraction, missing many fundamental related topics, with weak sourcing and several with inaccurate summaries of current scholarly consensus / pushing the POV of particular researchers. It would be great to have some experts work on improving this article and ideally expanding some of the pieces as separate articles. –jacobolus (t) 20:04, 7 January 2024 (UTC)

Because randomized trials provide clear, objective evidence on “what works” — good news, everyone! We don't need no stinking meta-analyses! XOR'easter (talk) 01:33, 8 January 2024 (UTC)

Agreed that this section is not good. I've made a small edit to read "Because of an opinion that randomized trials..." which I think is an improvement, although I don't have any expertise in these topics. Gumshoe2 (talk) 03:26, 8 January 2024 (UTC)

When I say Mathematics Didactics I make reference to the investigation of how to improve the way why teach maths. I know one journal specialized in this topic is call PNA https://revistaseug.ugr.es/index.php/pna/ the language of the papers can be three English/Spanish/Portuguese Lucas Varela Correa (talk) 20:53, 7 January 2024 (UTC)

why no we sorry Lucas Varela Correa (talk) 21:03, 7 January 2024 (UTC)

Also see Category:Mathematics education journals. —David Eppstein (talk) 23:01, 7 January 2024 (UTC)

Original proof of Gödel's completeness theorem

There is a dispute at Original proof of Gödel's completeness theorem. Dirsaka claims to have found a fundamental flaw in Gödel's original proof. (Dirsaka does not claim that the actual result is wrong, just that particular proof.) I do not have time at the moment to follow through all the arguments, but the chance that an error so basic, in such a prominent piece of mathematical history, would have escaped notice till now, strikes me as ... unlikely. If anyone wants to dive in and figure it out, that would be a service. --Trovatore (talk) 19:02, 5 January 2024 (UTC)

Well the latest addition obviously violated WP:OR and basic principles of how to write an encyclopedia article, and Dirsaka had never responded to the previous round of objections to their additions (several months ago), so I have reverted their addition. This did not require having an opinion on the underlying validity of either the proof or the objection. --JBL (talk) 19:16, 5 January 2024 (UTC)

Yeah, that's fine procedurally. It would still be nice to understand the objection on the merits, even if not strictly required for purposes of maintaining the article. --Trovatore (talk) 19:23, 5 January 2024 (UTC)

Here is my article explaining the error in Gӧdel's claimed proof of his incompleteness theorem better than my now deleted Wikipedia article comment does.--Dirsaka (talk) 04:56, 8 January 2024 (UTC)

I just had a glance at your article. I didn't understand all details, but here is why your article doesn't convince me:

You quote from some version of Gödel's proof "let F be a functional variable" which I read as "let F be a symbol for a (binary) relation (on natural numbers)". Lateron, your main point of criticism appears to be that Gödel doesn't show that "F is of degree 0". However, degree is a property of formulas in prenex normal form, essentially counting the number of $\forall$/$\exists$ changes. So F, or, more precisely, F(r,n), as it occurs in the formulas B and C, with r, n being two bound variables over natural numbers, is an atomic formula, without any quantifiers; therefore it of course has degree 0. - Jochen Burghardt (talk) 10:00, 8 January 2024 (UTC)

More on 0

There are a few remaining {{citation needed}} tags in the article 0. Almost half of them are in the "Computer science" section and can probably be sourced to technical manuals explaining the fundamentals of various languages. I have no will to push it through the GA or FA process, but it's highly visible as far as math articles go, and it'd be nice to have it free from flagged problems. XOR'easter (talk) 22:01, 13 January 2024 (UTC)

"differentiable symmetry"?

Hi Math folks. Noether's theorem starts out with this sentence:

• Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law.

The two words "differentiable symmetry" are both linked and the blue links make it appear to be one thing, a "differentiable symmetry", but the two links are to different articles. The pairing also appears in the section "Informal statement of the theorem" but no where else. It does not appear in Symmetry (physics) for example. Is it a thing?

If I search on Google for "differentiable symmetry" this exact sentence comes up again and again, making me wonder if the wikipedia version has become the source. I did not see "differentiable symmetry" anywhere in Noether's paper.

Things I read about symmetry use "continuous symmetry". For a physicist, we'd simply assume that a continuous symmetry was differentiable and vice versa until corrected by some math person. But is it true? I'm looking for a reference I can use for the combination. Johnjbarton (talk) 18:40, 8 January 2024 (UTC)

Here is an arxiv article and a published sequel on non-smooth extensions of Noether's theorem. --{{u|Mark viking}} {Talk} 18:53, 8 January 2024 (UTC)

I gather that your reply is equivalent to "differentiable symmetry is not required for Noether's theorem as evident by ..."? Johnjbarton (talk) 19:08, 8 January 2024 (UTC)

Right, continuity isn't sufficient, but it doesn't strictly need to be smooth, either. But in the common nomenclature, people say continuous symmetry without thinking too hard about differentiability requirements. I'd agree with linking to continuous symmetry. If editors felt a need, they could report on differentiability requirements farther down int he article. --{{u|Mark viking}} {Talk} 19:30, 8 January 2024 (UTC)

It should probably just be a link to Continuous symmetry. (That article could be considerably expanded with more analysis of concrete examples.) –jacobolus (t) 18:53, 8 January 2024 (UTC)

Yes, that's my reaction. Johnjbarton (talk) 19:13, 8 January 2024 (UTC)

Thanks, I edited the article. (but not all of the internet that quotes it!) Johnjbarton (talk) 19:33, 8 January 2024 (UTC)

Don't worry too much about quotations of old versions of Wikipedia floating around. There's nothing you can easily do about them, and they tend to have a relatively short half-life. –jacobolus (t) 20:17, 8 January 2024 (UTC)

I would expect the phrase "differential symmetry" to mean something like a diffeomorphism, which is a single symmetry defined by a smooth function. But instead, here it refers to a smooth family of symmetries. Maybe that could be clarified. (Also, "smooth" is usually usable in place of differentiable and is much less technical. It is somewhat vague as to how smooth is smooth, but I think at the start of the article that's an ok price to pay for reduced technicality.) —David Eppstein (talk) 21:27, 8 January 2024 (UTC)

I wouldn't assume everyone reads "smooth" as vague. I think it's reasonably common to use "smooth" to mean specifically $C^{\infty }$. --Trovatore (talk) 21:53, 8 January 2024 (UTC)

Unless explicitly specified in a source, this seems an abuse of terminology, and people should definitely not make that implicit assumption. "Smooth" is probably most commonly used to mean "continuously differentiable", but is generally a pretty vague term. –jacobolus (t) 22:59, 11 January 2024 (UTC)

Well, in any case it's what's used in Differential Topology by Guillemin and Pollack, which was the text for my introduction to the subject as a first-year grad student. I don't know how widely used it is. --Trovatore (talk) 22:21, 13 January 2024 (UTC)

I assume this book makes an explicit definition though. For instance, Lee's Smooth Manifolds has the disclaimer: "You should be aware that some authors define the word smooth differently—for example, to mean continuously differentiable or merely differentiable. On the other hand, some use the word differentiable to mean what we call smooth. Throughout this book, smooth is synonymous with C^∞." –jacobolus (t) 23:12, 13 January 2024 (UTC)

Vietoris-Rips filtration

I have been trying to fix a link to a disambiguation page on Vietoris-Rips filtration. Unfortunately, I have to admit that the article is way over my head. Can someone here solve this link and point is to the right article? Thanks in advance. The Banner talk 19:46, 11 January 2024 (UTC)

@The Banner: It might help if you said what the relevant disambig page was. --JBL (talk) 20:10, 11 January 2024 (UTC)

Never mind, I figured it out (and disambiguated). --JBL (talk) 20:12, 11 January 2024 (UTC)

Thank you very much! The Banner talk 20:13, 11 January 2024 (UTC)

I have just corrected the article's title so that it is called Vietoris–Rips filtration (with an en-dash, as required by WP:MOS) rather than Vietoris-Rips filtration (with a hyphen rather than an en-dash). I also corrected numerous occurrences of the phrase in the article, and fixed the links to the version with they hyphen.

I further corrected the omission of the links to the articles about the two eponyms, Leopold Vietoris and Eliyahu Rips.

One task that should be looked at by those familiar with the topic is to ascertain which other Wikipedia articles ought to link to this one and in particular whether the articles about the two eponyms should link to it. @The Banner: Michael Hardy (talk) 20:44, 16 January 2024 (UTC)

Mathematical theory

Mathematical theory and its history could use more attention. —David Eppstein (talk) 17:53, 16 January 2024 (UTC)

I think you should merge that article into Theory (mathematical logic). Johnjbarton (talk) 18:31, 16 January 2024 (UTC)

I agree that the current content is better addressed at the link you give, but is that the right target for the title? Theory (disambiguation) says that the topic is "an area of mathematical research that is relatively self-contained", but recent edits have taken over the title and moved it in a different direction. —David Eppstein (talk) 18:35, 16 January 2024 (UTC)

I think, to the extent that there's something for an article called (or redirected from) "mathematical theory" to be about, it has to be a theory in the sense of logic. It's certainly true that you can combine the words "mathematical" and "theory" in natural language to refer to other stuff, but we don't (or at least shouldn't) write articles to document how people can (or even do) put particular English words together according to the ordinary rules of English. There needs to be some encyclopedic "aboutness". Usually multi-word titles should be terms of art. --Trovatore (talk) 19:51, 16 January 2024 (UTC)

It seems worth trying to somewhere explain what the word theory in set theory, number theory, graph theory, group theory, etc. etc. is supposed to mean. This is not the same as Theory (mathematical logic). It's closer to scientific theory, but not quite the same. –jacobolus (t) 20:02, 16 January 2024 (UTC)

I suspect that's going to be kind of OR-y. No doubt someone somewhere has written on the subject, but I don't think there's a general accepted answer. In general I'm skeptical of attempts to abstract some commonality out of language and write about it in Wikipedia. --Trovatore (talk) 20:13, 16 January 2024 (UTC)

It's only worthwhile to the extent that suitable secondary references exist. I see zero in the current article. Johnjbarton (talk) 20:27, 16 January 2024 (UTC)

Honestly I would still find it concerning even if a ref or two could be dug up. I doubt there's any generally accepted account of what makes ring theory and fine-structure theory both "theories". I'm sure someone somewhere has made such a proposal, but just having written about it shouldn't entitle you to hijack general mathematical usage and make it sound as though everyone accepts your (ahem) theory on the subject.

If we do want to cover such an account, we should do it in a way that attributes it to the specific workers proposing it. --Trovatore (talk) 20:43, 16 January 2024 (UTC)

Well in that case perhaps Mathematical theory should just be a redirect to List of mathematical theories, maybe with a quick 1- or 2-sentence definition/explanation at the top. –jacobolus (t) 20:48, 16 January 2024 (UTC)

That sounds like a decent solution. --Trovatore (talk) 20:49, 16 January 2024 (UTC)

(Added after Jacobolus suggested a quick explanation at the top.) I think we need to be careful in any such explanation not to reify a particular abstraction of the notion of "mathematical theory". --Trovatore (talk) 20:52, 16 January 2024 (UTC)

I like Jacobolus's suggestion and have boldly gone ahead and done that. I also added Theory (mathematical logic) to the hatnote at the redirect target. —David Eppstein (talk) 20:57, 16 January 2024 (UTC)

LGTM --Trovatore (talk) 21:02, 16 January 2024 (UTC)

I don't think I agree with erasing the discussion of what a mathematical theory is. For example in the Gauge theory (mathematics) I made a clear distinction between the physical use of the term "theory" as in mathematical model of a particular physical phenomenon and the mathematical term "body of knowledge". I reject the implication that every use of the term "theory" in mathematics is "a set of sentences in a formal language" and given the level of confusion the layperson tends to have over the word "theory" in maths and science it seems particularly bold to erase that discussion altogether. Tazerenix (talk) 21:19, 16 January 2024 (UTC)

There is a bit of (unsourced) discussion remaining at Theory#Mathematical. –jacobolus (t) 21:22, 16 January 2024 (UTC)

Do you have a reference that the mathematical term is "body of knowledge"? That is the problem with the article, it is basically hearsay. Johnjbarton (talk) 22:51, 16 January 2024 (UTC)

Here's one example, doi:10.1007/978-3-319-90035-3_8. There's also some relevant discussion at JSTOR 2695275, JSTOR 2026666, JSTOR 2214851, doi:10.1016/S0039-3681(01)00007-3, doi:10.1007/978-94-015-9558-2_24, https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf, https://www.blackwellpublishing.co.uk/content/BPL_Images/Content_store/Sample_chapter/9780631218692/Jacquette.pdf. –jacobolus (t) 01:30, 17 January 2024 (UTC)

Per WP:LEAST, I have changed the target of Mathematical theory into Theory#Mathematical. Indeed, a reader searching for "Mathematical theory" will probably want a definition of the concept rather than an indiscriminate list of mathematical theories. I have also edited the new target.

About the above discussion: it is sure that, in mathematics, "theory" and "mathematical theory" are terms of jargon that are widely used and rarely defined. The number of our articles that have "theory" in their names is a testimony of this. So, this has to be explained in Wikipedia. However, I do not believe that there is much more to say about this than that it is already in Theory#Mathematical. So, for the moment, there is no need of a separate article, and it suffices to improve Theory#Mathematical. D.Lazard (talk) 16:34, 18 January 2024 (UTC)

FAR for Emmy Noether

I have nominated Emmy Noether for a featured article review here. Please join the discussion on whether this article meets the featured article criteria. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" in regards to the article's featured status. The instructions for the review process are here. Z1720 (talk) 20:30, 15 January 2024 (UTC)

I've long since lost any sense of what makes an article "featured", but what this article needs more than anything else is an algebraist who has a decent sense of which textbooks are the least incomprehensible to leave a few footnotes here and there. XOR'easter (talk) 00:19, 20 January 2024 (UTC)

History of Hindu–Arabic numerals images are almost certainly copyright violation

I just added the following comment at Wikimedia Commons Village Pump:

The image File:Evolution of Hindu-Arabic numerals.jpg is a very lightly modified version of a diagram from Karl Menninger's book Number Words and Number Symbols (1969), page 418, originally published in German (1934) as Zahlwort und Ziffer. This is a very clear copyright violation, though the author user:Hu741f4 claimed this as their own cc-by-sa licensed work.

A couple other images are almost certainly also copyright violation: File:Numeration-brahmi fr.png is translated into French, and according to the image description got the numeral images from Datta and Singh (1935) History of Hindu Mathematics which according to History of Hindu Mathematics and IA is in the public domain (I am not sure if that is accurate; the copyright page of these scans says "all rights reserved", but perhaps the copyright has expired in India). I can't immediately tell if this is true and the uploader user:Piero remade the image, or if this was also just scanned from Menninger then overwritten with translated labels, but either way this diagram is too closely based on Menninger's diagram to not be a clear-cut derivative work, and it's especially shady that there's no attribution to Menninger. This was then translated back into English as File:The_Brahmi_numeral_system_and_its_descendants.png by user:Tobus. Again Menninger is not credited, and this one has a description page which no longer makes any claims about where the glyph images come from.

It would be nice if someone would redraw an image that is not such a blatant ripoff. The wide use of these images across Wikimedia projects testifies to their importance. –jacobolus (t) 00:28, 22 January 2024 (UTC)

Andrew Wiles

Just reminder. The article Andrew Wiles is preparing for the possibly the next FA. However, the content of this article may need attention from an expert. It is already more than two months since PR. Dedhert.Jr (talk) 03:41, 22 January 2024 (UTC)

Fuzzy set

I noticed that Category:Iranian inventions and Category:Azerbaijani inventions have been added to Fuzzy set. I've never seen a category related to nationality added to an article about mathematics, so I find it a little strange. SilverMatsu (talk) 02:46, 23 January 2024 (UTC)

It was added in this edit back in March 2020. I agree that it seems odd to add nationality to mathematical 'inventions'. GalacticShoe (talk) 02:57, 23 January 2024 (UTC)

Thank you for your comment. I removed two categories related to nationality from the Fuzzy set. --SilverMatsu (talk) 15:31, 23 January 2024 (UTC)

Good article reassessment for Vector space

Vector space has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. ~~ AirshipJungleman29 (talk) 03:01, 25 January 2024 (UTC)

I'll be honest. Three articles have been nominated to reassess the quality by GA criteria. One of them is Derivative, which is already under control; two of them are still ongoing (E (mathematical constant) and Vector space). I do think there are some old GA Mathematics that could be potentially delisted. Dedhert.Jr (talk) 11:03, 25 January 2024 (UTC)

Sumudu transform

This discussion ought to be here on this page rather than at the Reference Desk. Michael Hardy (talk) 18:55, 21 January 2024 (UTC)

As well as Sumudu transform (re-created after a prod as a trivial variation of the Laplace transform) we now also have new articles Elzaki transform and Aboodh transform. These all have many citations in Google Scholar in what in many cases appear to be low-quality journals. Is this mainstream? Is it something we need to treat similarly to WP:FRINGE, something that can only meet our standards for neutrality if we have mainstream sources assessing it by mainstream standards? — Preceding unsigned comment added by David Eppstein (talk • contribs) 20:39, 21 January 2024 (UTC)

Both Elzaki transform and Aboodh transform are named after their inventors by their inventor themselves, in articles published in the same predatory journal. So the citations of these articles are probably authored by members of their teams. So, I'll PROD these two articles, and if the Prod tag is removed, I recommend to nominate the three articles to AfD. D.Lazard (talk) 09:52, 22 January 2024 (UTC)

There are many self-citations but there are many not. I think it would be more accurate to say that the citations are authored by members of the same subcommunity of researchers. But if the whole subcommunity largely publishes in predatory journals, then we should not take their citation counts as meaningful. —David Eppstein (talk) 23:46, 22 January 2024 (UTC)

@D.Lazard: Update: Aboodh transform has been unprodded. —David Eppstein (talk) 20:15, 28 January 2024 (UTC)

Feb 2024

Which publisher mathematics books that are reliable?

While improving some mathematics articles, I'm skeptical about adding references because some of them are reliable, whereas the rest are self-publishers. As far as I'm concerned, the only reliable publishers are Dover Publications, Cambridge University Press, Oxford University Press, Springer, AMS, and many more. However, what about publishers such as Bod (Book of Demand) and Read Books Ltd.? Are these remains reliable? Dedhert.Jr (talk) 02:11, 30 January 2024 (UTC)

Do you have a specific example book you are curious about? Sometimes if a reputable scholar self publishes a book it can be a reliable source, but some self-published books are about as credible as pseudonymous blog posts or forum comments. A book published by a university press (or similar) is clearly preferable if you can find it. –jacobolus (t) 02:41, 30 January 2024 (UTC)

@Jacobolus I do. One example while I was trying to improve the article Wedge (geometry) is this one [2]. Dedhert.Jr (talk) 02:46, 30 January 2024 (UTC)

That was published by Ginn & Company in 1893. They were a reliable publisher of textbooks. Old, but I suppose usable. The modern 'publisher' is just reprinting a public domain book since it has aged out of copyright. MrOllie (talk) 02:57, 30 January 2024 (UTC)

Ah. I see. Thank you. I am somewhat confused with some sources that are self-publisher. However, it seems that the sources do not have the specific pages, as I am more skeptical in the Google Books settings that exhibit the page, but not accurate. Dedhert.Jr (talk) 02:59, 30 January 2024 (UTC)

This is a book from 1893 published by Ginn of Boston. (Edit: beaten to the punch.) –jacobolus (t) 03:03, 30 January 2024 (UTC)

Really appreciate your work. Dedhert.Jr (talk) 03:04, 30 January 2024 (UTC)

For math books (or any other specialist book), if they get reviewed (and not mocked) by other mathematicians or pedagogues in a reliable publication, they're probably fine. The nice thing about using super-popular oft-reprinted math textbooks is they're easily verifiable and unlikely to have typos. The nice thing about that hidden gem book you might like to cite is that it may have some wonderfully illustrative example problems suitable for adapting to our WP articles (unlike, say, several notoriously difficult but ubiquitous textbooks; or perhaps Dover which is generously assigned because it's cheap, but may not always be the cleanest.) SamuelRiv (talk) 03:07, 30 January 2024 (UTC)

Dover reprints a wide variety of old out-of-print math books, some of which are solid and others of which are really excellent. It's cheap because they get the publishing rights cheaply from publishers uninterested in issuing their own new versions, so you're paying not that much more than the production cost for an average-quality paperback book. When citing material found in a Dover reprint, it's worth trying to figure out the original publisher and title (sometimes Dover changes it); usually, but not always, there's a decent scan at the Internet Archive. –jacobolus (t) 03:30, 30 January 2024 (UTC)

(ec) : I think "Books on Demand" is self-published, so not reliable. More reliable publishers: Addison-Wesley, Prentice Hall, and Wiley (publisher). And look to see if it is reviewed by the AMS! Bubba73 ^{You talkin' to me?} 03:12, 30 January 2024 (UTC)

But what about the case of sources that is taken from Wikipedia content? During the improvement of the same article again, I found this book with Springer as its reliable publisher, but the images are taken from the Wikipedia articles; or another example is in Reeve tetrahedra, where the journal source is taken the reference from the Wikipedia article Pick's theorem? Is it fine to pick them? Dedhert.Jr (talk) 03:21, 30 January 2024 (UTC)

Springer is a massive publisher owned for the past couple decades by a string of financial firms and therefore not especially caring about book quality anymore. Many of the monographs they publish are mediocre, and they also publish things like conference proceedings for niche conferences which can have mixed quality. Some Springer titles have excellent content, though unfortunately nowadays they almost all are printed on demand, with horribly bad printing/binding quality. You should look at the name/reputation of the author, try reading some of the book, look at reviews, etc. to decide if the book is the best source for a particular claim; just the name of the publisher is not a particularly strong indicator. –jacobolus (t) 03:37, 30 January 2024 (UTC)

I'm sorry to hear that about Springer - they were so good back in my day. I think their graduate-level books were called the "yellow peril". Bubba73 ^{You talkin' to me?} 04:14, 30 January 2024 (UTC)

I think their GTM series is still good, but other Springer series can require more care. I just recently ran into a case while adding sources to conical surface of a 2015 Springer book, Encyclopedia of Analytical Surfaces, that had clearly copied from us (at least one identical sentence with an earlier appearance in our article than the publication date of the book), making it unusable per WP:CIRCULAR. That's one reason I sometimes look for older books as sources: as well as being freely available online, they are not going to have that problem. And the mathematics may occasionally be stated in an out-of-date style, but in most cases it is unlikely to become incorrect. —David Eppstein (talk) 07:40, 30 January 2024 (UTC)

There's even worse available in Springer, see e.g. the last chapter of https://doi.org/10.1007/978-3-031-29046-6 which manages to combine modules of sheaves, Ricci flow, the positive mass theorem, and K-theory in the study of echocardiography. It reads like GPT-2. Gumshoe2 (talk) 13:32, 30 January 2024 (UTC)

Wow. Anyway, I think Cambridge University Press is reliably good, and Princeton University Press almost as good. Oxford University Press is likely good as well but I don't have so much experience with them. Springer and CRC are both rather more careless as these examples suggest. Unfortunately MAA Press can sometimes read as thrown-together web scrapings as well. The more researchy imprints of AMS are better. You might expect the Dover mathematics books to be dubious (because cheap paperbacks), but they are surprisingly good, because they are mostly well-chosen reprints of older books. (Disclaimer: I have published with both Cambridge and Springer.) —David Eppstein (talk) 18:26, 30 January 2024 (UTC)

@David Eppstein My question regarding about this problem is how do I know that a publisher is reliable? Dedhert.Jr (talk) 02:57, 2 February 2024 (UTC)

If you have serious doubts then you can ask on WP:RSN but they are going to say that all the publishers we are discussing are good enough. Beyond that I think it comes down to past experience and individual evaluation of how polished and accurate individual sources appear to be. —David Eppstein (talk) 03:09, 2 February 2024 (UTC)

You have to use your judgment. You can look at both internal signals such as how clearly written it is and whether the authors seem careful or sloppy about citing past work, or external signals such as what reviewers said about it, how highly cited the source (or other sources by the same author) is, what honors the author has received, and so on. Even without looking at external signals, some works will give you the sense that a deep expert wrote them with loving attention to detail and were then carefully copyedited, have nicely drawn figures, etc., and others just seem slapped together carelessly. YMMV. –jacobolus (t) 03:30, 2 February 2024 (UTC)

Noted. Thank you. Dedhert.Jr (talk) 04:53, 2 February 2024 (UTC)

Images wouldn't give me pause, especially when they are given proper attribution. Likewise material taken from wikipedia in an otherwise original work can be assumed to be have been vetted by that author, and thus becomes as reliable as the author. Headbomb {t · c · p · b} 03:38, 30 January 2024 (UTC)

WikiProject proposal related to Mathematics: Geometry

You can view the proposal here. Looking for interested Wikipedians. Writehydra (talk) 04:57, 2 February 2024 (UTC)

Wikipedia:WikiProject Polyhedra

Someone has just set up/revived this project. I am wondering whether it would be better placed inside the maths project because it seems a rather narrow field for a new project and will probably not become active as a result — Martin (MSGJ · talk) 19:21, 19 January 2024 (UTC)

As far as I can see the main use for this revival is quality assessment of articles: we can now find the Category:WikiProject Polyhedra articles, sorted by importance and by quality. This may be helpful after the banner shell Borg nuked the |field= parameter we used to use to find sorted collections of articles in mathematics subtopics. —David Eppstein (talk) 00:39, 20 January 2024 (UTC)

It wasn't the "banner shell borg" that nuked the 'field' parameter. This was changed in 2020 in special:diff/986062061 by @MSGJ. It could plausibly be un-changed somehow, but I don't know how worthwhile it would be (then the banner shell bots would need to be reconfigured to ignore the restored parameter, etc.). –jacobolus (t) 17:43, 20 January 2024 (UTC)

@David Eppstein, @Jacobolus, @MSGJ I'm planning for reviving this WikiProject. However, it seems that I forgot what was the reason. One thing that might pushed me to do so currently is to improve many articles on polyhedron in which tables only and facts are unsourced—sorry I totally forgot. Dedhert.Jr (talk) 13:54, 2 February 2024 (UTC)

Coxeter diagram

For the background, I and @Jacobolus are discussing the table explaining the bipyramids while improving the article Bipyramid. One problem if someone applied the table {{Bipyramids}} created by @Tomruen is the Coxeter diagram, which is somewhat technical to understand. Can someone explain what are these notations, and how to understand them? The article Coxeter diagram exists, but the content is already problematic. Dedhert.Jr (talk) 09:39, 27 January 2024 (UTC)

My understanding is that Coxeter diagrams describe Coxeter groups, which in this specific case can be described as groups generated by the reflections of a spherical triangle across its edges. The Coxeter diagram has a vertex for each mirror (three vertices for the three sides of the triangle) and an edge or non-edge indicating the angle at which two mirrors meet (no edge for π/4, an undecorated edge for π/6, and a number n for π/2n). So for a spherical bipyramid, the given diagrams describe the shapes of the faces and represent the symmetries generated by reflections across edges of the bipyramid. —David Eppstein (talk) 19:16, 27 January 2024 (UTC)

Coxeter diagrams for polyhedra represent Wythoff constructions of mirror planes, each node is a mirror. A ringed mirror is "active", with generated point off the mirror plane, generating an edge. This constructs unform polyhedrons. Uniform dual polyhedra are represented with a vertical line through the ringed node(s) of the dual polyhedron. They are indeed somewhat technical, and could be removed, but a useful system with basic understanding. Tom Ruen (talk) 23:29, 27 January 2024 (UTC)

@Tomruen The question is what are the basics to understand this notation? How do I write the notation for every polyhedron, including the bipyramid as mentioned by @David Eppstein? Let's see if I looked up at the table again, where there are some Coxeter diagrams representing the bipyramids.

Regular right symmetric n-gonal bipyramids:

Bipyramid name	Digonal bipyramid	Triangular bipyramid	Square bipyramid	Pentagonal bipyramid	Hexagonal bipyramid	...	Apeirogonal bipyramid
Polyhedron image						...
Spherical tiling image						Plane tiling image
Face config.	V2.4.4	V3.4.4	V4.4.4	V5.4.4	V6.4.4	...	V∞.4.4
Coxeter diagram						...

I've seen more examples of Coxeter diagrams describing four Platonic solids.[3], but it is somewhat different than our articles. Dedhert.Jr (talk) 04:05, 28 January 2024 (UTC)

@Dedhert.Jr The reason I think the discussion of symmetry should be kept (and indeed extended) is that crystallography is the primary application of bipyramids and related shapes. It would be helpful if someone who was an expert crystallographer could take a look though. In my opinion scalenohedron should be split into its own article with a short summary at bipyramid. The current text we have about this and the other related polyhedra is somewhat incoherent and overly technical, and seems to be a bit idiosyncratic / perhaps with some original research thrown in. –jacobolus (t) 07:32, 28 January 2024 (UTC)

@Jacobolus The only thing I could not create this new article is because of lack of sources. I could only found the definition of scalenohedra, but not the symmetry and many other related topics. If it does, I'm aware that it will be redirected again under WP:BLAR; this was already happened with our articles such as the family of duoprisms. Dedhert.Jr (talk) 09:56, 28 January 2024 (UTC)

A search for "scalenohedron" has >1000 sources in Google scholar. It's unquestionably a notable topic about which much can be said that is verifiable. I'm not an expert so couldn't by any means write that article off the top of my head, but if someone wants to put in the work to do a literature review it also shouldn't be inordinately difficult. –jacobolus (t) 10:01, 28 January 2024 (UTC)

Really? I never knew that numerous sources mentions about it. Unfortunately, I don't think I can make it because of the restricted access. Maybe I leave it to someone else. Dedhert.Jr (talk) 10:13, 28 January 2024 (UTC)

Aside: should Icosahedral bipyramid, Tetrahedral bipyramid, Cubical bipyramid, Dodecahedral bipyramid really be articles here? It seems like original research. The only source given is a personal web page, and I can't find any reliable sources about this (I can find this example of "dodecahedral bipyramid" being used to mean something clearly different). –jacobolus (t) 08:02, 28 January 2024 (UTC)

I have no idea how to deal with the original researches. Maybe AfD is the only option if there are no sources mentions about them? Dedhert.Jr (talk) 10:01, 28 January 2024 (UTC)

I also can't find any reliable sources using the name "Blind polytope". The cited sources are user:Tamfang's website https://bendwavy.org and the "Polytope Wiki". user:Tomruen do you have any reliable sources for these topics, or is this a neologism you and/or Tamfang coined? –jacobolus (t) 15:37, 28 January 2024 (UTC)

I'm don't know who first offered the categorical name. It could be moved to Convex polytopes with regular facets. Johnson solids were referenced in 1969 as "Convex polyhedra with regular faces", while the actual lists neglects regular and semiregular forms. I can't say who gave Johnson the honorific name, might also just be websites like MathWorld]. It could be Klitzing's reference is an original source [4]. Tom Ruen (talk) 04:47, 29 January 2024 (UTC)

The earliest example of "Johnson solids" Google scholar finds is Rankin, John R. (1988). "Classes of polyhedra defined by jet graphics". Computers & Graphics. 12 (2): 239–254. doi:10.1016/0097-8493(88)90036-2. But it's certainly plausible that Klitzing and/or MathWorld popularized the name. –jacobolus (t) 10:49, 29 January 2024 (UTC)

To clarify, I host Richard Klitzing's polytope pages at bendwavy.org, but have no hand in writing them. —Tamfang (talk) 05:10, 3 February 2024 (UTC)

Proposed deletion of Mina Ossiander

The article Mina Ossiander has been proposed for deletion because of the following concern:

Adjunct prof with h-index of 7

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Abductive (reasoning) 05:07, 3 February 2024 (UTC)

As the page is presently written there’s no evidence of notability, but low h index should be rejected as a standard to judge by. Gumshoe2 (talk) 10:14, 3 February 2024 (UTC)

True, but false statements about academic rank are an even worse standard. —David Eppstein (talk) 20:04, 4 February 2024 (UTC)

The PROD has been removed. In the future, proposed deletions of interest to this project are best listed at Wikipedia:WikiProject Deletion sorting/Mathematics. --JBL (talk) 17:25, 3 February 2024 (UTC)

Nothing in the article seems particularly notable here. It's just one more person who got a PhD in mathematics and the article lists irrelevant details of their personal life and the title of the thesis and name of the advisor. Not sure why that person was selected as worthy of a Wikipedia article. PatrickR2 (talk) 21:57, 3 February 2024 (UTC)

Anyone can, of course, send the article to WP:AfD if they want to. --JBL (talk) 19:40, 4 February 2024 (UTC)

Quantity of references in mathematics articles

I'm trying to get a better understanding of the content assessment criteria specifically for mathematics articles. I have noticed that mathematics articles often do not include many references. Take for example Ordinal number, many sections in this article don't have any references, or may only provide a single reference for a specific sentence or word in a section. Still, this article was once rated GA, and today is still rated B, indicating only minor problems exist. Can someone provide some advice on this? Mokadoshi (talk) 03:07, 5 February 2024 (UTC)

The Rater tool gives Ordinal number as C rating. That means it most resembles articles that humans have evaluated as C across Wikipedia.

Your observation also applies to physics article. The long-time editors have said that many articles written back in the 2000s where just typed in. But another factor is the huge number of articles.

If the content assessment for an article seems wrong, just change it. Or improve the article up to the current rating ;-) Johnjbarton (talk) 03:17, 5 February 2024 (UTC)

You are right that math articles on Wikipedia are systematically reference-light. I see two reasons.

First, mathematicians were early adopters of Wikipedia. Many math articles were written into decent shape long before there was so much insistence on reliable sources (as Johnjbarton implied above). And, in later years, many editors have not felt strong motivation to systematically add references to long-established, pretty good text.

Second, even professional math articles are reference-light compared to articles I've seen in the natural sciences, history, etc. This is because math is almost pure logic, which the diligent reader can verify or refute for themselves. (Moreover, the policy WP:CALC is interpreted to give broad leeway in math articles.) Mathematicians are simply not acculturated to reference-heavy writing.

Let me emphasize that I am not defending the lack of references in Wikipedia math articles. I am merely enunciating the reasons, as I see them. Regards, Mgnbar (talk) 03:51, 5 February 2024 (UTC)

Professional math sources also typically (not always) do a poor job of citing original authors or describing their work in its own terms: misnamed objects and ideas abound, a wide variety of mythical origin stories persist, and treatment of earlier sources is often anachronistic to the point of pure fantasy. Reading works mentioning math history requires some skepticism and care, as plenty of nonsense gets passed down uncritically. Recent professional mathematical historians have gotten better about this and are more careful to separate what is actually known from invented folklore, especially about older material. Wikipedia math articles could do a better job accurately describing (and citing original sources relevant to) the history of pretty much every topic. –jacobolus (t) 06:20, 5 February 2024 (UTC)

Of course, as soon as I posted this discussion, I came across this discussion from 2006 about this topic, which includes a link to Wikipedia:Scientific citation guidelines. If I'm understanding it correctly: On Wikipedia it is not required to provide a citation on every instance of uncontroversial knowledge. However, in scientific articles "uncontroversial knowledge" is defined broadly to be knowledge that would be known by anyone with an underground background in the field of study, and is covered in any common or obvious books on the topic -- even if this is not known by a layperson. Still, each section should have at least one reference to one of these common or obvious books on the topic, and these can be cited in the first or last sentence of a section (the rest of the section need no references if it contains uncontroversial knowledge).

Am I correct in this? If so, it might be helpful to include a link to this page on Wikipedia:WikiProject_Mathematics/Assessment. This might be obvious to many people, but that is the page I looked at before posting this discussion and found nothing there about citation guidelines. Mokadoshi (talk) 03:58, 5 February 2024 (UTC)

@Mokadoshi: I think the reader's background is supposed to be assumed to be undergraduate-level, rather than secret or subterranean! — MarkH₂₁^talk 04:12, 5 February 2024 (UTC)

My very rough personal scale is: if it supports more than one section, with more than one sentence in them and with a lead that properly summarizes those sections, it is at least start-class (otherwise it's a stub). If it covers the main ground and is adequately referenced but not very well written or organized, or (as in the case at hand) is thorough, competently written and organized, but badly sourced, it is C-class. If it is thorough, well-written, and mostly well-sourced, but maybe with a few topics missing or a few unsourced claims, it is B-class. And if it has all that, it is written as accessibly as reasonably possible, and careful read-throughs and literature searches can find nothing obvious that is still in need of improvement, then it is either GA-class or should be a nominee for GA-class. I don't consider FA-class worth the effort, so the scale stops there. As for Wikipedia:Scientific citation guidelines: I think it is outdated and should be marked historical. I don't think its recommendations to leave background material unsourced, or sourced only to general reference sections at the end, reflect current Wikipedia practice. —David Eppstein (talk) 06:33, 5 February 2024 (UTC)

Invite to join the February 2024 Unreferenced Backlog Drive

WikiProject Unreferenced articles | February 2024 Backlog Drive

1 1 ≠ 2

Many math articles do not have references. This drive wants to change that. The aim of this drive is to cite all unreferenced articles on Wikipedia and ensure its reliability. Barnstars will be awarded based on the number of articles cited. Remember to tag your edit summary with [[WP:FEB24]], both to advertise the event and tally the points later using Edit Summary Search. Interested in taking part? Sign up here.

CactiStaccingCrane (talk) 14:55, 21 January 2024 (UTC)

@CactiStaccingCrane: Where is the list of unreferenced mathematics articles? Michael Hardy (talk) 18:51, 21 January 2024 (UTC)

You can find them at https://bambots.brucemyers.com/cwb/bycat/Mathematics.html#Cites no sources. CactiStaccingCrane (talk) 18:55, 21 January 2024 (UTC)

I'd recommend not turning improving math articles into a race/speedrun. It would be significantly more valuable if someone picked one highly viewed start or C class math article and spent a few hours or days making substantial improvements, instead of trying to spend a few minutes each adding hastily chosen references as footnotes to sections that are already well written and describe well-known topics in a standard way. References found in haste in this way by searching (rather than either chosen by an expert who already knows the literature or carefully found by someone willing to do some significant literature research) tend to be low quality, and ticking off a binary checklist of "has a reference" vs. "doesn't have a reference" is not really very valuable to the Wikipedia project. –jacobolus (t) 20:39, 21 January 2024 (UTC)

No, we are not adding referenced to well-sourced articles. We are adding references to articles that do not have any citations at all and risk being AfDed for not demonstrating that this concept actually exist, especially for mathematics articles where "this concept exists" is not easy to verify. So yes, an article "has a reference" is indeed much better than an article that "does not have a reference". CactiStaccingCrane (talk) 00:34, 22 January 2024 (UTC)

Nevertheless, you are free to chip in at 'check for sloppy work in the drive' thread, as quality control should also play a big part in the drive. CactiStaccingCrane (talk) 00:37, 22 January 2024 (UTC)

It's really not practically helpful to readers to add shitty references to well-written articles, whether or not they already had sources. If something is verifiable it's not going to get deleted, and people sending obviously verifiable stuff to AFD based on a lack of footnotes are wasting everyone's time.

My point is: please don't try to add references to articles as some kind of speed race game in search of little meaningless wiki awards for being the fastest, but instead take the time to do the work properly so it doesn't need to be done over later.

If you (anyone reading along) want to find a reference to some mathematical article which is currently unsourced, take the trouble to find a source which is well written and respected, and then fill out a carefully written citation. This often takes skimming several sources, checking their citation counts in the academic literature, considering which one is most appropriate for the intended audience of a Wikipedia page, etc. It's even better to figure out a bit of the history of the topic and give some concept of the priority for an idea, or give multiple sources appropriate for different audiences. –jacobolus (t) 00:48, 22 January 2024 (UTC)

It might be helpful for you to read this discussion: Wikipedia:Requests for comment/Deletion of uncited articles CactiStaccingCrane (talk) 02:26, 22 January 2024 (UTC)

The tone of your response leads me to think that you care more about the superficial appearance of having little clicky blue footnotes than about the quality of the sourcing, and that you would like the outcome of the sort of speed race game that jacobolus warns against. Perhaps you can persuade me otherwise. —David Eppstein (talk) 02:34, 22 January 2024 (UTC)

Ok, just to clarify, I do agree that in the most ideal scenario, we would get people to give many citations to reliable sources for each article, enough so that the article is unambiguously notable and will be speedily keep in an AfD discussion. This drive's main goal is not to cite small percent of these uncited articles are well-written (e.g. 238 math articles/113000 total), but to cite barely notable articles that you might find in Special:Random, like articles about random places or random people. For a participant in the drive, it is much more efficient to cite these stubs to get those "little clicky blue footnote points" that you mentioned rather than citing math articles that require a lot of effort to find a reliable source. And frankly, who cares about these articles? For all we know citing these articles might not guarantee these articles will be kept. If somebody truly care about an article's existence, they would go above and beyond to cite these articles to meet GNG.

I do agree that this drive is not perfect, and I do want to say that I appreciate that you have raised concerns about the drive and about uncited articles in general. We might be relying too much on good faith here and a better solution might be needed. But it is ludicrous for us to require new articles to be fully cited while we are not making an active effort to cite our older unreferenced articles. We can do better than this. Because a lot of math articles are not cited, I want to send this notice ahead of time so that people like you who knowledgeable about the topic area can help address these articles. CactiStaccingCrane (talk) 02:54, 22 January 2024 (UTC)

@CactiStaccingCrane: As predicted: [5] —David Eppstein (talk) 08:13, 5 February 2024 (UTC)

So? CactiStaccingCrane (talk) 15:32, 5 February 2024 (UTC)

It seems like there are some editors who are really excited about deleting stuff (to rack up points?) whether or not it is notable or verifiable, and are constantly hunting for excuses to do so. That's indeed a problem, but the better solution is to educate them about the Wikipedia project's goals and community process, not to let them push you into wasting time jumping through bureaucratic hoops.

Again, I don't have any problem with the goal of improving the sourcing of poorly sourced math articles. I just don't think this should be turned into a speed game where the person who adds the most footnotes wins irrespective of whether they add any value. –jacobolus (t) 02:42, 22 January 2024 (UTC)

Anyway, don't let me discourage anyone from participating here if you want. I just hope anyone trying to add sources to math articles is doing so carefully and thoughtfully rather than prioritizing speed. My personal experience is that it takes me significant amounts of time and effort to carefully add sources for one small subsection of one article, mostly spent reading and thinking. This contest has badges for adding sources to 300, 500, or 750 articles during the month of February. I can't even imagine doing good work at anywhere close to that pace, even if I spent 10 hours per day for a month doing nothing but adding sources to math articles. YMMV. –jacobolus (t) 02:53, 22 January 2024 (UTC)

I appreciate your concerns about the drive in general. I don't want to give a false assurance here and say that the reviewing process will spot 100% fake references and bogus attempts. But again, the majority of article that will be addressed by these articles are geostubs, biostubs, school/universities and obscure music bands. As an example, there are 238 uncited math articles compared to ~113000 in total. Statistically speaking it is unlikely for people to randomly come across these articles and participants who will cite these math articles are likely to be those knowledgeable about mathematics and seek for these articles deliberately. CactiStaccingCrane (talk) 02:59, 22 January 2024 (UTC)

geostubs, biostubs, school/universities and obscure music bands – what's the point of getting a lot of people to spend their time marginally improving obscure never-read articles that nobody cares about? Personally I think it would be a better use of time for anyone here to make their goal for February something like: "improve one high-importance math article from C class to B class in the next month", including doing a thorough literature review, drawing some nice diagrams, and writing a clear and concise overview of the current expert consensus. Again, YMMV. –jacobolus (t) 03:04, 22 January 2024 (UTC)

I applaud your philosophy here, but not to be condescending, people can have different interests :) CactiStaccingCrane (talk) 03:35, 22 January 2024 (UTC)

Well, despite the disagreements above, the list of unreferenced articles provided by CactiStaccingCrane does at least provide a helpful way of finding some mathematics articles that are on good topics but need help, although many others are on marginal topics (that I would rather not waste my time on). I already took advantage of that list to find and clean up the sourcing in Arithmetic–geometric mean and Basel problem. I think there are plenty of others worthy of attention there. —David Eppstein (talk) 08:42, 22 January 2024 (UTC)

I hope you find them useful :D CactiStaccingCrane (talk) 10:59, 22 January 2024 (UTC)

From my perspective, this is not about adding references, but rather improving the articles. I have seen the tables listing many bunches of articles that may need to be improved. I do think that there are many articles without being tagged that may need to be improved as well, especially with the article that contains many no-context-and-what-to-do-tables. Dedhert.Jr (talk) 03:34, 23 January 2024 (UTC)

One could also view the announcement here as a warning: fix up your unreferenced articles by the end of January, before the cleanup drive starts, or some eager cleanup drive participant will get to them without as much care for detail. —David Eppstein (talk) 04:52, 23 January 2024 (UTC)

Why do you think that adding one citation to a mathematics article so damaging? Or let me be straightforward: why do you view the drive so negatively? CactiStaccingCrane (talk) 05:39, 23 January 2024 (UTC)

I think that it is important to provide high-quality sources for stubs on significant topics in mathematics, and to do something to clean out the many bad stubs on insignificant topics. I think it is important that this be done by people who are interested in the mathematics (not necessarily professional mathematicians!), and not just those interested in getting gold stars for sourcing lots of things, because interest leads to expertise and expertise leads to better choices for the sourcing. I think that having people add low-quality sources to indiscriminately chosen articles causes problems in two directions: it does not change the need for the significant topics to have high-quality sources, but it obscures the fact that they need them, and it does not change the need to clean out the insignificant topics, but by removing them from the lists of problem articles it makes it harder to find them. I hope that the sourcing drive does not lead to this problem of adding low-quality sources to indiscriminately chosen articles but I worry that it might. —David Eppstein (talk) 05:59, 23 January 2024 (UTC)

I think that's true and I should list some examples of what sources is encouraged/discouraged from use generally. But in general, I have to admit that this drive will be a pain in the ass to manage and it will keep me busy for the rest of this and next month ;) CactiStaccingCrane (talk) 09:59, 23 January 2024 (UTC)

I have looked up the list, and it confused me: why is the article decagonal bipyramid classified as "cite no sources", although it is a redirect article? Dedhert.Jr (talk) 10:33, 23 January 2024 (UTC)

Someone has redirected it recently. CactiStaccingCrane (talk) 10:35, 23 January 2024 (UTC)

The list is only updated weekly. In this case, I judged that there were no sources giving decagonal bipyramid independent notability from bipyramid, and redirected it per WP:BLAR in preference to trying to get it deleted. —David Eppstein (talk) 17:54, 23 January 2024 (UTC)

I just redirected the heptagonal and octagonal cases as well, and shrank the still-overwide tables. If there's anything to say about one or another specific n-gonal bipyramid, it can be put in a section of bipyramid. At the point the specific information grows to more than several paragraphs it can plausibly be re-split into a new article again. –jacobolus (t) 18:07, 23 January 2024 (UTC)

While we're here, Bipyramid is very weakly sourced, if anyone is looking for a page to improve sources on. –jacobolus (t) 19:39, 23 January 2024 (UTC)

Thank you for your work! CactiStaccingCrane (talk) 01:01, 24 January 2024 (UTC)

I already have some planning about the sketch of the structure and the improvement of the content, but there are some missing topics; for example, the bipyramidal graph is missing. I remember that there is a source that mentions about the graph of bipyramids, but it is not free access. Dedhert.Jr (talk) 01:51, 24 January 2024 (UTC)

R2 values

Could someone (find a source) and add a sentence to the top of Coefficient of determination that says something like "Generally, bigger/smaller numbers are better", or whatever top-line summary might be useful for someone completely unfamiliar with statistics? WhatamIdoing (talk) 17:51, 7 February 2024 (UTC)

I added a reference in the body of article. However summarizing the meaning of R-squared in a sentence is difficult. Larger values of R-squared imply regression models that are better at reproducing the input data. But "better" is not something R-squared can tell you. Johnjbarton (talk) 18:14, 7 February 2024 (UTC)

Thank you! I really appreciate it.

Some years back, someone was saying that the most dangerous thing in the world was a spreadsheet. Among the many things you can do/screw up with a modern spreadsheet is to select some data, click two buttons to make a graph, and then click another button to fit a regression. But there are options (e.g., linear vs logarithmic), and while there are doubtless better ways to go about it, I imagine that the most common way to pick one is to try all the options and then pick the one that you think looks best. The more advanced options require knowing what you're doing – like knowing whether it's better, if you just click through all the options, to pick the option whose automatically calculated R² is the biggest or the smallest in the list. This is the level of comprehension that I was hoping to address here. WhatamIdoing (talk) 18:37, 7 February 2024 (UTC)

Conformal linear transformation

Your input is requested to settle a dispute at Talk:Conformal linear transformation. Thanks. 100.36.106.199 (talk) 11:51, 8 February 2024 (UTC)

"univalent relations"

A recent edit at partial function by User:Rgdboer claims that a partial function is a "univalent relation". I googled that term, and the first hit was an entry at univalent added by Rgdboer.

I do not recall coming across this term with this meaning in the wild. I would be interested to know if anyone else has. --Trovatore (talk) 03:24, 28 January 2024 (UTC)

On Scholar Google, there are many hits for "univalent relation" (with the quotes). I did not check whether they correspond to the definition in Univalent relation, since I do not care very much about terminology of relations. In fact, User:Rgdboer's edits consisted of changing "functional relation" to "univalent relation", and redirect univalent relation to Partial function. As the latter article is not the place for defining a specific type of relations, I have restored (an fixed) the previous target, and left the change from "functional relation" to "univalent relation". D.Lazard (talk) 12:29, 28 January 2024 (UTC)

Some care is necessary to edit accurately. Functional relation is not a term supported by WP:RSs. All mention of it should be removed from the project. Partial function is not a function except on a subset S of the source set. Thus it is a misnomer and Univalent relation is preferred. — Rgdboer (talk) 22:40, 31 January 2024 (UTC)

Rgdboer, "partial function" is entirely standard in mathematics, and I'm afraid that the fact that you wish it weren't is of no concern here. Please do not attempt to change mathematical terminology by editing Wikipedia. You can go make your case in the real world.

That said, it does appear that the term "univalent relation" has some usage in this sense. Not a lot, but enough that I can agree it can be mentioned. --Trovatore (talk) 23:20, 31 January 2024 (UTC)

As to the separate question about functional relation — I have to say I am not familiar with this as a mathematical term of art. I can imagine someone talking about binary relations in general, and saying, well, these ones here are functional because they represent functions, but I am not aware of anyone using "functional relation" as a standalone precise term. Why wouldn't you just say "function", or maybe "partial function", depending on context?

Also I think it's reasonably likely that someone typing "functional relation" into the search box, or wikilinking it, intends something non-mathematical entirely, so it may well be reasonable to delete the redirect per WP:XY if for no other reason. --Trovatore (talk) 01:10, 1 February 2024 (UTC)

We do have a related (and sourced) redirect at functional graph. —David Eppstein (talk) 01:15, 1 February 2024 (UTC)

That seems much less likely to be searched for outside of mathematics. --Trovatore (talk) 01:15, 1 February 2024 (UTC)

As far as I know, the main uses of "functional relation" occurs in physics and applied mathematics in the case of two quantities that are related in such a way that one can be expressed as a function of the other. Scholar Google search for "functional relation" function ("function" is here for trying to eliminate non-mathematical articles) provides many examples of the use of this phrase, even in article titles. Most of the examples are in applied mathematics (data analysis), but

Friedli, F. (2016). A functional relation for L-functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L-functions. Journal of Number Theory, 169, 342-352.

is an example in pure mathematics. However, I have not verified the exact meaning of the phrase in these articles. D.Lazard (talk) 11:18, 1 February 2024 (UTC)

Here's an example from the philosophy of science:

Although scientific laws may take the form of any relation between variables in some specified set of objects, causal laws represent a specific kind of relation of special interest to humans. Causal laws are relations in nature that reveal what one would have to be able to do to effect specific kinds of outcomes unambiguously. And functional relations are an appropriate form for expressing these kinds of relations. Recall that a functional relation is a relation between two sets, a first set and a second set, such that to each element of the first set there corresponds one, and only one, element from the second set. Thus, functional relations as causal relations associate with any given value of some independent variable (which may be multivariate), a unique value of a dependent variable (which may also be multivariate), revealing thus the unique outcome associated with any given value of the independent variable. So, if I want to know how to achieve a specified pressure in a gas in some container with fixed volume, then I must heat the container and raise the temperature of the gas to a specific value; or, if I cannot do that, and the container's volume can be varied, then I must decrease the volume of the container to a specific value. The pressure of a gas varies as a function of its temperature and volume. Thus, whenever I specify a causal hypothesis, I specify causal directions between variables as a part of the causal hypothesis. I do this by specifying those variables that are functions of other variables.

Mulaik, Stanley A. (1986). "Toward a Synthesis of Deterministic and Probabilistic Formulations of Causal Relations by the Functional Relation Concept". Philosophy of Science. 53 (3): 313–332. JSTOR 187672.

–jacobolus (t) 16:00, 1 February 2024 (UTC)

I can also find a couple sources using "functional relation" as a synonym for what I have usually heard called a functional equation. For example: "A meromorphic function $F(\zeta )$ on this torus can be defined as a function satisfying the functional relation $F(\rho ^{2}\zeta )=F(\zeta )$ and having only poles in the annulus $\rho \leq |\zeta |<\rho ^{-1}.$ Such functions have been dubbed loxodromic functions." –jacobolus (t) 17:00, 1 February 2024 (UTC)

Let's not rabbithole on what "functional relation" means in mathematics, unless it can be established that at least the majority of uses of the term (and really we'd want a fairly solid majority) are mathematical at all. Otherwise I think it's WP:XY and probably should be deleted. That's without prejudice to the idea that there could possibly exist a functional relation (mathematics) redirect, but to be honest that sounds sort of pointless to me. --Trovatore (talk) 17:42, 1 February 2024 (UTC)

WP:XY seems totally irrelevant to this question. But anyway, the main use of "functional relation" I can find after skimming a bunch of papers, both in mathematics and in adjacent applied fields, is that it is broadly a synonym for "function", but some authors draw an explicit distinction when trying to emphasize one or another aspect of the function concept. My impression is that D.Lazard's summary above (two quantities that are related in such a way that one can be expressed as a function of the other) generally seems about right. –jacobolus (t) 18:19, 1 February 2024 (UTC)

How is it irrelevant? It seems very much on point to me. We can't know whether people linking or searching this term are looking for mathematics (or "adjacent fields") at all. If there were two or three clear meanings, we could make a disambig page, or use hatnotes if one of them is primary. But it's just all a big mush as far as I can tell, some people using it one way and some people in another, but without enough clarity to make the existence of the redirect preferable to Wikpedia's search engine. So we should delete the redirect to expose the search engine. --Trovatore (talk) 18:56, 1 February 2024 (UTC)

WP:XY is explicitly about titles of the form "X and Y", where X and Y are two things which typically go together but can also be discussed separately. As demonstrated by the examples there, sometimes it is valuable to keep a title like "X and Y" or a redirect from the name "X and Y" to a relevant section of an article (either X or Y or another) where the topic of X and Y together is explicitly discussed. Other times it is decided to delete these in cases where the existing articles cover the subject well enough independently, or where the category is inherently politically controversial, etc. WP:XY does not describe a concrete policy in which one choice or another is a priori correct – whether each such redirect should exist is decided by consensus case by case – but links to some previous examples for context, so "per WP:XY" doesn't mean anything. Either way, this has little if anything to do with whatever we're discussing here. –jacobolus (t) 20:38, 1 February 2024 (UTC)

Hmm. It didn't use to be, I think. Or maybe I misunderstood it when I saw it in an RFD discussion.

Anyway, even if I didn't have the exact right link, the substantive point stands. We don't need a redirect for every way writers have combined words together. There are many many things "functional relation" can mean, and none of them seems to be particularly "canonical". I don't see any value in keeping this redirect. Admittedly there's not a huge upside to deleting it either, but there could be some. For example users who see the term somewhere with a different meaning might not be misled by seeing it come up when they search for it, and editors who think it's a precise term with an agreed meaning might be disabused of that notion when they add the link and see it come up red. --Trovatore (talk) 21:37, 1 February 2024 (UTC)

(I might change my view if it could be established that non-mathematical uses are just using the two words in natural English but that the mathematical usage is a term of art. But it doesn't seem that the latter is true, at least not in any consistent and well-understood way.) --Trovatore (talk) 17:44, 1 February 2024 (UTC)

In the above discussion two meanings for "a functional relation" are given (another name for functional equation and a binary relation that is the the graph of a function or a partial function. None of these meanings can be easily infered from the dictionary definitions of the two words constituting the phrase.

As these two meanings refer to different concepts, I'll boldly transform the redirect Functional relation into a dab page. If there are some non-mathematical usages, they can easily be added to the dab page. D.Lazard (talk) 12:02, 2 February 2024 (UTC)

Dolciani versus Bourbaki

Mary P. Dolciani wrote textbooks where functions are defined as a particular type of relation. Millions of secondary students in North America used these algebra textbooks and learned about functions in the realm of relations. In France, Bourbaki advanced the theory of sets in French. A review of the Bourbaki approach was given by Wayne Aitken, writing in English in 2022 at California State University San Marcos. His pdf notes, on page 7, that Bourbaki used relation meaning formula, so a different slant is taken. "...each specific symbol is classified as either functional (Bourbaki: substantific) or relational."

On page 38 Aitken gives this

Remark: If (∃! x) R[x] is a theorem, then Bourbaki calls R[x] a "functional relation in x". In other words we can regard "R[x] is a function relation x" is synonymous with "(∃! x) R[x]". Recall that Bourbaki uses the term relation for our term formula.

Thus, the sources in English and French mathematics diverge, so editors with different backgrounds are in conflict. Rgdboer (talk) 02:33, 4 February 2024 (UTC)

Even in English there are two different definitions:

• The relational approach
• The categorical approach, In which a function is a triple $(D,R,F)$, where $\forall _{x}\in D(\exists y\in R)(x,y)\in F$

The categorical approach is standard in, e.g. Algebraic topology. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:09, 8 February 2024 (UTC)

Draft:Invariant set

Will someone please review this draft? Should it be accepted? Dammit, Jim, I'm a computer scientist, not a mathematician. Robert McClenon (talk) 06:06, 9 February 2024 (UTC)

The draft is a WP:REDUNDANTFORK of Invariant set. Also, it contains WP:OR terminology. D.Lazard (talk) 13:33, 9 February 2024 (UTC)

Calling this a "redundant fork" of 1–2 paragraphs in a different article seems unnecessarily sharp (and nowhere close to justified by the text of WP:REDUNDANTFORK – have you looked at it recently?). This subject can entirely plausibly be a separate article instead of a short section, if someone can find the sources to back more material. –jacobolus (t) 15:44, 9 February 2024 (UTC)

My comment in the draft is: We have already Invariant set, which covers the same subject. This is a section of Invariant (mathematics). It is possible that this section deserves to be expanded, and eventually to be split into an independent article, but this requires a WP:consensus at Talk:Invariant (mathematics). For the moment, this draft is a WP:REDUNDANTFORK. Also, the terminology ("one-sided invariant set", "two-sided invariant set", "a dynamics") of this article seems WP:OR.

By the way, I do not see any reason for not being sharp about an article where everything that is not in Invariant set is either WP:OR, or wrong (such as the sentence that follows the first "equivalently", or the generalization to categories) or very badly formulated (for example, the examples in the section 'Examples')" D.Lazard (talk) 16:38, 9 February 2024 (UTC)

The reason is that Wikipedia is a collaborative project that we want to encourage people to feel good about participating in, including newcomers and folks from different backgrounds. Ideally we can disagree about content, talk it over, and arrive at a consensus result without making it feel like a personal rejection. I agree that the business about "one-sided" vs. "two-sided" seems a bit confusing though.

@Robert McClenon, have you taken a look at Invariant (mathematics)? It seems like your interest is examples from probability theory. Does that article handle the subject well enough to explain those, or are there specific parts that you think should be expanded / split into a separate sub-article? –jacobolus (t) 18:42, 9 February 2024 (UTC)

@Jacobolus I don't see anything personal in D.Lazard's assessment of the article. It's just a statement of facts about the quality of the draft. Wikipedia is not about making people feel good. Anybody is welcome to participate, but their contributions should be up to par with the expected level of mathematical correctness and clarity of exposition, while following all the required Wikipedia guidelines, etc, etc (WP:OR in particular). PatrickR2 (talk) 07:25, 11 February 2024 (UTC)

I didn't say it was "personal" (and I don't think it was improper or done with any ill intent). I said it seemed unnecessarily sharp. I think we should try to err on the side of being as patient and generous as practical with newcomers, even when we don't want to take one or another specific contribution. Cf. WP:BITE. To elaborate: someone typically decides to make a new article or edit an existing article when they either (a) can't find what they were looking for, or (b) don't think the previous coverage sufficiently handled the specific topic/question they were concerned about. Usually those changes have their own flaws (as do many from established editors), but they can still give us valuable feedback if we try to take the effort to understand why someone thought it was important to contribute a change and reflect on whether the implicit or explicit criticism of the existing article(s) was reasonable, and start a dialog about what they think is missing. –jacobolus (t) 07:30, 11 February 2024 (UTC)

Has Bard chatbot expressed an interest in collaborating with the WMF?

This question is motivated by something Bard said at:

v:Chatbot math/Bard/Unitary Transformation & Matrix Symmetry#I will post this on Wikiversity and leave a note on a Wikipedia talk page. Don't worry, this problem will get solved. Goodbye, for now. I will sign off as I would on Wikipedia/Wikiversity --user:Guy vandegrift

I contribute to Wikipedia mostly by adding images (see list). But I mostly edit Wikiversity because I am too fun-loving to follow your editorial rules (rules of which I strongly approve!) Recently I have been playing with Bard, and am convinced that Bard's and Wikipedia's future are closely linked. I am not here to make any proposals regarding chatbots and Wikipedia. But I do invite you to think about this. And you might want to look at two conversations I recently had:

• v:Quantum mechanics/A conversation with Bard has a sister link on Wikipedia's History of quantum mechanics, but I made it clear to the editors of that page that I have no objections to deleting the link.
• v:Chatbot math/Bard/Unitary Transformation & Matrix Symmetry is an extremely long conversation in which I unsuccessfully resolve a question about symmetric matrices. A brief commentary is available at v:Chatbot math#Unitary Transformation & Matrix Symmetry

I am not ready to make any proposals or give any advice. But if anyone is interested in looking into the question of chatbots and Wikipedia, let me know.--Guy vandegrift (talk) 00:47, 7 February 2024 (UTC)

If you are treating anything a chatbot says as anything other than telling you what you want to hear, you are making a mistake. —David Eppstein (talk) 01:15, 7 February 2024 (UTC)

Please please please don't ever try to add AI-generated output to Wikipedia. What a disaster that would be. We have enough problem as it is with humans pretending to be bots; we don't also need bots pretending to be human. –jacobolus (t) 01:19, 7 February 2024 (UTC)

Ha ha ha. It looks like there will be very good AI/Proof Assistant combos available in a couple of years for maths. But we're not there yet, certainly not with ones like Bard. Yes it can help you with what yo're doing but I'd be very careful to check everything. We're not supposed to engage in any original research here so at most you're talking about using it for spotting problems and cheking citations and stuff like that. Generating good maths images from descriptions sounds like it could be a good use though of course it would have to be checked - but once proof checkers ae incorporated that should be a fairly reasonable job. NadVolum (talk) 12:58, 7 February 2024 (UTC)

I wonder - perhaps it would be possible to add a checker for normal reasonng as well which would staep through the rasoning and flag and maybe helps correct the various types of false arguments in what an AI comes up with. The problem with just training on what is out there like an LLM does is it copies all the bad reasoning and biases of humans. NadVolum (talk) 15:44, 7 February 2024 (UTC)

My experience with using AI assistants for "Generating good maths images from descriptions" has been...not good. I needed an image of a solid cone for a paper. I asked Adobe's AI assistant to generate one for me. It was unable to generate anything that looked like a cone. I had to figure out how to do it myself with gradients. Then, for a separate mathematics blog post, I wanted a picture of a pencil being sharpened with a long shaving coming out. The AI could draw pencils, and pencil sharpeners, but not believable shavings, and it insisted that the pencils went into the sharpener eraser-end first. In that case I gave up and found a close-enough photo from Commons. —David Eppstein (talk) 16:20, 7 February 2024 (UTC)

I just asked Google for images of 'pencil sharpener in acion', and Wow! I think I can see the problem an AI might have in getting a basic model of what one looks like! NadVolum (talk) 17:00, 7 February 2024 (UTC)

I've not tried Bard or math questions, but physics questions to Google's generative AI echo back Wikipedia content that I personally typed in. So it seems to me the collaboration is well underway ;-) Johnjbarton (talk) 16:16, 7 February 2024 (UTC)

The encyclopedic value of stochastic-parrot output is zero at most. XOR'easter (talk) 18:38, 14 February 2024 (UTC)

Can you please review Draft:Mathseeds

It's been a while since I submitted it for review, and I've tried the Education WikiProject. Faster than Thunder (talk | contributions) 03:33, 17 February 2024 (UTC)

I would say this does not belong to Wikiproject Mathematics. The Education WikiProject seems the right place for it. PatrickR2 (talk) 04:01, 17 February 2024 (UTC)

After you strip out the primary and poor-quality sources (like prweb, blogs), what are the WP:THREE best sources that remain? 100.36.106.199 (talk) 13:05, 17 February 2024 (UTC)

evaluation map

Currently, Evaluation map is a redirect to Initial topology#Evaluation. However, I think it may also refer to Apply#Universal property. What would you suggest I do? SilverMatsu (talk) 05:26, 18 February 2024 (UTC)

It may also refer to Polynomial ring#Polynomial evaluation or Polynomial evaluation, or also to function evaluation. (By the way, the definition given in Apply#Universal property seems to be nothing else that an abstract version of that of function evaluation).

So, the current target is certainly not a primary topic (I do not understand why is map is called an evaluation map). I'll rename Evaluation map as Evaluation map (topology), and create a dab page for evaluation map. D.Lazard (talk) 10:09, 18 February 2024 (UTC)

Thank you for creating the dab page. Also, I agree with clarifying the page name. By the way, I accessed the Apply#Universal property via the wiki-link in the Exponential object. --SilverMatsu (talk) 15:38, 19 February 2024 (UTC)

Drawing polyhedron

I would like to draw any polyhedron or group of polyhedron modeling on computers or laptops. Stella is the first software I searched on Google (as far as I remember), but some of the polyhedrons in this software have silver balls representing their vertices, so I prefer to find another one. Are there other recommendations for apps or software? Dedhert.Jr (talk) 12:13, 19 February 2024 (UTC)

I like https://prideout.net/blog/svg_wireframes/ — it generates images in vector rather than bitmap formats, which I think is better for Wikipedia illustrations when possible. It can do shading and lighting effects but I usually use it with a plainer style in which all faces are the same color and somewhat transparent, as in for instance File:Triaugmented triangular prism (symmetric view).svg and File:Translucent Jessen icosahedron.svg. —David Eppstein (talk) 19:50, 21 February 2024 (UTC)

Perhaps I would say that this is difficult to create using Python, and I can't do Python. But I think I will give it a try in the future. Dedhert.Jr (talk) 15:18, 23 February 2024 (UTC)

Edit warring and content disputes on Hindu–Arabic numeral system

Are any other folks interested in the history of number representation willing to wade into an ongoing content dispute / edit wars at talk:Hindu–Arabic numeral system? Sorry to drag anyone into what has become a bit of a mess, but this and related articles are in my opinion pretty mediocre (incomplete, poorly organized, poorly sourced, misleading, ...), but efforts to make even modest improvements are getting hit by instant reversion, and discussion gets repeatedly diverted away from content disagreements toward unproductive meta conversations. –jacobolus (t) 19:16, 25 February 2024 (UTC)

List of Johnson solids

The reviewer has gone AWOL during the nomination of List of Johnson solids. I welcome someone who is in favor of replacing the reviewer and providing comments for the sake of improvement. Dedhert.Jr (talk) 13:36, 26 February 2024 (UTC)

Mar 2024

Notability of John H. Wolfe

The article John H. Wolfe has gone through a PROD, but still has issues as it is based on one secondary textbook claim that his work on model-based clustering matters. It was created directly by a novice editor (Stat3472 33 edits). The article model-based clustering supports him as the inventor, but whether this is big enough for notability is unclear. Comments on that talk page please. Ldm1954 (talk) 09:57, 2 March 2024 (UTC)

≙

There is a discussion about the ≙ character that needs attention from mathematical editors at Wikipedia:Redirects for discussion/Log/2024 March 2#≙. Thryduulf (talk) 12:35, 2 March 2024 (UTC)

Mental calculation

Does anyone feel like cleaning up Mental calculation? It's roughly as disorganized as one would expect. XOR'easter (talk) 18:35, 3 March 2024 (UTC)

any, every, some

• For every number $\varepsilon >0,\ldots$

• For some number $\delta >0,\ldots$

It is clear that in standard English usage, the words "every" and "some" as used above are respectively universal and existential quantifiers.

"Any" can be a universal quantifier, as in:

"Any fool can see that."

(But "Anyone can be elected chair of the committee" doesn't mean the same thing as "Everyone can be elected chair of the committee.)

"Any" can also be an existential quantifier, as in:

• There isn't anyone here who can answer that question.

• Is there anyone here who can answer that question?

• If anyone knows the answer, please step forward.

I thought that there are three contexts in which "any" is an existential quantifier:

• negations,
• questions, and
• conditional clauses,

those being the three exhibited above.

But then in the article titled Causality conditions, I found this:

• A manifold satisfying any of the weaker causality conditions defined above may fail to do so if the metric is given a small perturbation.

Here, "any" is used as an existential quantifier, and it is not clear to me that it is one of those three kinds. Thus my list appears to be incomplete.

A grammar question rather than a math question, but one to which mathematicians are in more desparate need to pay attention than is perhaps anyone else.

What should be added to this list? Michael Hardy (talk) 18:51, 21 February 2024 (UTC)

In the above quotation, "any" is a universal quantifier. D.Lazard (talk) 19:02, 21 February 2024 (UTC)

You can still see "any" here as a universal quantifier, in the sense that "for all of these weaker causality conditions, a manifold satisfying said condition can fail to do so if <rest of sentence>." I would argue that the existential quantifier here is actually hidden in "can", in the sense that "a manifold satisfying said condition can fail to do so if..." is shorthand for "there exists a manifold satisfying said condition that fails to do so if..." GalacticShoe (talk) 19:09, 21 February 2024 (UTC)

Because pushing a negation through a $\forall$ flips it to a $\exists$ and vice-versa, examples involving negation — including "not", "fails", "never", etc. — can be argued about endlessly. It seems to me that math textbook authors solve this problem by stating each definition and theorem as clearly as they can, relying on the proof to clarify the exact meaning of a theorem in a pinch, and tolerating looser talk in discussions between theorems. Mgnbar (talk) 19:30, 21 February 2024 (UTC)

The correct phrasing is "for any (every) said condition, there exists a manifold satisfying it that fails to do so if...". So the hidden existential quantifier does not refer to the same thing. D.Lazard (talk) 19:36, 21 February 2024 (UTC)

The meaning of the expression "a manifold satisfying any of the weaker causality conditions defined above" is a manifold which falls into one or more of the classes defined by the previous causality conditions; as previously stated in the article, if it falls into one of them, it also falls into the previous classes, as they are nested with stricter conditions listed later. But the manifolds of particular interest for that section are the strongly causal ones (the immediately preceding condition). My understanding based on the article's text is that "stably causal" means a strongly causal manifold which remains strongly causal under any possible perturbation of a chosen (arbitrarily small) magnitude. Or another way of saying this: if a manifold is "stably causal", then there exists some specific size of perturbation for which every smaller perturbation of the manifold preserves the strong causality property. From what I can tell the perturbations of other kinds of causality-condition-satisfying manifolds are not at issue (beyond the initial mention, for context, that for each of the earlier conditions there exists some manifold satisfying it which can be perturbed into not satisfying it by an arbitrarily small perturbation). –jacobolus (t) 19:41, 21 February 2024 (UTC)

Some months ago, the was consensus that "any" should be avoided (in order not to require the reader to be familiar with discussions like the above one), see MOS:MATH#ANY. - Jochen Burghardt (talk) 20:10, 21 February 2024 (UTC)

Rephrasing this particular passage is more complicated than the examples given there, as it expresses a somewhat tricky logical claim. I don't think this one is really ambiguous in context, but it could be rephrased as e.g. "For each of the weaker causality conditions defined above, there are some manifolds satisfying the condition which can be made to violate it by arbitrarily small perturbations." –jacobolus (t) 21:43, 21 February 2024 (UTC)

Jacobulus last suggestion is perfect. To answer Micheal Hardy's original question, there is yet another sense of any: in this case, it's "menu choice": "pick any one item from this menu". Menu choice is similar to exclusive-or, but is not truth-valued, it is object-valued. Menu choice shows up as a fragment of linear logic (for example, the quantum no-cloning theorem, which says "you can only have one of these") but also in vending machines "for a dollar you pick one item" and in mutex locks in computing (one user at a time.) Menu choice is a really cool tool in foundational logic. 67.198.37.16 (talk) 07:34, 4 March 2024 (UTC)

Brouwer–Hilbert controversy

Should this article be renamed to Grundlagenstreit? This is the name often given in the literature to this debate. I do not know much about it but it seemed odd when I was looking for it. See for example Brouwer's biography ReyHahn (talk) 10:01, 4 March 2024 (UTC)

For me, naming an obscure topic from 100 years ago using an unfamiliar non-English word (German?) is the same as deleting the article.

Maybe "Grundlagenstreit, the Brouwer–Hilbert controversy"? Johnjbarton (talk) 15:45, 4 March 2024 (UTC)

Maybe the term Grundlagenstreit should be included in the lede; it seems common enough in writings about the topic. XOR'easter (talk) 16:18, 4 March 2024 (UTC)

Apparently Grundlagenstreit means "foundational debate", and was related to Hilbert's book Grundlagen der Geometrie. Seems fine to me to create a redirect and mention the name in the lead section (doesn't need to be bolded in my opinion). –jacobolus (t) 16:30, 4 March 2024 (UTC)

No, but theree should be a printworthy redirect from Grundlagenstreit to the article. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:28, 4 March 2024 (UTC)

Thank you all, I prefer to keep it bold but that can be discussed. As for the main topic I consider this  Done.--ReyHahn (talk) 21:06, 4 March 2024 (UTC)

Merge?

On pl wiki, User:Epsilon598 suggested AM–GM inequality, QM-AM-GM-HM inequalities and Generalized mean may need a merge. Thoughts? _{Piotr Konieczny aka Prokonsul Piotrus| reply here} 02:07, 26 February 2024 (UTC)

Actually, Pythagorean means should also be at least linked to the others. In Polish all of these inequalities are usually called simply "inequalities among means", which is also used in at least one of these articles. This name is not nearly as fitting in English as it is in Polish, but would be my first guess. Epsilon598 (talk) 02:45, 26 February 2024 (UTC)

I usually hear this called "Power Mean Inequality" in English (which is currently a redirect to Generalized_mean#Generalized_mean_inequality). Elestrophe (talk) 16:38, 7 March 2024 (UTC)

Notice of discussion

 Note: A discussion at Wikipedia talk:Good article nominations might be of interest to members of this project. ~~ AirshipJungleman29 (talk) 22:23, 7 March 2024 (UTC)

Inconsistent

In the interest of keeping this Project rational, it can be noted that as things stand, a function may be partial or total or multivalued or univalent. The terms "partial function" and "multivalued function" are self-contradictory, they are oxymorons. According to WP:Article names, consistency is one of the parameters of evaluation. Tolerating contradiction, as in the two article names, invites arbitrary deductions since any proposition may be deduced from a contradiction. A function is a type of relation so its variants are best described with properties of relations. A partial function is a univalent relation, and a multivalued function is a relation. Rgdboer (talk) 01:09, 10 March 2024 (UTC)

It's established mathematical terminology, and it's also pretty common in English generally (see, for example, Subsective modifier). - CRGreathouse (t | c) 01:17, 10 March 2024 (UTC)

Lots of things have names of the form [modifier] [something] to indicate that it is a generalization or variant form of something or something modified in a certain way rather than a special case of something. A Reuleaux triangle is not actually a triangle. A truncated icosahedron is not actually an an icosahedron, and a snub cube is not a cube. "Partial function" is no different. There is nothing inconsistent about this naming convention. See also WP:COMMONNAME and WP:NEO. —David Eppstein (talk) 01:29, 10 March 2024 (UTC)

Well put. I would add that a skew field may be a field but is not necessarily a field, which maybe is more directly analogous to the case at hand, since a partial function may be a function but is not necessarily a function. --Trovatore (talk) 03:28, 10 March 2024 (UTC)

I don't believe Wikipedia claims to be "rational", nor would we want it to be. Rationality has its limits; irrationality knowns no bounds. Johnjbarton (talk) 01:56, 10 March 2024 (UTC)

It's also often much harder to keep things rational. — MarkH₂₁^talk 03:51, 10 March 2024 (UTC)

You could argue that irrationality has its limits too :P GalacticShoe (talk) 04:09, 10 March 2024 (UTC)

The first goal of article names should be reflecting common usage among reliable sources, especially those from professional practitioners, with common alternative names listed/explained in the article text. This helps the widest range of readers to get up to speed with the terminology and conventions they will find in other sources. Other goals are subsidiary to that, and any "irrational" features of the most widely used and accepted nomenclature can be explained in text.

If you have a problem with widespread mathematical conventions, the place to fix it is in the mathematical literature, not in Wikipedia. (But making an explicit note when terminology is confusing, ambiguous, historically revisionist, politicized, a misattribution, etc. could be helpful.) –jacobolus (t) 04:27, 10 March 2024 (UTC)

Also, for considering the original example, the general meaning of "function" refers to univariate total function, but, in many texts, partial functions and multivariate functions are simply called functions. These generalized functions may be considered as functions in the first sense, by changing of domain. This is for this reason that I have added recently the subsections "Partial functions" and "Multivariate functions" to Function (mathematics)#Definition, with explanations on these terminology shifts. D.Lazard (talk) 09:54, 10 March 2024 (UTC)

Requested move at Talk:N = 2 superconformal algebra#Requested move 7 March 2024

There is a requested move discussion at Talk:N = 2 superconformal algebra#Requested move 7 March 2024 that may be of interest to members of this WikiProject. Killarnee (talk) 23:44, 14 March 2024 (UTC)

Torsion tensor

Could you join the dispute at Talk:Torsion tensor?

The summary of the discussion (in my view point) is written in the section Discussion between Tito Omburo and Idutsu.

---Idutsu (talk) 14:20, 14 March 2024 (UTC), editor of japanese Wikipedia.

I've spent a long time trying to make sense of the torsion tensor in terms of normal coordinate systems. I came to the conclusion a long time ago that the #Twisting of reference frames section of the torsion page was wrong. Not in interpretation, but literally mathematically incorrect. The relationships asserted between the torsion tensor and the development of a frame along a curve don't match: the expression people think of for the rotational development of a coordinate frame correspond only to the covariant derivative of the frame along the curve, not to the difference of covariant derivatives as appears in the torsion tensor.

I've never seen any source which actually went through the details of this interpretation and explained it, and I've seen many mathoverflow posts just like Bill Thurstons which wax lyrical about interpretations of torsion without ever explaining in mathematical detail how the formula of torsion relates directly to the development of a coordinate frame along a curve.

I don't have any skin in the game of your discussion but if it were me I would try to hold this to a very high standard of reference because it is a notoriously wishy-washy subject in differential geometry. The conclusions of Tu & Spivak that there is no actual detailed mathematical link between the name torsion and some of the more elementary interpretations of twisting of a frame around a curve seem to hold up to my scrutiny at least. Tazerenix (talk) 06:23, 15 March 2024 (UTC)

Is this the part you disagree with?

The foregoing considerations can be made more quantitative by considering a small parallelogram, originating at the point $p\in M$, with sides $v,w\in T_{p}M$. Then the tangent bivector to the parallelogram is $v\wedge w\in \Lambda ^{2}T_{p}M$. The development of this parallelogram, using the connection, is no longer closed in general, and the displacement in going around the loop is translation by the vector $\Theta (v,w)$, where $\Theta$ is the torsion tensor, up to higher order terms in $v,w$.

Gumshoe2 (talk) 13:36, 15 March 2024 (UTC)

No, that's the standard interpretation of the torsion tensor geometrically. However I reject that it has much to do with the english word "torsion". The section of the page I was referring to has since been removed. My comments were just general that care should be taken with this subject to get high quality sources! Tazerenix (talk) 22:09, 15 March 2024 (UTC)

The article has been substantially revised since the bad version that User:Tazerenix is referring to. I wrote the above description in terms of the tangent bivector to replace the mathematically wrong section that had been there before. What I wrote is correct and supported by sources. There may however be different factors of two in place in the article, which I have not checked in detail. So this interpretation is satisfied up to a factor of two that is subject to checking conventions.

The connection with development, however, is well-known and easily understood. I have given a detailed example in the image in the lede. Basically the idea is to take a closed curve $\gamma$ in the manifold, and a parallel coframe $\theta ^{i}$ along $\gamma$, and then solve the ODE $dx^{i}=\gamma ^{*}\theta$ for coordinates $x^{i}$. When the torsion vanishes (and the curve is null homotopic), the developed curve is also closed (a consequence of the Ambrose-Singer theorem, or alternatively even Stokes' theorem is sufficient.)

When the torsion does not vanish, it means that there is a non-trivial translation component to the holonomy for the affine group, and so the developed curve need not be closed. I think the current image at the top of Torsion tensor nicely illustrates this, and as a bonus shows the connection to Frenet-Serret torsion. Tito Omburo (talk) 20:15, 15 March 2024 (UTC)

Tom Ilmanen

Good day! Is there some experienced editor interested in helping me create an article about Tom Ilmanen? He seems like notable enough (many papers cited by hundreds each), but it's hard to find sources about him (not about his work). :( I've made a beginning draft: Draft:Tom Ilmanen. Thanks! Gererhyme (talk) 10:27, 15 March 2024 (UTC)

I wouldn't say that "his best known mathematical works are in cooperation with Gerhard Huisken," since they only have two research papers together. It would be better to say something like: "Huisken and Ilmanen used inverse mean curvature flow to prove the Riemannian Penrose conjecture, which was resolved at the same time in greater generality by Hubert Bray using alternative methods." This article could be used as a reference.

I also wouldn't refer to "the Huisken-Ilmanen conjecture" unless grammatically in the particular context of talking about a particular conjecture by Huisken and Ilmanen. As far as I know, there has not been anything widely known as "the Huisken-Ilmanen conjecture." Even the article by Dong and Song resolving the conjecture says only "This confirms a conjecture of G. Huisken and T. Ilmanen." (It's not clear to me how significant the conjecture or its proof should be regarded as being.) Gumshoe2 (talk) 13:31, 15 March 2024 (UTC)

Wow!!! Thank you very much, Gumshoe2!!! Gererhyme (talk) 13:34, 15 March 2024 (UTC)

Happy to help. Not sure what can be done to help establish wiki-notability, although I believe it's fully orthodox to regard Huisken-Ilmanen's paper as seminal and the other three publications you've listed as highly notable as well. (Speaking of which, his book should be regarded as a research contribution and not as a textbook.) You might have to just hope to come across a sympathetic admin when submitting the draft. Gumshoe2 (talk) 13:49, 15 March 2024 (UTC)

It may be a small help to cite Yau's well-known list of open problems where the Riemannian Penrose inequality is the fifteenth problem. Gumshoe2 (talk) 14:05, 15 March 2024 (UTC)

Thank you so much!!! "Review waiting, please be patient. This may take 8 weeks or more." EIGHT WEEKS OR MORE....... ZZZzzzzzZzZZzZ "be patient" hahaha. :) Gererhyme (talk) 14:30, 15 March 2024 (UTC)

And now in mainspace, and passed through NPP. A nice short article. My one constructive suggestion would be to use the Quanta article as a source to say something meaningful about Ilmanen, rather than just dump it into a "further reading" section. --JBL (talk) 23:00, 15 March 2024 (UTC)

Nice suggestion, JBL!! Thank you! ^^ I'll follow it, but I need some rest before doing so (yesterday I edited Wikipedia for something like 12 straight hours!). In fact, it was from Quanta Magazine I first heard of Ilmanen! Gererhyme (talk) 11:18, 16 March 2024 (UTC)

"Idealwise separated" listed at Redirects for discussion

The redirect Idealwise separated to the article Completion of a ring#Krull topology has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 March 18 § Idealwise separated until a consensus is reached. Kk.urban (talk) 06:22, 19 March 2024 (UTC)

Draft:Bianticupola

I have been looking for sources for my article on Bianticupolae. However, even after practically scouring the internet, the only mention I can find of them is on the Wikipedia article for cupolae. If anyone knows a good place to look, I would greatly appreciate that. Thank you! — Preceding unsigned comment added by Toxopid (talk • contribs) 17:32, 17 March 2024 (UTC)

@Toxopid please use the Add Topic button in Talk pages.

I fixed your problem: I deleted the word "Bianticupolae" from the article Cupola (geometry) so now the internet will not mention it.

Ok, sorry, that was mean. But the line was not sourced so we have no way to know if someone just made it up. The point of Wikipedia is to summarize knowledge: if you have no source then don't write an article. Move on to another topic. Every single wikipedia article has many ways to improve it, including I'm sure Cupola (geometry). Find some good sources and edit! Johnjbarton (talk) 21:43, 18 March 2024 (UTC)

Cupola (geometry) § Anticupola has no sources, and the only mention I can find in the academic literature is from a 2023 arXiv preprint. Perhaps the section should just be deleted as original research. "Bianticupola" does not seem like a notable topic. –jacobolus (t) 22:24, 18 March 2024 (UTC)

I just deleted the section. If someone can find reliable sources, feel free to restore it. –jacobolus (t) 22:40, 18 March 2024 (UTC)

@Jacobolus I added the tag unreferenced, because there are lot of sections that do not have any sources to cite the facts. Is there any possiblity that they could be removed? Dedhert.Jr (talk) 11:24, 19 March 2024 (UTC)

Levi-Civita symbol

I just reverted a pile of COI edits at Levi-Civita symbol and made some other small fixes. It currently has 3 {{citation needed}} tags; in particular, there's a long stretch of $n$-dimensional calculations without any indication that going beyond 3 dimensions is a thing that warrants all that detail. (Like a lot of math pages, the increase in verifiability between one reference per section and one reference per sentence would not be that great in practice. But it needs a little work to get up to the former standard.) XOR'easter (talk) 17:32, 17 March 2024 (UTC)

Looks fine to me in it's current form (but I only skimmed it). The 4-d version sometimes shows in general relativity contexts, and the n-dimensional version sometimes shows in riemannian geometry and differential geometry textbooks where the author wants to perform some detailed, explicit calculation showing the gory details of Poincare duality or maybe how to use the Hodge star to define some inner product on some space of forms or weak derivatives or something. Perhaps Jurgen Jost "Riemannian Geometry" textbook, he likes to do explicit calculations; but my memory is faulty. When I was in school, one homework problem was to take the n to infty limit of this tensor; turns out it is the same as some harmonic oscillator over grassman variables, a determinant of some feynmann path integral. I forget; it has some famous name attached to it - Berezin integral or something like that. The joke is that physicists know how to do only one integral. 67.198.37.16 (talk) 00:16, 22 March 2024 (UTC)

Confusing image at Quadratic formula

Quadratic_function_graph_key_values.svg is garbled in Firefox. Looking at its history, the previous version was fine, but the change to "fix rendering issues in Chromium" seems to have broken it. XOR'easter (talk) 15:33, 21 March 2024 (UTC)

For me, both versions seem to look fine (i.e. the same to each other), on both Firefox and Chromium. Felix QW (talk) 15:43, 21 March 2024 (UTC)

It's also ruined in my computer, for both Firefox and Chromium. Note that if I click through to the actual svg file it renders correctly, it's only garbled when I see it in the Wikipedia article or the Media Viewer. Tercer (talk) 15:50, 21 March 2024 (UTC)

Maybe we should just replace it with a PNG? XOR'easter (talk) 16:01, 21 March 2024 (UTC)

That would be a depressing choice. Clearly SVG is the appropriate format for this image, and by now it is very old technology. We should be capable of getting it to render correctly. Tercer (talk) 18:28, 21 March 2024 (UTC)

There's relatively little advantage to SVGs here for most readers. Wikipedia/Mediawiki renders them as a PNG image anyway, both in a thumbnail and when clicked to view larger on screen, and very few readers click through to the source file. The Mediawiki SVG renderer doesn't do a great job with antialiasing so the lines often look better when downscaled from a highish resolution raster image.

SVGs including text (including mathematical formulas) have to be carefully encoded/exported to make the font render properly, and the safest is often to resort to converting all of the fonts to explicit outlines. Getting the layout to exactly match the author's intentions can take extra work in an SVG. Wikipedia doesn't support any of SVGs interaction features that could plausibly make it an attractive format for animation or interactivity.

The main benefits of using an SVG are (1) if there is explicit English text, it can be more easily translated, and (2) if someone wants to take the image and print it in a book or put it on a billboard or something they might get a marginally better result. In practice many of our SVG images have ugly color and font choices, poor layout, etc., all of which are more important to get right than the choice of raster vs. vector format. –jacobolus (t) 18:50, 21 March 2024 (UTC)

As an explicit example, here are two images which nominally show the same subject (used in logarithm), but where the PNG image is significantly better than the SVG based on other graphical choices:

–jacobolus (t) 18:57, 21 March 2024 (UTC)

So what you are saying is that MediaWiki should stop ruining perfectly good SVGs and just deliver them as-is to the browsers, which do a good job of rendering them. Unlike MediaWiki.

One can make bad choices of font and colour in either format; the difference is that in a SVG it is trivial to fix them, whereas in a raster format it is not.

The fundamental point is that an SVG encodes information as what it is: paths as paths and text as text. This makes it much easier to do anything with it. (I have in fact used those capabilities. A PNG erases all the underlying data and gives us just a representation of the information.

The low resolution can be mitigated by using larger file sizes, as you say, but this is just another instance of an inferior solution. Tercer (talk) 21:04, 21 March 2024 (UTC)

Mediawiki has not changed in this regard in like 15 years, so I'm not holding my breath.

My point is just that there's nothing magical about one file format or another, and the choice of format is not the most important feature of an image. All else equal, the vector image would have some advantages, but often there's a trade-off and the choice isn't quite as clear cut. For instance, if a raster image saves any appreciable amount of effort, it can be an advantage to spend the time saved on making more images instead of fiddling with the file format of a few. File:Regular tetrahedron inscribed in a sphere.svg is a good example of an image with a lot of problems, some of which are unrelated to the format such as illegibly small labels which are partly blocked by lines and a poor choice of bright pink color for radii, and others of which might be improved by using a raster image, e.g. shading the sphere (you can get somewhat acceptable sphere shading using SVG gradients, but it's not obvious, kind of tricky, and often done poorly). –jacobolus (t) 21:37, 21 March 2024 (UTC)

Well have you opened a ticket in Phabricator? They won't change anything if people don't ask for it.

As for my figure, since it's an SVG you can easily change everything you dislike about it. If it were a PNG you wouldn't be able to. Tercer (talk) 21:52, 21 March 2024 (UTC)

What makes images easy to edit or not is only tangentially related to the output format. Most images are created using some other software application (or applications), and the best way to help someone edit them is to include a link, textual description, file, etc. of the original input format. For example this might be tikz source, POV-ray source, raw PostScript code, a Blender file, a layered Photoshop document, an SVG with Inkscape-specific editor metadata, or a link to a Desmos or Geogebra plot. What tools other editors can work with or find familiar is going to vary depending on their experience and available software. –jacobolus (t) 22:27, 21 March 2024 (UTC)

Anyway, sorry, I'm not trying to give offense. My point is not to call out this particular image, which I'm sure is much more helpful than not having an image, but only to point out that the file format is way down the list of important features, and argue that people shouldn't be "depressed" to see high-quality images of any format created for the project. –jacobolus (t) 02:29, 22 March 2024 (UTC)

It is depressing to let the technical flaws of MediaWiki dictate our choice of file format. I searched a bit on Phabricator, and I'm afraid you are right: they are never going to fix their SVG rendering T40010 and nor are they going to allow browsers to render SVGs instead T5593. Tercer (talk) 08:56, 22 March 2024 (UTC)

It also seems they are stuck on an old version of librsvg, so even smaller improvements (than native rendering or a better library) are blocked: T265549 —David Eppstein (talk) 16:13, 22 March 2024 (UTC)

And that's since 2020. It's frankly ridiculous. WMF can't do even the bare minimum to keep the website running. I'm going to stop donating. They are clearly not using my money for what matters. Tercer (talk) 16:24, 22 March 2024 (UTC)

Taking arbitrary user-generated files and serving them up is a huge new "attack surface" which most sites serving SVGs are not affected by, and I'm not sure there's a super obvious existing set of tools for mitigating it. So it's definitely not a trivial thing to tackle. But it would be nice if someone would devote some resources to this, since the potential of SVGs is also pretty big.

I'd love to work with people on making interactive math diagrams for Wikipedia, if it were possible. I think the best bet is to just host anything animated or dynamic off-site and include a static version in articles. –jacobolus (t) 17:43, 22 March 2024 (UTC)

Telling readers to go look at some off-site resource is an equally large attack surface, to be fair. At least if it were served up on Wikipedia it might be expected to have passed some sanity checks. —David Eppstein (talk) 22:58, 22 March 2024 (UTC)

Regular tetrahedron inscribed in a sphere.svg also has an issue unrelated to its format: the use of quantum mechanics notation for its labels makes it unsuitable for topics beyond quantum mechanics. —David Eppstein (talk) 22:12, 21 March 2024 (UTC)

The topic is quantum mechanics, the filename is a misnomer. Tercer (talk) 22:43, 21 March 2024 (UTC)

All the files in the history look equally useless to me. Far too many equations on the graph. Johnjbarton (talk) 16:11, 21 March 2024 (UTC)

For me, on Safari, there are two problems: Firstly, on all versions, commas are vertically misplaced (At the level of denominators instead as at the level of fraction bars). On most versions, the horizontal bars (fraction bars and vincula of square roots) are horizontally misplaced with respect to the remainder of the formula. This misalignment disappears when clicking on the image or on thumbnails of the history. So, the problem seems to come from the method of writing and inserting formulas.

I agree with Johnjbarton that there are too much formulas in the image. Moreover, the directrix, the focus and the vertex of the parabola, and their coordinates are clerly out fo the scope of ths article.

So, I recommend to remove this image. D.Lazard (talk) 16:37, 21 March 2024 (UTC)

OK, I have removed it from Quadratic formula and also from Quadratic equation. An improved version (reliable rendering, leaving out the focus and directrix, etc.) would be nice. XOR'easter (talk) 17:28, 21 March 2024 (UTC)

I tried purging the image (Commons:Help:Purge) but that didn't help, so it's not a caching issue. I think the file itself is not good. —David Eppstein (talk) 17:50, 21 March 2024 (UTC)

I think it's related to this regression in SVG rendering: https://phabricator.wikimedia.org/T97233 –jacobolus (t) 19:25, 22 March 2024 (UTC)

Argh this only gets more infuriating. The bug was reported upstream, who fixed it in 3 days. That was 4 years ago. WMF couldn't care less, apparently upgrading a library is too much work. They said they will only upgrade it together with the whole Debian distribution. The thing is, they can't be arsed to do that either. The Debian stable with the fix was released 3 years ago. Nothing. There was even another Debian stable release after that, last year. Nope. They are still on Buster, that was released in 2019. Fun fact, that will be end-of-lifed in 3 months, so we will have one the largest websites in the world running on unsupported software.

What on Earth are these clowns doing with out donation money? Tercer (talk) 21:12, 22 March 2024 (UTC)

@XOR'easter I've been working on this article recently, and intend to replace this image with several related images made in Desmos (I'm not sure if readers will notice, but anyone clicking through will then find a link to an interactive version), and also move the relevant section up toward the top and expand it. It will probably just be PNG images from a screengrab, since it takes at least twice the effort to get an SVG to render the same, and the benefit is relatively marginal. –jacobolus (t) 17:48, 21 March 2024 (UTC)

I'd welcome any other questions/requests/comments/recommended sources/collaboration on this article. It should be a high priority for us, as it gets a lot of page views (60k/month), more than related articles like quadratic equation, quadratic function, completing the square, or parabola, and seems likely to be routinely consulted by middle/high school students. –jacobolus (t) 17:49, 21 March 2024 (UTC)

I've put up a proposal on VPWMF to solve this issue. Tercer (talk) 16:06, 23 March 2024 (UTC)

I replaced the top image of this article, which wasn't very clear, and also added an image to the derivation by completing the square section, both shown here:

After looking at again it though, I think including the formula in the middle of the first image is too much text, and it would probably be better to cut out the explicit quadratic formula part, even though that's the article. I'll try to figure out how to clearly (but not too busily) show the analytic-geometry meaning of the discriminant and other parts of the quadratic formula in another image or two; it's hard to make such images simple and legible while still trying to demonstrate more than one thing in a figure. –jacobolus (t) 19:01, 23 March 2024 (UTC)

The middle of the first image does look a little text-heavy. (Maybe remove the $y=0\Rightarrow x=$ part and just show the evaluation of the formula?) But thanks very much for working on this. XOR'easter (talk) 20:26, 23 March 2024 (UTC)

Requested move at Talk:Flatness (mathematics)#Requested move 19 March 2024

There is a requested move discussion at Talk:Flatness (mathematics)#Requested move 19 March 2024 that may be of interest to members of this WikiProject. Favonian (talk) 10:17, 24 March 2024 (UTC)

Is Wolfram Mathworld reliable?

Related to the previous discussion, is Wolfram Mathworld reliable? I took the reviewing Talk:Arithmetic/GA2, and I claim that Wolfram Mathworld is not reliable sources, but the nominator claimed the otherwise. Now I'm very confused. Dedhert.Jr (talk) 07:12, 2 March 2024 (UTC)

I believe it's been discussed here before, although I can't find it now. In my opinion a mathworld source is better than no source, but not much beyond that. (I think that was also the general consensus from previous discussion.) Gumshoe2 (talk) 17:01, 2 March 2024 (UTC)

It seems to never have been discussed at WP:RSN, but it has been discussed here many times, including the following:

• 2006/04 (several threads on that page are relevant)
• 2011/01
• 2011/06
• 2011/12 (also mentioned in two other threads on that page)
• 2014/01
• 2016/01
• 2019/04
• 2019/10 (two consecutive sections mention it)
• 2021/03

I would say that these threads indicate a consensus among math editors that MathWorld is a usable but mediocre source, reliable for basic factual questions, but questionable as an indicator of notability and questionable when it comes to issues of terminology. --JBL (talk) 18:57, 2 March 2024 (UTC)

Mathworld usually doesn't make outright false mathematical claims, but has a tendency to repeat (or invent?) dubious historical/naming claims. –jacobolus (t) 19:40, 2 March 2024 (UTC)

It is now open for discussion. Dedhert.Jr (talk) 13:50, 28 March 2024 (UTC)

I agree with the above two comments. It is not so unreliable that it must be immediately removed and replaced by a [citation needed] tag, as some sources are, but it is so frequently error-riddled that it is almost always better to use a different source. For a Good Article review, in particular, I think that better sources should be used. For Arithmetic, I replaced one MathWorld source by a much better one (a chapter in The Princeton Companion to Mathematics) and removed the other one as it was redundant and used only to source some alternative terminology, the sort of thing MathWorld is worst at. There still remains a MathWorld external link, of dubious value according to WP:ELNO #1. —David Eppstein (talk) 19:37, 2 March 2024 (UTC)

It seems Eric Wolfgang Weisstein created and maintains MathWorld, which is licensed by Wolfram Research. It is not self-published and from Weisstein's credentials, I don't see a good reason for categorizing this as an unreliable source. Are there any obvious points from WP:RS that suggest otherwise? Phlsph7 (talk) 13:39, 6 March 2024 (UTC)

It's not the worst ever source (Weisstein doesn't write outright nonsense and usually cites some other sources), but I'd put it on par with some professor's blog, course notes, math overflow answers, or similar: content written by someone with expertise in the general topic, but not vetted or carefully fact-checked. It's much less reliable as a source than e.g the articles by O'Connor and Robertson at MacTutor, and even those are often not a perfect reflection of the current scholarly consensus. Where possible it's best to compare multiple recent sources by subject-specific expects. –jacobolus (t) 15:19, 6 March 2024 (UTC)

Weisstein's degrees were all in astronomy. And I'm not even aware of anybody trained in mathematics who could be a reliable source for so much mathematical material. Gumshoe2 (talk) 17:44, 6 March 2024 (UTC)

I don't particularly care about Weisstein's credentials, but I have too often found mistakes and neologisms in MathWorld to give my full trust in it. There are of course also many mistakes in Wikipedia itself, but we don't allow Wikipedia to be used as a reference. —David Eppstein (talk) 18:29, 6 March 2024 (UTC)

@David Eppstein I'm curious now. Can you give me an example of some mistakes in MathWorld? Also, what about external links? Can MathWorld be used for external links as well? Dedhert.Jr (talk) 04:02, 7 March 2024 (UTC)

Mathworld can be used as either a source or in the 'exernal links' section, but also doesn't have to be. If a particular Mathworld page doesn't add anything that isn't in an article or other accessible sources, I'd take it out from the external links section. If another better source can be cited for any particular claim, I'd cite that one instead of Mathworld. Any claim sourced to Mathworld should be double checked in better sources anyway, as it's often a bit sloppy. At that point you can just cite the other source you found. –jacobolus (t) 05:04, 7 March 2024 (UTC)

@Jacobolus Ahh. I see. What I meant is not for Arithmetic, but for whole articles in general. An example is GA Malfatti circles, or GA Square pyramid in which two MathWorlds being used in external links. Should they (as well as the rest of them, if possible) be excluded in this case? How did one know that whether some kind of website or any sources will be included as external links? Dedhert.Jr (talk) 05:44, 7 March 2024 (UTC)

I wouldn't rush out to automatically remove Mathworld from all articles; that would be controversial and probably harmful. But if I'm otherwise looking at an article and its sources, I'll click the mathworld link and review whether it really seems helpful to readers to include, and when it doesn't I just take it out. –jacobolus (t) 05:56, 7 March 2024 (UTC)

One example of a mistake in MathWorld, since you're focused on polyhedra: at the time I brought Jessen's icosahedron up to GA status, the MathWorld article gave an incorrect construction based on the coordinates of a regular icosahedron. The current version fixes that.

Another example of what I think is a mistake, of terminology for polyhedra: Isohedron describes as a "trapezoidal dodecahedron" (bottom right corner of table) a shape that I think is properly called a "deltoidal dodecahedron" [6]. The trapezoidal dodecahedron is something else, not an isohedron [7]. See Special:Diff/1150447755.

Again, it is not hard to find similar mistakes in Wikipedia itself, but that is not the same kind of problem because we don't use Wikipedia as a reference. When we use MathWorld as a reference we need to be careful, more than with some other sources. —David Eppstein (talk) 07:34, 7 March 2024 (UTC)

Ahh... I see, then. Just in case, I think I prefer to find better sources for the external links. Dedhert.Jr (talk) 12:32, 7 March 2024 (UTC)

Just realized the article Triaugmented triangular prism, where MathWorld says that it is constructed by erecting regular tetrahedron onto each square faces of an equilateral triangular prism. [8]. I remember you have explained this in the edit summary before you nominated it to GA. Dedhert.Jr (talk) 13:54, 28 March 2024 (UTC)

Yes, Special:Diff/1112387125. They still haven't fixed that, I guess? —David Eppstein (talk) 17:44, 28 March 2024 (UTC)

I wanted to check this against my field of expertise and found this article: https://mathworld.wolfram.com/ProofTheory.html

It currently starts with "Proof theory, also called metamathematics", which is just bs. The Wikipedia articles are much better.

Metamathematics is much more general, e.g. it includes semantics from model theory, whereas proof theory is syntactic. The latter two fields are subfields of mathematical logic, but metamathematics does not even stop there. It was mostly subsumed by mathematical logic to increase rigor, so I guess this is where the confusion originates.

Apart from this mistake, the author seems to know barely anything about proof theory. The description is more one of metamathematics. Formal proofs and their systems, the only things being examined in proof theory, are not even mentioned by name. 134.61.97.95 (talk) 13:13, 18 March 2024 (UTC)

I linked to a few other discussions in my general advice essay. MathWorld being untrustworthy for terminology has been an ongoing theme. XOR'easter (talk) 17:20, 6 March 2024 (UTC)

I'd agree with assessment above that Mathworld is a mediocre but usable source and one needs to apply some common sense when using it. But imho it isn't really worse than many other (properly) published mediocre math sources out there such as various small math dictionaries and lexicons. Much of the Mathworld content is also published in book form for by CRC press btw.. For a freely accessible online resource for math history topics the MacTutor History of Mathematics Archive is usually a better alternative.--Kmhkmh (talk) 08:49, 7 March 2024 (UTC)

It seems to conflate distinct concepts and to make general statements that are only true in specific contexts. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:33, 7 March 2024 (UTC)

While in my experience MathWorld is particularly bad (on terminology issues; the actual math is usually right), even if it were better on that, it would still be a tertiary source, as is MacTutor, as is Princeton Companion (at least arguably), and as are "various small math dictionaries and lexicons". We should really strain to avoid using tertiary sources when good secondary sources are available. (Though it's reasonable to point readers to a link inside a tertiary source in "Further reading", as an aid to readers who want to look something up quickly.) --Trovatore (talk) 22:44, 7 March 2024 (UTC)

While often very useful, I wouldn't characterize MathWorld as a WP:RS. I would presume that for "basic" stuff it would be relatively accurate, but less so the farther afield one goes. I personally wouldn't use it to cite something I didn't already know to be true. Paul August ☎ 15:53, 18 March 2024 (UTC)

Draft:Orientational terms

I have the opposite of the usual problem. We have articles on technical concepts of orientation in math and science, but no article on the basic concept of "some things have a top and bottom and front and back". I'm trying to write something that is very everyday life/explain it like I'm five-oriented. Who's good at that? BD2412 T 02:47, 19 March 2024 (UTC)

Take a look at Anatomical terms of location § Main terms. –jacobolus (t) 07:13, 19 March 2024 (UTC)

The challenge, I think, is describing what it means for something to be the front or back of an object without just repeating that it is in front, and without using more complex and technical terminology to describe the relation. The anatomy article may at least provide some inspiration. BD2412 T 15:10, 19 March 2024 (UTC)

I had similar challenges when editing Shape. It can help to look at how the brain psychologically maps out directions; a quick google search brought this up as an example, it may be worth pursuing this vein of research further:

[9]https://econtent.hogrefe.com/doi/abs/10.1027/1864-9335/a000065?journalCode=zsp Brirush (talk) 16:03, 19 March 2024 (UTC)

Excellent, thanks. This is very useful, and I can see how challenging it would be to write a topic like Shape. BD2412 T 17:42, 19 March 2024 (UTC)

I have worked the draft up some. What do you think? BD2412 T 20:11, 29 March 2024 (UTC)

Piecewise

I'm confused by Set theorist's recent move of Piecewise to Piecewise-defined function. Shouldn't we have an article about the general concept "piecewise" (when applied to some property of a function, rather than a definition), which subsumes piecewise linear function, piecewise constant function, piecewise continuous function, piecewise differentiable function, etc.? (The last 2 links redirect to Piecewise-defined function which I consider misleading since the properties are independent of the way in which a function is defined.) - Jochen Burghardt (talk) 11:11, 29 March 2024 (UTC)

I agree, and I have reverted back to the previous title. D.Lazard (talk) 11:46, 29 March 2024 (UTC)

I have rewriten the lead for making clear that "piecewise-defined function" and "piecewise property of a function" are essentially the same concept. Much further work would be useful for this article. D.Lazard (talk) 12:36, 29 March 2024 (UTC)

Someone should write something about the higher dimensional case, especially surface interpolation and connections with many areas (e.g., computer graphics). Tito Omburo (talk) 15:06, 29 March 2024 (UTC)

Higher dimensional examples are significantly more complicated/diverse; I'm not sure if the name "piecewise" is ever used for this per se, but perhaps. E.g. in the 2-dimensional case there are some such functions based on regular square or triangular grids, some based on arbitrary triangulations or division into assorted rectangles, and some based on arbitrary divisions into regions of other shapes. –jacobolus (t) 17:17, 29 March 2024 (UTC)

This concept is not only about functions. See piecewise linear manifold and piecewise linear curve, for instance. —David Eppstein (talk) 19:13, 29 March 2024 (UTC)

Generally adjectives make bad article titles (see also WP:NOUN). In mathematics specifically, they often seem to be explanation-of-jargon articles, which in my opinion we should generally not have. I'm not convinced there's a good rationale to explain all the different mathematical uses of "piecewise" in a single article. A blurb in glossary of mathematics might be OK, and the search term could redirect there. --Trovatore (talk) 19:50, 29 March 2024 (UTC)

Since the article, as it now stands, is only about piecewise defined functions, it should be moved to Piecewise-defined function and then a new Piecewise disambiguation page should be created, with links to Piecewise-defined function, Piecewise linear manifold, and other "piecewise" things. Michael Hardy (talk) 02:24, 30 March 2024 (UTC)

I disagree: The lead of the article defines and is linked to piecewise linear function, and I have just added in this article a hatnote linking to piecewise linear (disambiguation). As Piecewise linear manifold is about a very advanced matheatical concept, one can presume that interested readers will not search for "piecewise", and that the new hatnote is sufficient. D.Lazard (talk) 11:05, 30 March 2024 (UTC)

Piecewise linear 2-manifolds, as polyhedral surfaces, are actually a quite familiar and not very advanced concept. Similarly piecewise linear curves are commonplace and familiar. It is only in higher dimensions that they get more advanced. —David Eppstein (talk) 20:06, 30 March 2024 (UTC)

Moreover, all articles whose name begin with "piecewise" refer to the same meaning of this adjective. In this case, WP:DABCONCEPT discourages to create a dab page, and recommends an article on the general concept (WP:Broad-concept article). D.Lazard (talk) 11:25, 30 March 2024 (UTC)

The big risk with "broad-concept articles" is that we might be abstracting out a "broad concept" on our own, that sources have not isolated as a particular object of study. We are not supposed to do that. Can you find sources that bring together all these meanings of "piecewise" in a single place? If not, then we shouldn't either. --Trovatore (talk) 18:36, 30 March 2024 (UTC)

Apr 2024

How to deal with this example/proof heavy article? (Cauchy's theorem)

I was asked to edit the article on Cauchy's theorem (group theory). There are two example sections which are earmarked for lack of citations. But when I read them, they do not seem particularly appropriate for the encyclopedia format at all. Putting aside typoes and poor grammar for a moment, the examples are both presented like problem book exercises, and could be shortened to a one-sentence description, if they are even interesting enough to warrant inclusion at all.

I'm also surprised that the article includes not one, but two entire proofs of the theorem. There must surely be textbooks online with complete proofs of their own. The style manual suggests "as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result." - by this metric I would vote to remove proof 1 entirely, and heavily abbreviate proof 2.

I have ideas for content that could be added, but I thought before removing 50% of the article I should get a second opinion. Danielittlewood (talk) 21:02, 1 April 2024 (UTC)

I also am a fan of proof 2. As far as a citation for this proof goes: it is an exercise in Isaacs _Finite Group Theory_. The original proof is by J McKay in a 1959 article in the Amer. Math. Monthly. Russ Woodroofe (talk) 21:23, 1 April 2024 (UTC)

Thank you very much for that reference. I managed to find the exact reference (although I can't access it, I'll take your word for its content). I'll add that to the article.

https://www.jstor.org/stable/2310010 Danielittlewood (talk) 21:07, 2 April 2024 (UTC)

A few examples showing some basic consequences of a theorem generally seems like a good idea to include. It would be nice to show some picture with these. Any wikipedia article explicitly about a theorem should include at least one proof if it is not inordinately long, or a proof sketch if all of the proofs are extremely cumbersome. If there are multiple proofs with substantially different ideas, then including more than one proof is nice. The style guide you are quoting is discussing the use of proofs in articles that aren't explicitly about particular theorems. In an arbitrary mathematical article (something like Circle or Matrix (mathematics) or Differential calculus or Real number), including a proof of every statement would be a distraction. –jacobolus (t) 22:43, 1 April 2024 (UTC)

In this case i completely agree with removing (at least most of) the examples. The first one has nothing to do with Cauchy's theorem: it should be removed. The second one uses it (in a confusingly oblique way) while usually the result is deduced from Lagrange's theorem; it can conceivably remain if it is rewritten correctly. jraimbau (talk) 05:06, 2 April 2024 (UTC)

I'm certain there are better applications. I think the ones in the article currently can be abbreviated to a single sentence while losing nothing of value. I'll try to find some better examples, ideally that lead to proofs of deeper theorems. Danielittlewood (talk) 21:08, 2 April 2024 (UTC)

I think both proofs are good to include, since they're very short and the page is about the theorem. To my personal preference the second proof could be written a little condensed, something like this:

Given any group G, the cyclic group Z_p acts on the set of tuples (g₁,...,g_p) in G with g₁...g_p = e, by cyclic permutation of the elements. If p is prime and G is finite, it follows from the orbit-stabilizer theorem that each orbit of the action has size either 1 or p. Orbits of size one are in natural bijection with group elements g such that g^p = e. If there is no such element other than e, it follows that the cardinality of the set of tuples is not divisible by p (since it is equivalent to 1 modulo p); since it can be checked that the cardinality of the set is divisible by the order of G, it follows that the order of G is not divisible by p. So if the order of G is divisible by p, then there must exist a non-identity element g with g^p = e.

(with obvious room for improvement, and provided there's a reference given with details). If there's a similar way to slightly reduce the first proof, I think that would be ideal. But I also think that both as currently written are acceptable in terms of detail. Gumshoe2 (talk) 23:37, 1 April 2024 (UTC)

Inner measure

The inner measure article had an unsourced and incorrect definition from almost 14 years ago, which I have now removed. It leaves the article pretty spare. Thoughts on what to do are invited on the talk page. --Trovatore (talk) 05:50, 3 April 2024 (UTC)

Original research on Wikipedia

Hello, I am a mathematician from the German Wikipedia. There we had recently a user that basically "misused" the German Wikipedia to publish his own "research" (if you can call it even that...). Basically the user computed a LOT of things with Wolfram Alpha and published all his computations in the German Wikipedia to a point where the articles became unreadable. He even invented his own names for functions and the user - according to his own words - does not have a formal degree in mathematics. In my opinion most of the stuff was not even relevant for an encylopedia. In the end a lot of his entries were deleted and after a heated discussion the user got banned. Long story short the user was/is also active in the English Wikipedia (see Special:Contributions/Reformbenediktiner). I am not so familliar with the English Wikipedia policies but I know that original research is also not allowed, so I thought I should maybe notify people here and they could at least have a look at some of the affected articles like for example Theta function, Rogers–Ramanujan continued fraction, Fubini's theorem#Example Application, Jacobi elliptic functions, Rogers–Ramanujan identities etc. If you see some math in color, that was probably done by this user. In the German Wikipedia the user did not use any source material and just computed things with Wolfram Alpha. Whether it all was correct or not, I am not even sure. It would be good if people would have a look at the affected English articles as well and give their judgement.--Tensorproduct (talk) 19:42, 22 February 2024 (UTC)

FYI: User:Reformbenediktiner. PatrickR2 (talk) 19:48, 22 February 2024 (UTC)

Thanks for this report. I just removed a lot of this from Poisson summation formula (two long and almost entirely unsourced sections). Probably the others listed above and the contributions of this user need similar scrutiny. —David Eppstein (talk) 20:28, 22 February 2024 (UTC)

Yes, unfortunately every post by him needs scrutiny. In the German Wikipedia eventually almost all of his math edits were removed. Many users asked him many times to provide sources but he kept on editing without providing any source. It seems to be the same here as Jacobolus' example below shows--Tensorproduct (talk) 21:18, 22 February 2024 (UTC)

Example discussion: Talk:Lemniscate_elliptic_functions#Sources? –jacobolus (t) 20:49, 22 February 2024 (UTC)

Thanks for letting us know. Bubba73 ^{You talkin' to me?} 21:03, 22 February 2024 (UTC)

Here was another recent discussion: Wikipedia_talk:WikiProject_Mathematics/Archive/2023/Jul#Theta_function. --JBL (talk) 18:58, 2 March 2024 (UTC)

Huh. I spotted the stuff at theta function, and scratched my head a bit about it. I would be happier if much or most of this was removed, or maybe moved to a distinct article. Many of the relations are cool-looking! Yes, it is not uncommon for stuff similar to this to be published in journals. However, the cutting edge academic journals & books will say things similar this in the intro: In 1837, Kummer listed three identities for hypergeometric functions; this was extended to 50 by 1880, and 240 in 1920 and a general algorithm to generate a countable number of such identities was given in 1960. However, it did not list all of them, and neither did algorithms x,y,z proposed in 1980 and in this paper we explore the structure of algorithmic generators ... and so you realize these guys are talking about a kind-of fractal splattered all through this landscape of inter-related identities, and how to best understand/describe that fractal. (As far as I know, there aren't any articles on WP that even scratch the surface of this topic, and it would be cool if there were... but, whatever.) The problem is that the enthusiastic amateur is unaware that he's dong the algebraic equivalent of publishing cool-looking zooms of the Mandelbrot set. Yes, its still cool looking. But is not where the action is, and it is a clutter and distracting, if you were reading the article to find something else, e.g. look up some factoid about riemann surfaces, and that factoid is now buried in reams of wild identities. 67.198.37.16 (talk) 08:13, 4 March 2024 (UTC)

It's up to you guys if you want to check every edit of him, whether it is legit or not (like we did in the German Wikipedia), or you want to save time and just remove them. For me is "computing stuff with Wolfram Alpha and not adding to the mathematical theory" not mathematics and hence not relevant for an encylopedia.--Tensorproduct (talk) 22:05, 8 March 2024 (UTC)

I literally just came across a few edits by that user at the article Jacobi elliptic functions while looking for articles to translate into Spanish. Unfortunately that user's article edits go back to 2022, and I can't justify reverting that far back since I can't integrate other people's edits while deleting that user's edits. I can confirm that a good chunk of their vocabulary is gibberish from at least 19 March 2024, but because the topic is somewhat beyond me, I can't even confirm the tremendous amount of notational modifications that user also made since 2022. I do suspect that reverting all of that user's edits is the right move. JuanTutors (talk) 00:21, 26 March 2024 (UTC)

Wow, yeah. Vast stretches of Jacobi elliptic functions and Theta function are garish, under- or unreliably sourced, and basically impenetrable. There's no way to tell what is important and what is just a formula included for the sake of having a formula. XOR'easter (talk) 01:35, 2 April 2024 (UTC)

I'd go so far as to say that Theta function should be reverted to the version of 14 April 2022. XOR'easter (talk) 22:34, 3 April 2024 (UTC)

I agree with this. It seems that there were some intervening good edits, but it seems like the simpler approach would be to merge those in manually. Tito Omburo (talk) 10:45, 4 April 2024 (UTC)

I can hit revert myself, but I'd have to clear time/gather energy to do manual merging of any intervening good edits. Perhaps some of the additions to these various pages could be saved in a List of identities for the such-and-such function kind of article (like Exact trigonometric values and List of trigonometric identities). But we'd need better grounds for preserving such material than "Wolfram Alpha says so" or "one random preprint on ResearchGate includes it". XOR'easter (talk) 18:11, 4 April 2024 (UTC)

I've removed a section of geometric series by this editor that was obvious offtopic original research. I looked at their edits to Fubini's theorem, which I consolidated into Fubini's theorem#Calculation examples and I don't feel very strongly about it (although it badly needs edits for style). Tito Omburo (talk) 10:39, 4 April 2024 (UTC)

Note: It seems like @A1E6: has had a lot of interactions with this editor in the past, and presumably could weigh in. Tito Omburo (talk) 10:55, 4 April 2024 (UTC)

Some of his work exceeds the limits of what WolframAlpha can do. But what matters is that he often harms the Wikipedia project by adding his original research that is clearly beyond WP:CALC and not only that; the research is sometimes hardly notable/interesting from a mathematical standpoint. I've had a conversation with him on several occasions; you can check out my Talk page if you want.

When I first started editing Wikipedia, I had a similar mindset like Reformbenediktiner – but that changed (a long time ago) when I understood what this project is about.

I'm not active on Wikipedia anymore though; otherwise I would have already done all the "dirty work" myself – like deleting some of his contributions (or adding warnings about original reseach for readers) and discussing on the Talk pages – I'm familiar with all the mathematical articles that he edits.

But don't get me wrong – some of his contributions are good... A1E6 (talk) 12:44, 5 April 2024 (UTC)

This is an area that I also have some familiarity with, but I am not a great expert. If I have time, I will try to clean up some of these articles and keep you posted. Tito Omburo (talk) 19:11, 6 April 2024 (UTC)

Copy-pasting proofs in articles

I just deleted some technical proofs in the Coppersmith's attack article, because they were pretty much copy-pasted from some of the sources with a few words changed. Given the article is not about most of the proofs, they're probably better deleted anyways, but I was wondering what the policy was on proofs in articles and how similar they're allowed to be, because obviously Wikipedia can't have its own proof of every subject, but I think it's a copyright violation if you copy-paste (even with a few words changed) the exact wording. Does anyone know if that's correct? I looked for any policy pages but could not find them. Mrfoogles (talk) 00:56, 11 April 2024 (UTC)

Sounds about right. Review Wikipedia:COPYVIO. Perhaps if you spent a lot of time and determined that the sources were CC-by-SA, and so they could be copied, the question still remains if mathematical proofs in articles adds any value. Usually, they don't. See Category:Article proofs and Category:Articles containing proofs and Wikipedia:WikiProject Mathematics/Proofs. My knee-jerk reaction is you're dealing with a form of spam from a novice editor with good intentions but lacking experience. On closer inspection, that article was created whole, including the proofs, in 2011, by an editor who created two WP articles in two days, and never-ever edited WP ever again. The intricacy of detail suggests that the author is copying directly from their own thesis, i.e. they are probably copying their own work. Probably. But since they're anon, can't quite tell, and since they're not active, can't ask them.

One more comment about proofs. If they are added by a clear subject-matter expert (as is the case here) then they're OK (because likelihood of correctness is high, and the maintenance burden is low.) When they are added by a college sophomore studying for a mid-term exam, then they must be exterminated with prejudice. If they clutter the article, they can be wrapped with one of the auto-expander click-thru box templates, so that they don't take up space when not expanded. 67.198.37.16 (talk) 02:46, 11 April 2024 (UTC)

Please see Wikipedia:Expert editors:

• "Wikipedia does not grant additional powers or respect to subject-matter experts."

Who added content or under what circumstances is not relevant. Johnjbarton (talk) 16:22, 11 April 2024 (UTC)

True. And it is also the case that a contribution from a subject-matter expert is more likely to be correct than one from a "college sophomore studying for a midterm exam". :-) PatrickR2 (talk) 23:19, 11 April 2024 (UTC)

Hodge conjecture

Hello, I think there was some vandalism on the Hodge conjecture. I tried to revert to what looked to be last good version of the article. However, I am not sure given the maths in the article. If someone can take a look at the diffs and content of the article that would be much appreciated! Classicwiki (talk) If you reply here, please ping me. 22:03, 3 April 2024 (UTC)

Current version looks OK. It's identical to [10] Tito Omburo (talk) 22:12, 3 April 2024 (UTC)

@Tito Omburo, thanks for reviewing! Classicwiki (talk) If you reply here, please ping me. 22:13, 3 April 2024 (UTC)

@Classicwiki and Tito Omburo: I notice that the article was edited heavily by Darcourse in 2023 and 2022; this editor is singularly incompetent in my opinion (though not a vandal), so if you're checking what the last good revision is, you might inspect their edits, too. (The I looked a little bit and wasn't convinced one way or the other.) --JBL (talk) 18:20, 4 April 2024 (UTC)

I'm not really qualified to judge most of the article for mathematical accuracy, but I would say that on a cursory reading it seems ok. Tito Omburo (talk) 19:01, 4 April 2024 (UTC)

@JayBeeEll - unfortunately I am in the same boat and can not judge the mathematical accuracy, so it is tough for me to determine if the edits are appropriate. Classicwiki (talk) If you reply here, please ping me. 22:09, 4 April 2024 (UTC)

Ok, no worries -- thanks both. --JBL (talk) 17:45, 12 April 2024 (UTC)

Featured article review for 0.999...

I have nominated 0.999... for a featured article review here. Please join the discussion on whether this article meets the featured article criteria. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" in regards to the article's featured status. The instructions for the review process are here. voorts (talk/contributions) 20:58, 11 April 2024 (UTC)

On the subject of FAR, would anyone like to try fixing the mild under-citation at Emmy Noether? XOR'easter (talk) 14:14, 13 April 2024 (UTC)

Possible duplicate logic articles

Does it really make sense for "Logical connective", "Boolean function", and "Truth function" to all be separate articles? If I were more sure, I wouldn't be asking. I get how "Logic gate" is a separate article, but the other ones seem to cover the same territory, although I'm not sure which one(s) should be merged into which. Thiagovscoelho (talk) 12:21, 17 April 2024 (UTC)

Hi @Thiagovscoelho: These are distinct topics. Logical connectives are used to connect (logical) expressions in first-order logic, second-order logic and set theory in general, to express axioms, theorems, inference rules, etc. By contrast, Boolean functions are functions (things having input and output) that operate on elements of a boolean algebra. These may be finite, countable or uncountable sets. See Stone representation theorem for details. Note that the elements of a boolean algebra are NOT logical expressions! The truth function article deals with the most limited, narrow case, where "truth" is taken to be a single value T or F. A single letter, a single bit. This is distinct from elements of a boolean algebra, which can be large complex things, and it is also distinct from logical connectives, which apply to the text strings of a term algebra or a model theory. So, very distinct concepts which magically happen to have the same notation. Which, yes, can lead to confusion. Perhaps the ledes of these articles should be amended to clarify this, state this up front. 67.198.37.16 (talk) 20:46, 19 April 2024 (UTC)

(p.s. The word "magic" is fun. Formally, it is called the semantic/syntactic distinction, and there are a collection of theorems from the 1930's that clarify this relationship. Turing's incompleteness theorem is perhaps the most famous; there are others. e.g. Skolem-Lowenheim upward/downward, the completeness theorem, and the assorted variants of it from Godel, Post, Gentzen, Bernays, Kleene.) — Preceding unsigned comment added by 67.198.37.16 (talk) 21:03, 19 April 2024 (UTC)

Hi @Thiagovscoelho: I noticed that you just went through a major, massive rewrite of the very long article on propositional calculus. Are you sure that this is a good idea, given the confusion you expressed above? The old version of the article seemed to get to the point, right after the first two introductory paragraphs; the new version seems to take some tortuous detour, before starting to explain what it is half-way into the article. I cannot help reviewing this, but perhaps more wisdom and fewer facts would help. 67.198.37.16 (talk) 22:27, 19 April 2024 (UTC)

I've replaced disorganized sections that did not cite sources with organized sections that do cite sources, and I'm doing this by reading all the sources. The sources are naturally textbooks on logic, and they mostly only mention connectives, which, semantically, are only defined by means of their associated truth functions, whereas syntactically they are of course not properly "defined" at all, but may have their behavior described by inference rules prescribing their introduction or elimination. As it stands, the Logical connective article has no coverage of introduction/elimination inference rules, so its coverage overlaps a lot with what Truth function ought to cover. As to Propositional calculus, the old version "got to the point" by failing to define terms that are defined in all the sources, introducing notation without explaining what it means, failing to keep syntax and semantics clearly distinct, failing to distinguish between a formal language and the proof system used with it, and, most of all, not citing any sources at all and therefore not describing any of the variation between authors on the topics. You are welcome to edit it and improve it, but there is no Wikipedia standard by which the old article was better. Thiagovscoelho (talk) 23:05, 19 April 2024 (UTC)

Yes, the current version of Boolean function actually specifies "truth function" as an alternative name for it. If you are sure that there is such a sharp distinction, it would be good for you to edit the article and cite the Reliable Sources that you are familiar with for this statement. I have not read any of the literature that specifically refers to "Boolean functions", but the idea of such a sharp division surprises me, since George Boole was a logician, after all, and I mean, just look at the article, it features all the normal connectives from logic. Thiagovscoelho (talk) 23:27, 19 April 2024 (UTC)

My experience is that at least in computer science "Boolean function" is usually, but not invariably, used to mean functions that take values in the two-element Boolean Algebra. This is how the textbooks I currently have access to use the term. I don't currently have access to Rudeanu's classic on the subject, but I could check his terminology in the library next week if needed. At least Steinbach and Posthoff do also explicitly mention truth function as a common synonym. Felix QW (talk) 08:15, 20 April 2024 (UTC)

References

Accessibility of Newton's method

Can someone here take a look at the recent changes at Newton's method and discussion at talk:Newton's method, and maybe help resolve the edit war there? user:Fangong00 insists on a substantial rewrite, especially of the first few sections, which I think makes the article significantly worse, most importantly rendering it, in my opinion, almost completely illegible to most of the intended audience. They don't seem too interested in having a discussion about the trade-offs involved in of various possible choices of scope/focus for the article or its early sections, but I don't really want to spend all day revert warring. Maybe someone else can phrase concerns about this in a way that gets through? –jacobolus (t) 02:23, 21 April 2024 (UTC)

The previous page for Newton's method is outdated. That version only presents Newton-Raphson method. In today's numerical analysis, Newton's method most often means Simpson's extension and also include the Gauss-Newton iteration and the newly discovered the rank-r Newton's iteration. Furthermore, the crucial convergence theorems such as Kantorovich Theorem and alpha theory were not included.

Why does jacobolus insists on keeping the outdated version? When someone tries to look up Newton's method, he or she is entitled to see the what Newton's iteration is today. Fangong00 (talk) 02:35, 21 April 2024 (UTC)

@Fangong00 the basic real-function version of Newton's method is not "outdated", but is used ubiquitously, and anyone working with computer software involving numerical calculations is likely to come across it sooner or later. It is taught to early undergraduate students and frequently encountered by people with relatively limited pure math background. It is essential that a Wikipedia article about such a basic and widely used tool start out in its first few sections with explanation which is legible and accessible to the broadest possible audience. If you want to include detailed technical discussions of advanced niche generalizations, then that is fine, but it must be done much further down the page and clearly contextualized so that readers can figure out what is being discussed and why.

As a simple example, a computer game programmer with a high school level math background might plausibly read fast inverse square root and come across a wikilink there to Newton's method; if they click through they must not be confronted with a wall of jargon expecting several years of preparation they don't have. –jacobolus (t) 02:48, 21 April 2024 (UTC)

Raphson's method is not out dated, it is now a special case of what we call "Newton's method" in numerical analysis. The most widely used Newton's iteration is not Raphson's but Simpson's and Gauss-Newton. To make the page a useful reference for the broadest possible audience.

Why do you not want a vistor to see the most widely used Newton's method? Fangong00 (talk) 12:56, 21 April 2024 (UTC)

Fangong00, you are incorrect. The page in its previous state does have a section for systems of equations and for Banach spaces, where the Gauss-Newton iteration and (what you call in a nonstandard way) "Simpson's extension" belong. The rank-r Newton iteration seems to be from a 2023 paper and it is not at all clear that it is notable enough for mention. The Kantorovich theorem is also already mentioned there.

Smale's theorem is certainly appropriate for inclusion, and could go for example in the Analysis section. Gumshoe2 (talk) 02:54, 21 April 2024 (UTC)

I know the page mentioned Simpson's version serveral pages later. Users visiting the page is unlikely to see it when they thought only Raphson's method is Newton's iteration. Fangong00 (talk) 12:58, 21 April 2024 (UTC)

The Gauss-Newton method and the Banach space Newton method are also already mentioned further down the page in the previous version. I don't think there would be any objection to expanding the text in that context.

I also don't think there would be any objection to drawing attention to this by mentioning, perhaps in a couple sentences, in the lead section that there are important multidimensional extensions of Newton's method. The lead section, after all, is meant to be a brief summary of the article. (See Wikipedia:Manual of Style/Lead section; I think neither version of the article has a satisfactory lead section.) Gumshoe2 (talk) 13:17, 21 April 2024 (UTC)

I think this content should be restored. I have commented at Talk:Newton's method. Tito Omburo (talk) 12:18, 21 April 2024 (UTC)

Adjoint functor theorem

I think that people searching for "Adjoint functor theorem" are looking for explanations about the Freyd's adjoint functor theorem, so I suggest changing the redirect target to the Formal criteria for adjoint functors. SilverMatsu (talk) 15:35, 24 April 2024 (UTC)

Ths is a possibility. However, there is an anchor "Freyd's adjoint functor theorem" in Adjoint functors. I have changed the redirect for pointing to this anchor instead of to the lead. Note that Formal criteria for adjoint functors is linked to just above this anchor. I have no clear opinion about your proposed change of target, but, in any case, Freyd's adjoint functor theorem and Adjoint functor theorem must have the same target. D.Lazard (talk) 16:24, 24 April 2024 (UTC)

Thank you for clarifying the redirect target. By the way, there are two versions of Freyd's adjoint functor theorem, which are sometimes called General adjoint functor theorem and Special adjoint functor theorem. --SilverMatsu (talk) 00:19, 25 April 2024 (UTC)

Requested move at Talk:Basic Math (video game)#Requested move 24 April 2024

There is a requested move discussion at Talk:Basic Math (video game)#Requested move 24 April 2024 that may be of interest to members of this WikiProject. RodRabelo7 (talk) 05:33, 28 April 2024 (UTC)

Wigner probability distribution

It might be good to have some people watch Wigner semicircle distribution, with someone having just added back some extensive material I deleted a couple months ago. I think it's pretty incoherent, and not good material for the page regardless. Gumshoe2 (talk) 16:22, 28 April 2024 (UTC)

"Distinct" definition

The use of the word "distinct" , should be reviewed , so that its usage becomes clear, here are the pages I have noticed them in: Constructible polygon, ,Carl Friedrich Gauss ,Exact trigonometric values ,Constructible number

The constructible polygon page says : A regular n-gon can be constructed with compass and straightedge if and only if n is a power of 2 or the product of a power of 2 and any number of distinct Fermat primes.

Whereas , the Constructible number page says:

• powers of two
• Fermat primes, prime numbers that are one plus a power of two
• products of powers of two and any number of distinct Fermat primes.

Notice here the second bullet point is separate to the third ; is that to say that "any number of distinct Fermat primes" does not include one Fermat prime appearing on its own. And would zero Fermat primes be considered a distinct number of Fermat primes?. This should be specified. EuclidIncarnated (talk) 13:48, 28 April 2024 (UTC)

The formatting of the post above is difficult to read. As far as I can tell, the issue is more about "any number" than about "distinct". I think that it is best treated by editing those specific pages to address that specific issue. Mgnbar (talk) 14:03, 28 April 2024 (UTC)

Sorry about my bad formatting , I am relatively new to Wikipedia writing and thank you for bringing to my attention , "any number", which should be defined more clearly. I would say that so does "distinct". For example , consider one number is it distinct? or is there required a second number for it to be said to be distinct?. Such things should be made more clear. EuclidIncarnated (talk) 14:44, 28 April 2024 (UTC)

As an example, I have edited Constructible polygon#Conditions for constructibility. I did not clarify what "distinct" means, but I did clarify (some might say too explicitly) what "any number" means. What do you think of this solution? Does "distinct" still require clarification? Mgnbar (talk) 15:03, 28 April 2024 (UTC)

I changed the ·bullets to asterisks to make a proper list. —Tamfang (talk) 19:38, 28 April 2024 (UTC)

The last bullet point includes the first two bullet points as special cases. –jacobolus (t) 14:22, 28 April 2024 (UTC)

I don't see how the first bullet point is a special case of the last bullet point , could you explain what you mean? EuclidIncarnated (talk) 15:03, 28 April 2024 (UTC)

In the third bullet point, let 2^j be the power of 2 involved, and let k be the number of distinct Fermat primes involved. The first bullet point is the special case where k = 0. The second bullet point is the special case where k = 1 and j = 0. Mgnbar (talk) 15:44, 28 April 2024 (UTC)

Yes this is going off of the definition that the product of a number is itself and thus a power of 2's product is itself. This is what Product (mathematics) says is the definition of products : "Originally, a product was and is still the result of the multiplication of two or more numbers." Therefore your definition of product is not this. EuclidIncarnated (talk) 17:47, 28 April 2024 (UTC)

Sorry; I don't quite understand your post. No one here has defined the word "product", have they? The Wikipedia article Product (mathematics) is not a Wikipedia:Reliable source. Anyway, products and powers can take on slightly different meanings in different contexts. When stating a theorem, it is a good idea to make the intended meaning explicit and clear.

Have you seen my recent edit to Constructible polygon#Conditions for constructibility, which I mentioned above? Is it not clear? Regards, Mgnbar (talk) 18:01, 28 April 2024 (UTC)

It seems fine to me , your edit. EuclidIncarnated (talk) 18:11, 28 April 2024 (UTC)

@EuclidIncarnated Mathematicians define the "product" of any (possibly empty) collection of elements all belonging to some structure where multiplication is well-defined. An empty product is equal to the multiplicative identity, which is 1 in the case the quantities being multiplied are numbers. The "product" of a single quantity is just the quantity itself. –jacobolus (t) 00:09, 29 April 2024 (UTC)

All true, but this is a point we should be careful of when writing articles for non-mathematicians who may become confused by 0-element and 1-element products. —David Eppstein (talk) 00:29, 29 April 2024 (UTC)

Is there anywhere in Wikipedia that has such a definition. EuclidIncarnated (talk) 07:12, 29 April 2024 (UTC)

@EuclidIncarnated This is described in Product (mathematics) § Product of a sequence. While a sequence per se is an ordered list of numbers (or other quantities), if multiplication is commutative (true in many but not all contexts) the order doesn't matter and you could just as well take the product of an unordered collection like a multiset. –jacobolus (t) 07:15, 29 April 2024 (UTC)

And Product (mathematics)#Empty product is all about the case where 0 numbers are being multiplied. Mgnbar (talk) 11:59, 29 April 2024 (UTC)

May 2024

Emmy Noether FAR final citations and checks

The Emmy Noether article has been at featured article review for a couple months now. If anyone wants to take a look, most of the issues seem to have been fixed but the contributions to mathematics and physics section would likely benefit from a couple more citations and a quick survey (including of the typsetting) by someone more qualified than I am. Sgubaldo (talk) 15:20, 16 April 2024 (UTC)

In particular, does anyone feel like tackling the subsection Emmy Noether#Ascending and descending chain conditions? XOR'easter (talk) 17:00, 1 May 2024 (UTC)

Frobenius theorem

Could someone take a look at my suggestion here? Alaexis_¿question? 13:08, 6 May 2024 (UTC)

Log vs ln

On Talk:Ordered Bell number, an editor is arguing that we should use ln rather than log for the natural logarithm. My position is that for mathematics articles, the standard convention is to use log; ln is for engineers and this is not an engineering article. The same editor also claims that writing $\log _{2}e$ is "stupid" and that we should always write it ${\tfrac {1}{\ln 2}}$ instead. Mathematically-literate opinions welcome. (Note that the article is currently in the middle of a GA review; the editor disputing the notation is not the GA reviewer.) —David Eppstein (talk) 18:30, 1 May 2024 (UTC)

Maybe we can add this to a style guide somewhere. I think it's worth using ln in articles about engineering and possibly also in high-school-level topics such as those related to trigonometry or introductory calculus. I'd rather use log everywhere else, wherever it isn't ambiguous. –jacobolus (t) 18:35, 1 May 2024 (UTC)

I prefer $\ln x$, but as long as the article clearly sets out the nomenclature that it's using, it's no big deal.

WRT "${\tfrac {1}{\ln 2}}$", eschew obfuscation; it's confusing and ugly. I see nothing wrong with $\log _{2}e$ -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 21:20, 1 May 2024 (UTC)

How about Logarithmic integral function? You wouldn't write $\int _{0}^{x}\log _{t}e\ \mathrm {d} t$. IntGrah (talk) 22:22, 1 May 2024 (UTC)

Whether to write 1/log_e2 depends on the context. For starters, what if you're informing students of the basic facts about logarithms, which they just heard of today? Then you might state, as an example, that 1/log_e2 = log₂e, and then you'd need to write 1/log_e2. Michael Hardy (talk) 21:10, 2 May 2024 (UTC)

Presumably someone reading Ordered Bell number isn't learning about logarithms for the first time. –jacobolus (t) 21:55, 2 May 2024 (UTC)

• "My position is that for mathematics articles, the standard convention is to use log;"

All you need is a reference to cite this standard convention. Johnjbarton (talk) 22:32, 1 May 2024 (UTC)

You don't need a reference for this. This is prevailing practice throughout the mathematics literature. (It's not hard to find such references, but throwing them in is off-topic for whatever article, and gratuitous.) However, it could help to briefly note, in contexts where some readers might be confused, that log means the natural logarithm, with a wikilink. –jacobolus (t) 22:35, 1 May 2024 (UTC)

In the early days of Wikipedia, user:AxelBoldt was the author of a majority of mathematics articles on Wikipedia, and argued that ln is better than log because it is unambiguous.

I prefer log or log_e. Notice that exp does not mean base-10 exponential.

Undergraduates not majoring in mathematics sometimes say "Do you mean logarithm, or natural logarithm?" (to which the correct answer is usually "yes."). The use of ln has misled them to think that the natural logarithm is not literally a logarithm. (They have also often been taught to call the inverse tangent function the inverse tangent function and have never encountered the word "arctan". If you write "arctan θ" then one of them asks whether "arctangent" is the same as "cotangent.") Michael Hardy (talk) 20:56, 2 May 2024 (UTC)

If using ⁠$\,\arctan \theta \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{\color {RawSienna}{\tfrac {\qquad \quad \ \ }{}}}\ \theta =\arctan x$⁠ in some arbitrary article, it can be helpful to add an inline definition, along the lines of "where ⁠$\arctan$⁠ is the trigonometric inverse tangent function". –jacobolus (t) 21:55, 2 May 2024 (UTC)

If I came across ⁠$\arctan \theta$⁠ I'd worry I'd done something wrong! NadVolum (talk) 14:11, 3 May 2024 (UTC)

I think that $\ln x$ makes it clear that anti-logarithm x is a real number rather than making it clear that the base is e. In particular, clarify that the domain of a function of the $\ln x$ is real numbers. see principal value. --SilverMatsu (talk) 04:45, 3 May 2024 (UTC)

I was going to say I didn't mind what was used but I agree, yes you're right. lt does make it clear one is working with real numbers. NadVolum (talk) 14:11, 3 May 2024 (UTC)

Is there any Wikipedia article on which this technicality is worth bringing to the attention of the readers?

(FWIW despite being about combinatorics the context for the log in the article initiating this discussion actually does involve complex numbers.) —David Eppstein (talk) 18:04, 3 May 2024 (UTC)

This is not a universal convention, so I don't think it is a good idea to pretend it is. —Kusma (talk) 19:26, 3 May 2024 (UTC)

1 to Kusma. When I see $\ln$ I do not necessarily automatically assume that the domain is the reals. I've seen that convention so it wouldn't especially surprise me to find someone using $\ln$ and $\log$ distinctively in that way, but I don't think it makes the domain unambiguous without further comment. --Trovatore (talk) 19:48, 3 May 2024 (UTC)

In Logarithm#Complex logarithm the convention is used with good effect in the definition of the complex logarithm. NadVolum (talk) 17:25, 6 May 2024 (UTC)

I find the use there to be confusing, inconsistent, and idiosyncratic. YMMV. I would much prefer if the multi-functions for argument and logarithm were capitalized, with names for the principal branch left all lowercase, matching the names of single-valued functions used elsewhere in the article and the more typical convention found in the literature (though this is a place where literature is notoriously inconsistent and confusing). –jacobolus (t) 19:00, 6 May 2024 (UTC)

By the way there is a standard to use lb for the binary logarithm but I don't know of anyone who does that! And using a base with ln is just silly. Only a total massochist would try using any base other than e with a complex logarithm so there's no point in specifying it in that case. NadVolum (talk) 17:39, 6 May 2024 (UTC)

I have often seen lg for the binary log. —Tamfang (talk) 01:12, 7 May 2024 (UTC)

Yes, that's pretty common, and approved by the Chicago Manual of Style, despite ISO explicitly reserving lg for common logarithms instead. (I have never seen any actual use of lg for common logs outside of ISO documents.) It's also pretty common for computer scientists (and sometimes information theorists) to use log for binary logarithms (without any base subscript), unfortunately, with hard-to-spot disclaimers that they're doing so. —David Eppstein (talk) 07:00, 7 May 2024 (UTC)

Knuth uses "lg" for the binary logarithm, and people probably pay more attention to Knuth than to the ISO. XOR'easter (talk) 16:16, 7 May 2024 (UTC)

FWIW I've seen several computer science papers using log for the base 2 logarithm, a single one using lb, and non using lg. Tercer (talk) 20:24, 7 May 2024 (UTC)

I can find several of my papers using lg. Nowadays I might be more likely to use log₂. But in much of computer science the logs are wrapped in O-notation and it doesn't matter what the base is; I think in that context log is the most likely notation. —David Eppstein (talk) 20:45, 7 May 2024 (UTC)

Request review of Local analysis

Could someone please take a look at the article Local analysis, which has had zero references since July 2008? Is it a valid topic for a standalone article? If so, would you be able to add a citation? If not, should it be redirected somewhere? Cielquiparle (talk) 22:24, 7 May 2024 (UTC)

I'm not keen on this edit. Generally an article should have a single topic, and not give distinct unrelated meanings of the same term. Lack of references is a problem, and I think merging to Hasse principle might be one solution. Tito Omburo (talk) 10:32, 8 May 2024 (UTC)

Yes, lumping together unrelated, separate meanings of the same term is more dictionary-style, rather than encyclopedic. XOR'easter (talk) 16:49, 8 May 2024 (UTC)

For the current article, a sensible thing might be to turn it into a disambiguation page for Localization of a ring and a subsection (to be added) of Sylow subgroups. For the latter, a p-local subgroup is the normalizer of a nontrivial p-subgroup; this could be sourced e.g. to Isaacs' Finite Group Theory book. I don't think the Hasse principle is a great redirect, although I could be missing something. Note that p-local subgroup currently redirects to this article, and there may be other redirects targeting here. Russ Woodroofe (talk) 18:15, 8 May 2024 (UTC)

Merger of Unitary operator and Unitary transformation.

We have these two articles: Unitary operator, Unitary transformation. Should they get merged? Michael Hardy (talk) 21:04, 2 May 2024 (UTC)

I always thought the map C² → C³ given by sending (u, v) to (u, v, 0) would be an example of a unitary operator, with 'unitary' referring just to the preservation of a hermitian inner product. The notion suggested here is what I would call "unitary isomorphism." Have I been using the term in an unusual way? Gumshoe2 (talk) 18:59, 3 May 2024 (UTC)

The text is incorrect. A bounded linear operator U : H → H on a Hilbert space H that satisfies U*U = UU* = I need not be surjective unless H is finite dimensional. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 19:03, 9 May 2024 (UTC)

No, this statement is correct. (Since $x=Ix=UU^{*}x=U(U^{*}x)$.) Tito Omburo (talk) 20:26, 9 May 2024 (UTC)

The content of Unitary transformation which describes isomorphism between Hilbert spaces should be migrated to a section on Hilbert space, which currently has no discussion of morphisms of Hilbert spaces (in fact the word "isomorphism" is used only 8 times and never in the context of describing the natural notion of isomorphism of Hilbert spaces!). The rest of it is just a copy of content in Unitary operator which is a much more commonly discussed notion.

Should also point out there will be quite a bit of overlap with Unitary matrix and indeed Unitary group but I think unitary operators (i.e. automorphisms of infinite-dimensional Hilbert spaces, especially function spaces) are studied in their own right as a primary topic that is distinct enough in flavour and techniques (and of course in level of difficulty for the average reader to understand) that it makes sense to keep Unitary matrix/operator/group as 3 separate pages. Tazerenix (talk) 05:35, 10 May 2024 (UTC)

This seems sensible to me. Tito Omburo (talk) 09:16, 10 May 2024 (UTC)

request: birkhoff universality theorem

i began investigating my my belief that optimal function estimation of a 'target function', using purely geometric properties (i.e. properties of the curve wrt to the unit interval) was cyclical.

as a preface i want to emphasise to my peer group my understanding that using very finite-valued integers (i.e. in the hundreds or thousands) to describe cardinality on the real interval is asking to get slaughtered, but i need to lay some groundwork for my request. anyways!

i observed behaviour where the 'optimal function' estimating the target would exist in cycles. that is, define A > B > C \in \mathbb{Z}_ as the cardinality of the set of uniformly-spaced points on the domain for which we have values of target function f. i.e. we have f(a) for all a \in A, etc.

whilst possible for B = A 1, i often found there was a 'gap' between A, B and C. again, ANYWAYS:

assuming the vertical line test is enforced, it seems that the 'optimal function' for a 'target function' can be (easily) estimated via composition of functions from, say, the space of square-integrable functions.

this lead me to the work of Joel Shapiro, which seems to point to Garrett Birkhoff's 1929 paper which, as i understand it, is considered the "birkhoff universality theorem".

don't you guys think we need a page for this? it seems kind of important in the era of function approximation and the ensuing evaluation of its optimality, for which the cyclical nature of the composition of functions are incredibly relevant.

https://math.osu.edu/sites/math.osu.edu/files/Birkhoff.pdf

George D Birkhoff. Démonstration d’un théoreme élémentaire sur les fonctions entières. C. R. Acad. Sci. Paris, 189(14):473– 475, 1929.

pinging the wikipedia math legend @D.Lazard: to see if this meets the WP notability.

toodles, my dear PEER GROUP 162.157.84.254 (talk) 22:53, 11 May 2024 (UTC)

Aaron Naber and Robin Pemantle

If anyone would like a suggestion on new wikipages to write, Aaron Naber and Robin Pemantle are mathematicians recently elected to the National Academy of Sciences (NAS, AMS). With this qualification there should be no issue on notability. Gumshoe2 (talk) 15:03, 12 May 2024 (UTC)

In the same spirit there's Vladimir Sverak, recently elected to the American Academy of Arts and Sciences (AMS news). Gumshoe2 (talk) 22:39, 14 May 2024 (UTC)

Biographical notability

I just posted the following, to Wikipedia talk:WikiProject Physics. Cross-post here, because WPM has exactly the same problem.

The physics project template counts the number of articles ranked by importance, and quality. Here: Wikipedia:WikiProject Physics/Quality Control There are currently 700 articles with unassesed priority (marked "???"). Clicking through, almost all of these are biographies. I suspect that no one particularly wants to tackle this, because of the unpleasantness of tagging someone's biography as "unimportant". That, plus the true difficulty of actually assigning a relative ranking -- you have to be very cross-disciplinary to be able to assess such comparisons. And that's just within physics, never mind something like "my biologist is more important than your physicist" or god help us, "our TV anchor is more notable than your physicist". Thus, I'm wondering if perhaps there might be better to avoid this issue entirely? I'm thinking of allowing the template to have an "importance=biographical" value. Or maybe there is some better way to do this?

Please discuss there.

BTW, the WPM assessment is here: Wikipedia:WikiProject Mathematics/Assessment and clicking through to the server shows almost all unassessed articles are biographies, with a sprinkling of societies, journals and awards. 67.198.37.16 (talk) 00:18, 16 May 2024 (UTC)

Requested move at Talk:One half#Requested move 17 May 2024

There is a requested move discussion at Talk:One half#Requested move 17 May 2024 that may be of interest to members of this WikiProject. Remsense诉 13:18, 17 May 2024 (UTC)

Expectile

I have created a somewhat stubby new article titled Expectile.

• It could use further work.
• Its uses in mathematical economics could possibly be mentioned. I don't know enough about those to do that.
• Three articles link to it: Quantile, Expected value, and Risk measure. Possibly other links should be there.

Michael Hardy (talk) 17:32, 17 May 2024 (UTC)

Edit war in Tournament (graph theory)???

Just across the article via contributions, watchlist, or whatever it is, the article Tournament (graph theory) apparently has some kind of edit war (I suppose) between User:David Eppstein and User:Closed Limelike Curves. I have no clue about graph theory, but probably need some discussion per WP:BRD. Dedhert.Jr (talk) 15:31, 18 May 2024 (UTC)

CLC has now three times changed the lead to a wrong definition involving complete directed graphs. Tournaments are not complete directed graphs. Complete directed graphs have edges in BOTH directions between each pair of vertices. Tournaments have an edge in exactly ONE direction between each pair of vertices. They are orientations of complete UNDIRECTED graphs. The undirected part is important. CLC should be reverted a third time, at least. I reverted twice but more eyes would help. —David Eppstein (talk) 16:04, 18 May 2024 (UTC)

@David Eppstein Not to mention, the article has problems with citations, and more importantly, why does the article even put the theorem box in the first place? Will take care of these problems as much as I can. Let me know if someone has a different idea.

But seriously, for verifiability that tournaments are not the complete directed graphs, is it possible to expand the article, pointing it out alongside the supported sources, avoiding confusion or misinterpretation? Another problem here is the lead may already give some WP:TECHNICAL, and it seems that CLC relates this terminology to the round-robin tournament, from which I could not see anything about them instead of the list of see also section in the edit source. Dedhert.Jr (talk) 16:12, 18 May 2024 (UTC)

Hi David—very sorry if my last edit was unclear, my intention wasn't to start an edit war. The last time I edited this, however, I described tournaments as "Oriented complete graphs", which I believe to be correct. (I don't see any difference between "oriented complete graphs" and "orientation of a complete graph"—the term "oriented complete graphs" means you start with a complete graph, then orient it.)

I believe most people would understand the term "complete oriented graph" refers to a tournament by slight abuse of terminology (the meaning is clear because an oriented graph can't be complete, so it must mean "as complete as possible"). My citation of the Mathematica wiki shows the wiki using the term "complete oriented graphs".

If you think "Orientation of a complete graph" would be more technically correct language, I think that's reasonable, but I'd prefer if you edited that term directly rather than reverting the edit as a whole. –Sincerely, A Lime 17:16, 18 May 2024 (UTC)

Re your "I described tournaments as "Oriented complete graphs", which I believe to be correct": maybe you can argue that this is correct in a pedantic WP:TECHNICAL sense, if one understands the technical word "oriented" to mean adding directions to the edges of an undirected graph and "complete graph" to mean "complete undirected graph". However, it is also confusing, misleading, and totally inappropriate for the lead sentence of an article. When we talk about directed graphs, the natural interpretation of "complete graph" would be a complete directed graph, and casual readers are unlikely to notice the distinction between oriented and directed. These are not complete directed graphs. —David Eppstein (talk) 18:51, 18 May 2024 (UTC)

PS also please stop putting CS1-formatted citations into their own separate templates. This article uses CS2 (the citation template, not the cite templates) with short footnotes. When you put a citation into a template, rather than leaving it in the main text of an article, and then make a short footnote to it, it will always generate a harv linking error (look at the hidden categories). In addition, this violates WP:CITEVAR. —David Eppstein (talk) 18:55, 18 May 2024 (UTC)

In this case David Eppstein's edit is certainly better since it is clearer. However, Closed Limelike Curves' proposed definition as "oriented complete graph" seems to be identical, at least according to the lead sentence of Orientation (graph theory). The sentence "A tournament is an orientation of a complete graph" also appears on that page. If this is actually in error, presumably because of wiki conventions on graph theory language, perhaps that page needs to be changed. Gumshoe2 (talk) 19:51, 18 May 2024 (UTC)

Again, a definition that can be argued to be technically correct, if one uses the precise technical meanings of each term, can still be seriously misleading, if an un-expert reading of those terms would likely lead readers to a wrong understanding. We should aim for understanding, not merely technical correctness. —David Eppstein (talk) 20:11, 18 May 2024 (UTC)

Adjoint functor theorem, axiom of choice and anafunctor

I noticed that in the Formal criteria for adjoint functors it says that "for simplicity ignoring the set-theoretic issues". Does this refer to axiom of choice? Also, it seems that axiom of choice can be avoided by introducing a concept called anafunctor. It would be great if you could give me some advice or help with the draft (Draft:Anafunctor). SilverMatsu (talk) 05:16, 17 May 2024 (UTC)

I think it is not appropriate to ignore set theoretic issues in the statement of the theorem, because one of the conditions is essentially a set theoretic smallness condition already (it holds trivially in small categories for instance). MacLane states the theorem for (small-)complete categories with small hom sets. As far as I am aware, the proof uses choice. I don't know about anafunctors. Tito Omburo (talk) 10:52, 17 May 2024 (UTC)

Thank you for your advice. I think so, too. I think the theorem (SAFT) requires an axiom of choice. By the way, I'm thinking about whether to add Category: Axiom of choice to a new draft. --SilverMatsu (talk) 17:36, 21 May 2024 (UTC)

Also, Roberts (2011) says that, the etymology of anafunctor is an analogy of the biological terms anaphase/prophase. By the way, wiktionary has an wikt:anafunctor, and wikipedia has a profunctor. --SilverMatsu (talk) 15:46, 23 May 2024 (UTC)

Thanks for sharing. That's an interesting remark. Tito Omburo (talk) 15:56, 23 May 2024 (UTC)

Merge Measurable space into Measure space

This seems sensible, doesn't it? IntGrah (talk) 23:45, 26 May 2024 (UTC)

Maybe, maybe not. The benefit of having two separate pages is that it makes it clear that the notions are different. This also allows other pages that reference these concepts to reference specifically the definition they need and thereby to minimize possible confusion. Note also that each of these two pages has "Not to be confused with ..." link at the top, and also shows the contrast with the other notion. But I can see that this could be debated. PatrickR2 (talk) 06:00, 27 May 2024 (UTC)

I think they should not be merged, since they are different concepts. Note that the Springer EoM also has separate articles for the concepts. Tito Omburo (talk) 12:19, 27 May 2024 (UTC)

Fair enough. I was hoping that one concept would just be described in a sentence in another article, like Weighted graph in Graph, but I see otherwise now. IntGrah (talk) 13:17, 27 May 2024 (UTC)

The two concepts are importantly rather different, especially in applications of measure theory (e.g., probability and dynamics). Tito Omburo (talk) 15:05, 27 May 2024 (UTC)

Agree w/Tito, Patrick. 67.198.37.16 (talk) 02:04, 29 May 2024 (UTC)

Jun 2024

Degenerate bilinear form is unreferenced

Request for an esteemed colleague from WikiProject Mathematics to please review and find a source for Degenerate bilinear form, which has been tagged as "Unreferenced" since August 2008. Cielquiparle (talk) 09:58, 25 May 2024 (UTC)

I see this has been fixed; surely though the right title for this topic is Nondegenerate bilinear form? They're the important ones .... 64.26.99.248 (talk) 18:24, 30 May 2024 (UTC)

I'm guessing there is a stupid Wikipedia reason for this bizarre state of affairs. Tito Omburo (talk) 21:35, 30 May 2024 (UTC)

The reason is probably history rather than policy. IAC, rather than renaming the article it might be better to merge it into Bilinear form with {{R to section}} in the redirects. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:39, 31 May 2024 (UTC)

That sounds reasonable. XOR'easter (talk) 00:26, 6 June 2024 (UTC)

Uncited statements at 0#Computer science

A few statements at 0#Computer science need support from manuals, textbooks, and/or histories. I know math people aren't necessarily computer people, but it seemed a good idea to raise the signal here too. XOR'easter (talk) 02:42, 6 June 2024 (UTC)

Doi will be added to the Theory and Applications of Categories

See this blog post. SilverMatsu (talk) 15:31, 6 June 2024 (UTC)

SVG rendering bug is fixed

I'm happy to announce that MediaWiki has finally updated their SVG rendering library to a less obsolete version, and as a result plenty of bugs were fixed, including the one that sparked a discussion here back in March. Tercer (talk) 20:23, 6 June 2024 (UTC)

Thanks for the good news! —David Eppstein (talk) 20:31, 6 June 2024 (UTC)

History of the definition of the real numbers

I am confused by the Wikipedia description of the history of the definition/construction of real numbers:

• In Real number § History: The first rigorous definition was published by Cantor in 1871. No indication on the method (infinite decimals?)
• In Construction of real numbers: Nothing
• In Foundations of mathematics § Real analysis: In 1858, Dedekind proposed a definition of the real numbers as cuts of rational numbers
• In Dedekind cut, the note 3 refers to Dedekind, Richard (1872). Continuity and Irrational Numbers. Apparently, 1972 is the date of the English translation, not of the original in German. This seems confirm that Cantor's definition was not the first one.
• In fr:Charles Méray (translated): In 1869 he is the first to give a rigorous construction of the real numbers. This construction is based on equivalence classes of Cauchy sequences of rational numbers.

Similarly, it depends on the Wikipedia article whether the first (ε, δ)-definition of limit must be attributed to Bolzano, Cauchy or Weierstrass.

Could someone provide a clarification? D.Lazard (talk) 18:28, 12 June 2024 (UTC)

I'd hazard that the 1858 date is the erroneous one for Dedekind. Stetigkeit und irrationale Zahlen was published in 1872 [11]. However I think the question of priority is the wrong frame for the construction of the real numbers. One first needed integers (Peano), rationals (maybe Dedekind), infinite sets (Cantor), by which point of course "the real numbers" were already in some sense defined! Tito Omburo (talk) 22:20, 12 June 2024 (UTC)

According to Kline, Dedekind had given lectures in 1858 where he realized real numbers hadn't been properly formalized, but these ideas weren't published until 1872. It also looks like Meray (1869), Heine (1872), Cantor (1871) and Dedekind (1872) all published some constructions of the irrationals in around the same time frame, but its difficult to locate the primary sources. Weierstrass claimed to have presented a rigorous construction in 1859 that was never published. Tito Omburo (talk) 22:39, 12 June 2024 (UTC)

Clarification should be in the form of a reference to a history. Johnjbarton (talk) 22:25, 12 June 2024 (UTC)

There's an issue of publication vs. discovery. See the following (bolding for emphasis):

Dedekind worked out his theory of Dedekind cuts in 1858 but it remained unpublished until 1872.

Weierstrass gave his own theory of real numbers in his Berlin lectures beginning in 1865 but this work was not published.

The first published contribution regarding this new approach came in 1867 from Hankel who was a student of Weierstrass. Hankel, for the first time, suggests a total change in out point of view regarding the concept of a real number [...]

Two years after the publication of Hankel's monograph, Méray published Remarques sur la nature des quantités in which he considered Cauchy sequences of rational numbers [...]

Three years later Heine published a similar notion in his book Elemente der Functionenlehre although it was done independently of Méray. [...] Essentially Heine looks at Cauchy sequences of rational numbers. [...]

Cantor also published his version of the real numbers in 1872 which followed a similar method to that of Heine. His numbers were Cauchy sequences of rational numbers and he used the term "determinate limit". [...]

As we mentioned above, Dedekind had worked out his idea of Dedekind cuts in 1858. When he realised that others like Heine and Cantor were about to publish their versions of a rigorous definition of the real numbers he decided that he too should publish his ideas. This resulted in yet another 1872 publication giving a definition of the real numbers.
— O'Connor, John J.; Robertson, Edmund F. (October 2005), "The real numbers: Stevin to Hilbert", MacTutor History of Mathematics Archive, University of St Andrews

I think this is also covered in some of MacTutor's cited references. So Dedekind is often credited with the first construction in 1858, the first publication is credited to Hankel in 1867, the first publication with a "rigorous construction" is credited to Méray in 1869 or Cantor in 1872 or Dedekind in 1872. — MarkH₂₁^talk 22:44, 12 June 2024 (UTC)

Many thanks (I have fixed the parameters in your reference to Mac Tutor). D.Lazard (talk) 08:29, 13 June 2024 (UTC)

Can someone explain what Riemannian circle is supposed to be?

My guess is that the article Riemannian circle has an incorrect definition; as it is described there it seems like an obfuscated synonym for great circle, which should just be redirected there. But it wouldn't make any sense to call a great circle a "Riemannian circle" instead, so I imagine the term is probably supposed to mean something different instead. However, I don't really have the background or patience to sift through old sources trying to figure out precisely what. Can someone who knows about Riemannian geometry figure out what is going on there? –jacobolus (t) 02:40, 13 June 2024 (UTC)

Just WP:BOLDly redirect. The article has offers references and even if it did the content would be better in great circle. Johnjbarton (talk) 03:01, 13 June 2024 (UTC)

I don't want to do that because my expectation is that Riemannian circle means something different; if so, it would be better to delete the page instead of redirect. However, it would be better still if someone can replace this with a more accurate definition. (Doesn't have to be anything fancy; it's fine if the page remains a stub.) –jacobolus (t) 03:12, 13 June 2024 (UTC)

To me, as defined there, it appears to be an obfuscated definition for the metric space of arc length around a circle. Embedding it as a great circle on a sphere and then using geodesic distance on the sphere doesn't change anything. Also the part about Gromov is described better at filling area conjecture.

Searching Google Scholar for this phrase finds varying definitions:

• This definition, the arc length metric on a closed curve of length $2\pi$
• Arc length metric on any closed curve
• Arc length metric on a closed curve embedded as a rectifiable curve in a Euclidean space
• "A curve in a Riemannian space whose development in a tangent space is a circle"

The first three are not different except for scale, and seem like the majority of uses.

We probably should have an article on the arc-length metric on simple closed curves, and this title seems like a plausible place to put it if it doesn't already exist elsewhere with better content. So my tendency would be to attempt a rewrite along those lines, removing the definition about geodesics on a sphere between points of a great circle except more briefly as the conjectured answer to the filling area conjecture. —David Eppstein (talk) 04:34, 13 June 2024 (UTC)

Rewrite done and moved to metric circle, somewhat more common and less ambiguous. —David Eppstein (talk) 07:50, 13 June 2024 (UTC)

Thanks! –jacobolus (t) 08:52, 13 June 2024 (UTC)

While we're here, is there any place where this topic can be put into context and related to nearby topics? I feel like our collection of circle-related topics are somewhat atomized and not fit together into any particularly coherent narrative, many are incomplete, they don't do all that much interlinking, etc., and we're lacking much high-level overview. We have Circle, Circle group, Angle (but no separate "Angle measure"), Turn (angle), Radian, Arc length § Arcs of circles, Directional statistics, Circular distribution, Circular mean, Periodic function, One-dimensional symmetry group, Trigonometric functions, Fourier series, Root of unity, Cyclic group, Modular arithmetic, .... Some kind of summary should be in a section Circle but that article also has to discuss the way circles fit into other spaces making it a poor fit for substantial expansion in this direction. I'm not sure if the name Metric circle is used widely enough or if that article quite fits as a central place for discussing the use of the circle as a geometric space though.

As a separate aside, should we have an article Periodic interval or the like? We currently don't, but it seems worthwhile (though it overlaps with many of the topics I listed above). –jacobolus (t) 21:11, 17 June 2024 (UTC)

Let's not forget Jordan curve, pseudocircle, and quasicircle as topological forms of circles.

Anyway, in my rewrite I wanted to focus on specifically the one-dimensional compact Riemannian manifolds (a phrase that unfortunately does not turn up much good sourcing). One can find circle-like objects as Euclidean shapes, objects in topological spaces, rings, etc., but I think trying to write a single article about all of them would be too incoherent. —David Eppstein (talk) 21:45, 17 June 2024 (UTC)

A-class

As far as I remember, WP:WPM was no longer to include A-Class. However, the article Stanislaw Ulam has become an A-class in Military History Project. If that's the case, is it possible that WP:WPM (as well as the other WikiProjects) also consider this article as A-class instead of GA? Dedhert.Jr (talk) 03:18, 21 June 2024 (UTC)

Why? Who cares? The little green plus badge seems fine. If someone cares enough someday they can try to put a little gold star on there instead. –jacobolus (t) 06:08, 21 June 2024 (UTC)

A-class is defunct everywhere except milhist. We cannot consider it to be A-class for other projects because being A-class requires a project-specific dedicated review process that no other project has any more. Technically A-class is a higher rating than GA (but below FA). The solution is to list it as GA in all other projects but with an exception as A-class for milhist. —David Eppstein (talk) 07:13, 21 June 2024 (UTC)

Weren't that time many WikiProjects did some review for A-class? I understand that many of them become defunct nowadays, except for the military history, but is there any solution to change the whole assessment system so that the A-class may also be included in different ways? Wasn't there any discussion about this problem? There was actually if I am not mistaken. It's probably gonna awkward for some WikiProjects does not have A-class, except for that one, in my opinion. Dedhert.Jr (talk) 12:24, 21 June 2024 (UTC)

The solution is to eliminate A-class altogether. But you would need to take that up with the milhist people. —David Eppstein (talk) 18:29, 21 June 2024 (UTC)

@Dedhert.Jr, is there a particular reason you want to have an A class? I think if "B" as basically "whoever rated it thinks it has high quality but it never went through an explicit review", then both GA and FA just tell whether a reviewer gave the article a (hopefully careful) review and then agreed with the nominator that a visible corner badge was warranted. @David Eppstein, maybe we should remove all discussion of "A" class from Wikipedia:WikiProject Mathematics/Assessment. –jacobolus (t) 23:06, 21 June 2024 (UTC)

I went ahead and took A class out of Wikipedia:WikiProject Mathematics/Assessment, as well as making the description there of B class sound a bit more polished than previously. My impression is that B class should generally be at least approaching GA quality; we have both "C" and "Start" to describe articles that still need significant work. –jacobolus (t) 01:04, 22 June 2024 (UTC)

@Jacobolus. Well, if anybody wants to have an A-class, then I guess I can give them support, but I have no idea where to start. It reminds me about the discussion of GAN in which someone enticed to nominate the article to higher class FA: Prime number, Reversible cellular automaton, and Prince Rupert's cube. But for nowadays, this is fine. Dedhert.Jr (talk) 09:07, 22 June 2024 (UTC)

OR cleanup at an Archimedean topic

Wikipedia:No_original_research/Noticeboard#The_Method_of_Mechanical_Theorems is of interest to this WikiProject. It concerns The Method of Mechanical Theorems, about a work by Archimedes that was rediscovered in 1906. I am in the process of cleaning up the explanation of the propositions, which has no references and is written like a textbook, and have already completely rewritten the explanation of the lead. My current idea is to summarize each proposition in accordance to the principles of MOS:PLOT, with possible secondary sources about the text; an English translation by the discoverers of the text is in one of the current references. –LaundryPizza03 (dc̄) 21:38, 21 June 2024 (UTC)

I don't think there is any problem explaining a proof. In fact, WP:TECHNICAL explicitly encourages editors to write things in a way that can be understood by a broad audience. In particular, this section blanking removed content that is not only not original research (it is broadly consistent with Heath's summary of the method), but also is extremely useful in understanding the article as a whole (and in fact is a very lucid exposition of Archimedes method of proof). Accordingly, I have reverted the removal of this introductory section, as well as the removal of the section on volumes. I think the substantive problems are mostly over style (phrases like "we see that", common in mathematics exposition). Finally, please don't coopt WP:PLOT. This is a real scientific topic, and there is absolutely no reason not to explain the method in an "in universe" tone, like we would with any other scientific topic. Tito Omburo (talk) 23:43, 21 June 2024 (UTC)

More mathematically literate editors are badly needed there. The article is quite good, given that it is supposedly rampant with "original research". Much clearer than either Heath's summary of The Method or The Method itself. Tito Omburo (talk) 00:12, 22 June 2024 (UTC)

Setting all other issues aside momentarily, I don't see the relevance of MOS:PLOT here. That is about summaries of fictional works; the concerns addressed there are orthogonal to the ones relevant here. XOR'easter (talk) 16:35, 22 June 2024 (UTC)

I'm not sure it's worth carefully following, but much of the concrete advice in MOS:PLOT seems more or less applicable to technical books too. For instance we want to keep a neutral "out of universe" tone, using a "narrative present" tense, it's worth being explicit about the difference between description of the text vs. commentary, it's usually better to write summaries as prose instead of lists or timelines, and it's reasonable enough to cite a work itself as a primary source about its own content. Much of the advice is fiction-specific though. One part that shouldn't be forced on technical-book articles is "Plot summaries cannot engage in interpretation and should only present an obvious recap of the work." We should be clear about which part is summary vs. interpretation, but these could certainly be organized per chapter or per topic instead of rigidly separated into different top-level sections of the article. –jacobolus (t) 17:37, 22 June 2024 (UTC)

I prefer to base descriptions of the content of non-fiction books purely on what published reviews of those books say the books are about. MOS:PLOT is in a guideline whose full title is Manual of Style/Writing about fiction; as that title makes clear, it does not apply to nonfiction. —David Eppstein (talk) 21:09, 22 June 2024 (UTC)

Pythagorean quadruple, Formulas for generating Pythagorean triples

Both recently (well, a few months ago) edited heavily by Tetraso, mostly focused on citing the work of one Robert Amato. This was also true the last time this editor appeared on WP, in 2017 (see User_talk:Tetraso#Your_edit_in_Pythagorean_triple). Could perhaps use some more eyes; I'm particularly skeptical of the fact that it comes with the disappearing of an earlier, obviously reliable, source. --JBL (talk) 20:30, 21 June 2024 (UTC)

Jay Bee Ell‬,

Let's start with the topic 'Formulas for generating Pythagorean triples.' I would just like to contribute by adding some results that improve knowledge and are not focused on citing a scientific article. Several experts in the subject have cited or used the result that I added. In this regard, please see https://www.scopus.com/authid/detail.uri?authorId=57195007076. Regarding the author, please see https://orcid.org/0000-0002-7058-2128. I have only reported the results, trying to be concise. Those who wish to see the proofs of the reported results should have access to the references of the scientific article. The results are innovative and suitable for obtaining new results and applications in fields such as geometry, trigonometry, linear algebra, and number theory, as you can see in 'A Novel Approach for Studying Pythagorean Triples Suitable for Students at all Educational Levels' (https://ejpam.com/index.php/ejpam/article/view/5133). Regarding the topic 'Pythagorean quadruple,' I have just corrected an injustice. Wacław Sierpiński, in the article 'Pythagorean Triangles' pp. 102–103, did not cite that the result is based on the results of the article published in 1981, which you can find at https://zbmath.org/0586.51019. I have reported the 2017 article because it contains comprehensive results and because it is impossible to find the 1981 article, as the journal where it was published no longer exists. The cited journals were indexed (at least in the year of publication) in Scopus and Web of Science. Thanks. Tetraso (talk) 09:17, 22 June 2024 (UTC)

The long section in Formulas for generating Pythagorean triples looks undue, particularly given that it is only supported by a single primary source that has mostly been cited by its own author. XOR'easter (talk) 16:32, 22 June 2024 (UTC)

I had the same impression. The added citations seem good otherwise, though I haven't checked them carefully. Tito Omburo (talk) 17:10, 22 June 2024 (UTC)

The long section is the concise statement of two theorems that allow, given a predetermined integer, to find all the Pythagorean triples that contain it or only the primitive triples. The primary sources are two and distinct. Tetraso (talk) 18:04, 22 June 2024 (UTC)

@Tetraso I think the concern is that your only contributions to Wikipedia consist of promoting your own publications, and your published articles seem to be in journals with lax editorial standards. In general Wikipedia is not intended to be a venue for self promotion, and articles should try to be neutral with weight given to various aspects of the topic / particular sources in proportion to their importance as recognized in the literature broadly. Sometimes expert Wikipedians cite their own papers or cite papers by people they have directly worked with when they think it is necessary for the article (e.g. the first or an important source about an essential claim), but most are modest about this, giving credit where due to other sources, minimizing self aggrandizement, and trying to keep the articles balanced as best they can; citing themself is typically a tiny proportion of a Wikipedia author's effort. When a Wikipedian has a clear conflict of interest others treat those contributions with necessary skepticism, and when a Wikipedian focuses on self promotion and makes no other contributions it's often abusive or disruptive, and those contributions are commonly reverted. –jacobolus (t) 18:37, 22 June 2024 (UTC)

Dear Jacobolus, I don't understand how you can say that the articles are published in journals with lax editorial standards. These journals are indexed in Scopus or Web of Science. This is simply offensive. I don't see any self aggrandizement in wanting to contribute results that can be useful for the topic. Is including references self aggrandizement? You are discouraging participation in the community and the free exchange of information. I have no personal advantage in adding results to Wikipedia. Tetraso (talk) 19:02, 22 June 2024 (UTC)

I didn't investigate closely, but in User talk:Tetraso#Your edit in Pythagorean triple D.Lazard mentioned a predatory journal.

In general, we should aim to cover aspects of a topic that are mentioned in highly cited and well respected secondary sources such as textbooks or survey papers. Sometimes newer sources are are worth citing in regard to some new details about existing topics, but typically as one source among many.

Novel work about new aspects of a subject that is published in somewhat obscure journals and hasn't yet had time to garner community feedback and respect is often best to just wait on. If it proves to be important, then over the following years that will be made clear as it is discussed and built upon by other authors, summarized in survey papers, etc.

As with most other decisions in Wikipedia, there are no black and white rules for these editorial decisions, and ultimately what sticks around in articles depends on Wikipedians' consensus.

If you are an expert about Pythagorean triples, presumably you know some things that are not yet in the article but discussed in the literature (not specifically your own published paper), which would be worth adding with a clear summary and the appropriate citations. After all this is a topic which is centuries old and which has been written about by hundreds of authors. But from what I can tell you haven't tried to do that.

It's hard to imagine that the only thing any expert can think of that is missing from some article(s) but is essential to include is their own personal work. So if all a Wikipedian does is cite themself, that raises red flags: it seems more like an effort to use Wikipedia to direct readers to the author's own work, and less like an attempt to make the article the best it can be. It shortcuts the work of doing serious literature survey and the hard decisions involved in writing the encyclopedia, instead forcing that work on other volunteers who must rush to evaluate the cited source and its impact and rewrite the appropriate sections to weigh it against other sources and put in in proper context. –jacobolus (t) 20:54, 22 June 2024 (UTC)

JP Journal of Algebra, Number Theory, and Applications (which published the 2017 paper [12]) was de-listed from MathSciNet; it is published by Pushpa, which was on Beall's List. Also it is beyond bizarre to complain that Wacław Sierpiński (who died in 1969) didn't cite (in his publication from 1962) a paper written in 1981. (I also do not understand how this would be a justification for citing your own work from the past decade but not any of these prior works.)

Based on the discussion here I am inclined to revert both additions, the next time I have 30 minutes free. --JBL (talk) 21:29, 22 June 2024 (UTC)

Regarding Pythagorean Quadruples, I made a mistake because the year 2003 confused me. I am sorry. I have already provided the reference before. For Formulas for generating Pythagorean triples, do as you see fit. Tetraso (talk) 22:42, 22 June 2024 (UTC)

Cut locus

Two different stubby articles about the Cut locus were just merged together, but the result is still quite a mess, and some parts are a bit incoherent. Can someone who is more familiar with differential geometry literature take a look and clean it up a bit, ideally adding a couple of better sources? –jacobolus (t) 17:02, 23 June 2024 (UTC)

A related topic that should probably be mentioned at cut locus: source unfolding. The Miller&Pak reference from source unfolding may also be usable at cut locus. —David Eppstein (talk) 18:39, 23 June 2024 (UTC)

Lagrange inversion theorem

There is a dispute there which would benefit from additional input; see the last two talk-page sections at Talk:Lagrange inversion theorem. --JBL (talk) 17:37, 26 June 2024 (UTC)

0.999... still at Featured Article review

I think it's at a point where only some tidying remains, but I'm not sure when I'll have time to do that tidying. XOR'easter (talk) 01:26, 24 May 2024 (UTC)

This needs an evaluation to see if the FAR can be closed. XOR'easter (talk) 20:53, 17 June 2024 (UTC)

This is still waiting (final?) evaluation. XOR'easter (talk) 23:43, 26 June 2024 (UTC)

Tables usage in mathematical articles, especially in geometry

Whenever I'm thinking about tables, it reminds me of many tables in mathematical articles, including in geometry. In the past, there was tension about Cairo pentagonal tiling, where a user added tables for something floating things. More strongly, there are many articles about polyhedrons using many tables for representation as spherical polyhedrons, duals, related polyhedrons, and honeycombs together with the vertex configuration. Tetrahedron is another example, which not only contains those, but also contains tables such as the symmetry (and its difference with irregular ones), Coxeter planes, and many more.

My point in asking this is to reduce the excessive tables (unless there is generally being used in higher-class, as in WP:FL). Does Wikipedia actually have some manual of styles about tables? Does WP:WPM (including WP:3TOPE) have some kind of restriction about the tables' usage? Should this be added, whenever possible? Dedhert.Jr (talk) 01:22, 27 June 2024 (UTC)

WP:NOTGALLERY might be relevant. —David Eppstein (talk) 04:36, 27 June 2024 (UTC)

MOS:EMBED is also relevant. Indeed, many tables that are encountered in math article would better be transformed into bulleted lists or prose. D.Lazard (talk) 08:46, 27 June 2024 (UTC)

CfD discussion concerning Category:Symplectic_topology

I believe the discussion at Wikipedia:Categories_for_discussion/Log/2024_June_21#Category:Symplectic_topology would benefit from more opinions. Mathwriter2718 (talk) 12:45, 27 June 2024 (UTC)

FA Archimedes

Some discussion in the article FA Archimedes about its low standard criteria FA. Opinions from a third point of view are voluntarily welcomed. Dedhert.Jr (talk) 02:27, 29 June 2024 (UTC)

Advice on dealing with questionable citations in lead

I'd like some advice on how to handle a problem which I encounter quite often in articles covering basic topics that are widely used in other fields.

The typical scenario goes like this: A is a central notion that was introduced a while ago and on which there are plenty of old and recent textbooks. A is now used in many fields outside of mathematics, and maybe in a trendy field such as machine learning. Some people keep adding references to recent textbook or articles on A in the lead.

Sometimes the references are research articles published in obscure journals, and in that case this is not really a problem (even though one might need to remove the same reference several times). But in some cases the references are legit — or at least "legit-looking" — textbooks, and then because Wikipedia does not have very clear guidelines regarding citations in the lead, I am not always sure what to do and end up losing time.

Maybe a concrete example will help: Have a look at the recent [as of 11/06/2024] history of the article Markov chain, more specifically at this diff and this one. Here we have two different IPs located in Romania who are actively monitoring the article and who seem extremely upset that a textbook by a Romanian author is not listed first to back-up:

• the definition of a Markov chain;
• the assertion that "Markov chains have many applications as statistical models of real-world processes";
• the fact that Markovian and Markov can be used to refer to something that has the Markov property.

Of course, that makes me think that the person behind these IPs is either the author of said textbook; or someone who really likes this textbook.

The problem is that, as far as I can tell without reading it, this does indeed seem like a legitimate textbook on Markov chains. In fact, by some metrics it even seems to be a popular textbook: despite being fairly recent, it is already cited 900 times. That is of course impressive...But also not very surprising, considering that it has been the first reference of the Wikipedia article on Markov chains for a while.

(in fact, to try to get an idea of whether most people citing that book actually did so to reference specific properties and theorems, or simply to add a citation after their first use of the phrase "Markov chain". I am not going to copy and copy and paste excerpts, so as not to point fingers; but some authors seem to think that Gagniuc invented Markov chains, others that think that he recently discovered the game-changing fact that the rows of a stochastic matrix sum to 1, etc).

So, on the one hand I think that reference should be removed from the lead (and probably from the article altogether), because there are tons and tons of excellent textbooks on Markov chains, and I have some suspicions of self-promotion with this one (not to mention that I have no idea whether it is any good). On the other hand, this seems to be a legitimate reference (again, I have not read it) and so I can't really base myself on any clear Wikipedia policy to do so.

I would of course appreciate if someone could help me with this specific example (especially since it looks like some IP users are ready to engage in edit-warring). But I am mostly asking for general guidance here, because it is a problem I encounter regularly.

Best, Malparti (talk) 23:49, 10 June 2024 (UTC)

I'm inclined to agree that these fairly innocuous statements shouldn't be cited in the lead (per the guideline WP:LEADCITE) but instead in the body. The Gagniucs citation is particularly silly as it is used because it cites a 200 page book without giving a page number. I suggest migrating citations out of the lead into the corresponding places in the body, leaving WP:LEADCITE in your edit summary; if you actually do run into any trouble (your idea about this doesn't seem entirely supported by data) then bringing the issue up here (and perhaps in parallel on the article's talk-page) and seeing if the angry IP pretending to be two different people engages. --JBL (talk) 00:28, 11 June 2024 (UTC)

This can also happen more innocently, when some random editor asks for a citation of some claim and then, to clear the citation needed tag, another editor does a search and finds a random citation that matches the claim. Especially in cases where a claim is a basic fact that everyone working in a subject knows but few bother to write down (because it is so basic), or when the terminology has shifted and the texts haven't been updated to match, finding the claim in a standard textbook rather than in a recent research work can sometimes be difficult. —David Eppstein (talk) 00:42, 11 June 2024 (UTC)

@David Eppstein I agree; but I think that it is usually possible to distinguish the situations I am referring to and the more innocent situations that you describe. For instance, Gagniuc's book is repeatedly cited to back-up statements that do not really need a reference, such as "Markov chains can be used to model many games of chance". So to me it really looks like someone — not saying it is Gagniuc; it could be, e.g, a student that worships him — tried to promote his book. Malparti (talk) 23:48, 11 June 2024 (UTC)

Oh, I agree in this case, but "Markov chains can be used to model many games of chance" is exactly the sort of obvious statement that you're likely to see editors demand citations for. For this sort of thing, expository articles rather than research articles or monographs might be a better fit; I found for instance "How long is a game of snakes and ladders?" Math. Gaz 1993 and "Snakes and Ladders and Intransitivity, or what mathematicians do in their time off" Intelligencer 2023. Also those editors may well argue that "many" is WP:PEACOCK and that we should provide specific examples (of which snakes and ladders is one). —David Eppstein (talk) 00:07, 12 June 2024 (UTC)

@David Eppstein Arf, yes you are right; I've actually taken part in unproductive debates on this topic on Wikipedia in another language, and would rather avoid this on en.wiki (all the more so since I tend to be a bit more on the WP:BLUE end of the spectrum than most editors). But thanks a lot for the references, they are indeed much better suited than the current ones so I'll add them to the article over the weekend; ideally, I should take the time to do the same thing for all other such citations... Malparti (talk) 00:19, 12 June 2024 (UTC)

@JBL Thanks, that is useful advice. In fact I don't think that migrating citations out of the lead is needed: in my opinion the body of the article already contains quite a lot of unnecessary citations... Malparti (talk) 23:56, 11 June 2024 (UTC)

Uncontroversial statements discussed later in the article don't need any citation in the lead section, and it can be more legible for readers to defer those footnotes until later. (Of course, it can also be fine to include footnotes in the lead, e.g. when linking to the original source where something was first described.) More generally, when trying to support uncontroversial widely known claims, there are often hundreds of sources that could be cited. If you have one easily available, I would recommend leaning on popular and widely cited textbooks or survey papers rather than more obscure sources. People shouldn't be trying to use Wikipedia for self promotion via citation spam. –jacobolus (t) 01:55, 11 June 2024 (UTC)

I generally support moving citations out of the lead into the body or into {{refideas}}, with a comment to the effect that the citation should be deferred to the body. Is there a template with the semantics this is the wrong place for a citation?

I'm a bit hesitant to complain about citation spam, because there are often articles whose contents are garbage but that contain useful citations. In fact, sometimes I use wiki as a search engine and go straight to the references -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:43, 11 June 2024 (UTC)

@Jacobolus "when trying to support uncontroversial widely known claims, there are often hundreds of sources that could be cited. If you have one easily available, I would recommend leaning on popular and widely cited textbooks or survey papers rather than more obscure sources." → Yes of course. But my problem is specifically in cases where there is already a source, and it looks like a legit textbook (here: Gagniuc's book is published by a reputable publisher, and very cited) but it still looks like there is something fishy going on. I see it quite frequently. Less frequently than the situation where someone adds an irrelevant paper published in an obscure journal (but, as I said this is not a problem because in that case it takes me very little time to see what is going on and to remove the citation); but still frequently enough that I am starting to feel like this is making me waste my time. Malparti (talk) 00:04, 12 June 2024 (UTC)

If the source clearly supports the claim and is in a highly cited legit textbook, then I wouldn't worry too much about including it in the article somewhere. The lead of Markov chain is currently absurdly overstuffed^[1][2] with gratuitous footnotes.^{[3][4][5][6][7]} In my opinion these should be either removed to the body of the article or consolidated into no more than a couple per paragraph, for legibility. If Gagniuc's book is clear and well written, I think it would be fine enough to include book among a list (inside a single footnote) of relevant survey sources supporting some particular claims in the lead, but it would also be fine to entirely defer those references to the body. Gagniuc's book should be moved down to the "References" section, and a specific page mentioned for each time it is used as a reference. A 20 page research paper is fair enough to cite as a whole unit for a list of claims, but vaguely waving at a 200 page textbook is too much. –jacobolus (t) 00:30, 12 June 2024 (UTC)

I concur with the sentiment expressed above that uncontroversial statements in the intro that are adequately elaborated upon in the main text don't need footnotes. In this particular case, that block of four citations in a row is just silly. Actually, that whole sentence has problems. The main text of the article doesn't say anything more about "cruise control systems in motor vehicles" (which sounds like a weirdly niche application to advertise up top), or queuing at an airport specifically, or currency exchanges. I'd cut that line after "of real-world processes" and replace the rest with a better summary. XOR'easter (talk) 16:07, 11 June 2024 (UTC)

@XOR'easter I agree that the article has many problems... In fact I think this is one of these articles on a popular topics that suffers a bit from "constant-growth" and needs to be trimmed on a regular basis; but that's a somewhat different issue. I might try to rewrite the lead over the weekend (but I'm pretty sure that if I remove oddly specific examples, they are going to be replaced by other ones in no time). Malparti (talk) 00:06, 12 June 2024 (UTC)

I tried tidying it up, but you're definitely welcome to do a more thorough job! XOR'easter (talk) 21:11, 12 June 2024 (UTC)

Well now, for what it's worth, the IP editor comments in an edit summary that Gagniuc is "the most reliable book on the subject, and the one that is part of ChatGPT training set." A different IP editor calls it the "top representative book on the subject". –jacobolus (t) 00:21, 13 June 2024 (UTC)

It's been a while since an edit summary made me want to scream into a pillow. XOR'easter (talk) 01:22, 13 June 2024 (UTC)

For what it's worth: it seems that the references to Gagniuc's book were introduced here by (the now-banned) MegGutman. That user also wrote "After seeing the book on Wikipedia in 2017, I contacted Dr. Gagniuc for a collaboration proposal on a EU research project, which he kindly accepted. So, I'm personally involved.". I also found claims that Gagniuc's book is rubbish because it contains basic mistakes. I am going to skim through it to see about that for myself.

Rubbish or not — and irrespective of the identity of the person trying to promote the book — being referenced in this Wikipedia article seems to have paid off. So I think that show the importance of my initial question: how to deal with these kind of simulations without investing unreasonable amounts of time? If it was only about reading a few diffs and flipping through a textbook, it would already be annoying. But if each time some IP users pop up out of nowhere to reintroduce the reference, I need a simple protocol. Malparti (talk) 14:39, 13 June 2024 (UTC)

Update: what follows is only my opinion... but this book is worse than I thought. I'm not going to detail, as this would be a waste of time for everyone, but despite the book being called "from theory to implementation", there is not an ounce of theory — most of the basic concepts are not presented. The book is full of approximations, and the way things are written gives the impression that the author does not understand the basics... Not to mention the >100 pages of computer code which I doubt anyone is ever going to read (it is even hard for me to comprehend how Wiley could agree to print something like this in 2017). So my assessment is that the negative comments that I read were fully justified. I am going to remove this book entirely from the article, and replace it with more suitable references. Malparti (talk) 15:21, 13 June 2024 (UTC)

Take it out! MegGutman's other edits seem to 100% consist of adding citations to Gagniuc's papers and book, e.g. special:diff/859029968, special:diff/869317521, special:diff/804290077, special:diff/804294275, etc. At File:The electrical activity map of the skin in normal subjects and diabetic subjects.png they uploaded as their "own work" an image from one of Gagniuc's papers, to be used in special:diff/865158092. If anyone feels motivated, it might be worth running a search across Wikipedia for Gagniuc's work and just remove anything that was added as citations by editors without non-promotional edits. –jacobolus (t) 15:45, 13 June 2024 (UTC)

@Jacobolus I've just had a look at the recent history of the article, and things took a pretty absurd turn pretty quick. And because the user seems to know how to use different IPs, dealing with this is probably going to be a pain. The good thing is, that person is... Not very subtle. So it's pretty easy to see what's going on here; this may not always be the case... Malparti (talk) 19:06, 13 June 2024 (UTC)

I think the page should be semi-protected for a bit. Malparti (talk) 19:08, 13 June 2024 (UTC)

I've submitted a request at WP:RPP. I agree with Jacobolus that killing all the Gagniuc references is a good idea. --JBL (talk) 19:14, 13 June 2024 (UTC)

I was about to file a request at WP:RPP until I saw that you already had; thanks. I also concur that zapping citations to Gagniuc would be a worthwhile cleanup job. It sounds like where they aren't irrelevant (e.g., citing the definition of a Markov chain), they should be replaced with pointers to more dependable references, even apart from WP:COI concerns. XOR'easter (talk) 19:28, 13 June 2024 (UTC)

I have to take a break now; would anyone else like a stab at Stochastic matrix? XOR'easter (talk) 21:56, 13 June 2024 (UTC)

@XOR'easter I am going to take care of this (running a search across Wikipedia for Gagniuc's work) before the end of the week, most likely over the weekend. Thanks again for your help — although I guess I will likely run into more trouble and will writing more here... Malparti (talk) 22:57, 13 June 2024 (UTC)

We're down to one article remaining (Promoter (genetics)) -- the spamming is quite old, it seems: [13]. --JBL (talk) 17:53, 14 June 2024 (UTC)

I've asked for help on that one. (The other additions were made by an account with a Romanian connection.) XOR'easter (talk) 23:15, 14 June 2024 (UTC)

For those following along at home, the page has been protected for one week, and the two most aggressive IP addresses have been blocked for c. one day. (A third IP has not been blocked.) It seems reasonable to expect a resumption of similar behavior on other related articles once the blocks expire; that can be dealt with via a trip to either WP:AIV or WP:3RRN (or just a note to the blocking administrator Daniel Quinlan). --JBL (talk) 23:48, 13 June 2024 (UTC)

As foreseen: They're back... XOR'easter (talk) 20:33, 29 June 2024 (UTC)

I left a message at User talk:86.120.188.100 § June 2024. If they persist in edit warring rather than discussing, Markov chain can be semi-protected for a longer time and the IP can be blocked. –jacobolus (t) 21:01, 29 June 2024 (UTC)

Despite Malparti warning that "it would be a waste of time for everyone" I took a look at the book myself. 60 pages of badly-worded boring worked examples with no theory before we even get to the possibility of having more than two states. As Malparti said, there is no theory, or rather theory is alluded to in vague and inaccurate form without any justification. For instance the steady state (still of a two-state chain) is first mentioned on 46 as "the unique solution" to an equilibrium equation, and is stated to be "eventually achieved", with no discussion of exceptional cases where the solution is not unique or not reached in the limit, and no discussion of the fact that it is never actually achieved, only found in the limit. Do not use for anything. I should have taken the fact that I could not find a review even on MR and zbl as a warning. —David Eppstein (talk) 23:53, 13 June 2024 (UTC)

I didn't have time to read much of it apart from discovering that it actually said nothing about one of the claims it was being used to support. But having had time since to evaluate it more, I have to agree: it's a sloppy book. The writing confuses urn draws with and without replacement, events probably happening versus definitively happening, etc. XOR'easter (talk) 23:26, 14 June 2024 (UTC)

Envelope model

In this deletion discussion, it was just barely decided to delete the article titled Envelope model. The article can be seen here. The originator of envelope models is R. Dennis Cook, noted for Cook's distance and the Cook–Weisberg test for heteroskedasticity. Prof. Cook is now retired.

This seems to have been a deletion without prejeudice to re-creation. About a year after this deletion, Dennis Cook's book An Introduction to Envelopes was published.

Although this topic was primarily the creation of Dennis Cook and some of his Ph.D. advisees, I believe some of his colleagues and students in his graduate courses have also influenced the topic. (In particular, the term "central subspace" was suggested by David Nelson.)

It appears to me that with the publication of the book, the time is ripe to think about re-creating the article, written in a more beginner-friendly way, perhaps under the title Envelope model (statistics) or Envelope (statistics).

The original creator of this article, user:Anthony Appleyard, is reported to have died. Michael Hardy (talk) 21:34, 29 June 2024 (UTC)

: Michael Hardy (talk) 21:34, 29 June 2024 (UTC)

One question. Why is this here in Wikiproject Mathematics? Isn't there a corresponding Wikiproject for Statistics, which would be more appropriate for this topic? PatrickR2 (talk) 05:36, 30 June 2024 (UTC)

It does exist. It appears to be significantly less active than this project. —David Eppstein (talk) 07:56, 30 June 2024 (UTC)

Jul 2024

Proposed move of Trammel of Archimedes to Ellipsograph

In the past couple of days I spent some time researching the name "trammel of Archimedes", sometimes applied to the instrument for the several centuries previously and still often today called an elliptic trammel or elliptic compass (a "trammel" or beam compass is a wooden or metal rod or beam along which slide metal "trammel points", used to draw circles). This is a type of ellipsograph (tool for drawing ellipses). I learned that Archimedes had nothing to do with this tool, which may have been invented in the early 16th century by Leonardo da Vinci, and which operates on the same mathematical principle as a mechanism investigated by Proclus (5th century) based on the one Nicomedes (3rd century BC) used to trisect angles. Circa 1940 the name "trammel of Archimedes" showed up in the work of Robert C. Yates, apparently out of the blue (I speculate this may have been based on some confusion by Yates or whoever he got the name from between Nicomedes and Archimedes). Judging from searches of books/academic papers, the name "trammel of Archimedes" remained quite rare through the 20th century, but there have been a nontrivial number of people calling it that in the past couple of decades, perhaps partly under the influence of webpages like Wikipedia.

Anyway... I think this article would be improved by reorganizing it to discuss the general topic of ellipse drawing, so I proposed at Talk:Trammel of Archimedes § Requested move 1 July 2024 that it should be moved to the title Ellipsograph (which currently redirects there), with "Elliptic trammel" turned into a top-level section. Then we can add other sections about the pins-and-string method for drawing ellipses, as well as various other interesting ellipse drawing tools/methods, and some further discussion about how these tools were used in practice. –jacobolus (t) 05:43, 1 July 2024 (UTC)

Discussion on links in the lead sentence of mathematics

Please take a look at talk:mathematics#Overlink issue in lede. --Trovatore (talk) 22:02, 3 July 2024 (UTC)

Question about a redirect

Is 3^^^^3 a proper way of notating Graham's number? voorts (talk/contributions) 19:12, 4 July 2024 (UTC)

That's an awkward ASCII way of writing $3\uparrow \uparrow \uparrow \uparrow 3$, which is the first term in a sequence whose 64th term is Graham's number. The particular number $3\uparrow \uparrow \uparrow \uparrow 3$ is mentioned in the lead section of the article Graham's number. --JBL (talk) 19:42, 4 July 2024 (UTC)

Thanks. I'll mark the redirect as patrolled. voorts (talk/contributions) 20:05, 4 July 2024 (UTC)

Quasilinearization article may need some input

There is a new article Quasilinearization which was restored from a deleted form and has been moved directly to main. I know that using linear approximations is very common in optimization and similar problems, and it is of course everywhere in science (first order expansions). I don't know if there are other articles on this, hopefully someone in the applied math area has a better feel for what is already on Wikipedia. For certain I think Quasilinearization can do with better and wider context, but perhaps there is more that should be done. Over to others. Ldm1954 (talk) 19:27, 6 July 2024 (UTC)

We do have the article linearization, which is about more general use of linear approximation. The article in question seems to be about a more specific set of techniques (and that set of techniques is known as quasilinearization); see https://encyclopediaofmath.org/wiki/Quasi-linearization for example. —- Taku (talk) 20:04, 6 July 2024 (UTC)

Mixing (mathematics) and Mixing (physics) merge proposal

See Talk:Mixing_(mathematics)#Merge_proposal. Please leave comments on that talk page and not here. Mathwriter2718 (talk) 01:15, 9 July 2024 (UTC)

Cube buildings

I have recently expanded the article Cube, one of them is the Cube#In architecture. However, one source says that Kaaba is a nearly cube building [14], which I have not included in the article. If that's the case, should this be included elsewhere, the Square cuboid, or keep it in the article Cube but quote what is the source saying? I don't want to have a conflict because of my editing. More opinions are extremely needed. Dedhert.Jr (talk) 13:03, 8 July 2024 (UTC)

The Cube is such a ubiquitous shape that making lists of cube shaped things is not really helpful. MrOllie (talk) 13:07, 8 July 2024 (UTC)

@MrOllie I see. Then I guess six-faced dice and Rubik's cube should not included as well in the pre-planned section "In popular culture". I do not get why someone reverted about the architecture one, like, do we actually have a manual of style in Wikipedia about those? Why do articles like Isosceles triangle also mention the architecture, or ubiquitous shape like Mobius strip in popular culture? Dedhert.Jr (talk) 13:09, 8 July 2024 (UTC)

Because there are not many pieces of architecture that incorporate a proper Möbius strip, so when one does it becomes more unusual and interesting than a piece of architecture that incorporates a cube, a cylinder, or a hemisphere. —David Eppstein (talk) 05:44, 9 July 2024 (UTC)

It is possible that there are particular buildings that are notable for being exactly cubical, but one would want to see extremely good sourcing for that to pass WP:DUE. I don't think there's anything wrong in principle with noting, somewhere in Cube, the ubiquity of cubes and including mention of some examples like dice. --JBL (talk) 18:18, 9 July 2024 (UTC)

The ubiquity of cubes would need to referenced just like anything else. Johnjbarton (talk) 18:28, 9 July 2024 (UTC)

The Kaaba (literally "cube") is a pretty notable example of a cubical structure. If someone wants to make a general point about the popularity of cube-shaped buildings with examples, Mukaab and Cube Berlin have wiki pages, and there is surely discussion to be found about other examples in some architecture journal or another. –jacobolus (t) 22:11, 9 July 2024 (UTC)

@Jacobolus Another interesting building. I previously wrote Genzyme building and the interior building of Duchess Anna Amalia Library, and sources were supplied. If these can be written again, buildings from the West and the Arabic may be split in the pre-planned section "In architecture". Do you think this is fine? I also can't put them in popular culture because of my reasoning from the very beginning. Dedhert.Jr (talk) 06:03, 11 July 2024 (UTC)

I don't think an article cube has to have an architecture section, but there's certainly enough that has been written about this topic that it could be supported. I probably wouldn't make it longer than a single unified section. (Does the Borg Cube count as a building? :P ) –jacobolus (t) 06:11, 11 July 2024 (UTC)

@Jacobolus It seems like a "popular culture" to me. Dedhert.Jr (talk) 06:19, 11 July 2024 (UTC)

@MrOllie I agree with this conclusion but not the reasoning. A list of cube shaped things is only notable if references make it so. Specific examples of notable cubes could nevertheless be listed with due discussion. The Kaaba for example was discussed as having a singular appearance, quite the opposite of ubiquity. Johnjbarton (talk) 18:37, 9 July 2024 (UTC)

Template:Unsolved, dark mode, CSS

If you know anything about CSS and templates, there is a request for assistance involving Template:Unsolved that perhaps you could help with. --JBL (talk) 17:55, 11 July 2024 (UTC)

Riemannian manifold

Hi all, I have spent much time over the past week and a half editing the C-class article Riemannian manifold and I think it is ready for a reappraisal. I would also be very happy if others have ideas for how to improve the page or to make it more accessible and readable. I would love to have an image at the top of the page, but I couldn't think of a good one. Mathwriter2718 (talk) 20:37, 4 July 2024 (UTC)

It starts at the deep end. Shouldn't readers learn much earlier that Euclidean spaces and smooth surfaces embedded in them form Riemannian manifolds? —David Eppstein (talk) 22:25, 4 July 2024 (UTC)

Agreed. The content of the article is all important and should be there, but especially the lead could be a bit more general, especially given that a Riemannian manifold is quite an understandable concept (if not the details). For example a better first sentence or two might be something like

"in differential geometry, a Riemannian manifold is a (possibly non-Euclidean) geometric space for which traditional geometric notions of distance, angle, and volume from Euclidean geometry are defined. These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside (and indeed any Riemannian manifold may be viewed this way due to the Nash embedding theorems) but the modern notion of a Riemannian manifold emphasizes the intrinsic point of view first developed by Bernhard Riemann, which makes no reference to an ambient space and instead defines the notions of distance, angle, and volume directly on the manifold, by specifying Euclidean inner products on each tangent space with a structure called a Riemannian metric. The techniques of differential and integral calculus can be used to transform this infinitesimal information into genuine geometric data about the manifold, and for example distance between points on the manifold along a path, the arc length, can be determined by integrating the infinitesimal measure of distance along the path given by the metric."

I also strongly recommend adding a section to the lead about applications, especially of Pseudo-Riemannian geometry to physics, and of the basic ideas of Riemannian geometry in design and engineering. Some of the technical stuff in the lead can be kept, but a good lead should have a little something for everyone. Tazerenix (talk) 01:51, 5 July 2024 (UTC)

This could still be less technical and more concise.

• The first paragraph here needs to link to (and ideally gloss) manifold or possibly differentiable manifold.
• "(possibly non-Euclidean)" is awkward.
• "First developed by Bernhard Riemann" seems oversimplified/imprecise. Maybe just in this very specific way? People were thinking about e.g. the sphere intrinsically many centuries before that (back to Menelaus of Alexandria if not before), and there are surely more general examples from the 18th or early 19th century. Where does Gauss fit in this story?
• "Genuine geometric data" is a confusing phrase.
• I recommend deferring mention of tangent spaces and Nash embedding theorems past the first paragraph, until such a space as they can be unpacked (briefly but) clearly where mentioned.
• I recommend adding "locally", e.g. "... are locally defined", maybe with a wikilink to Local property. Though some more explicit phrase might be better, "in the vicinity of each point" or the like.

It would likely be clearer to keep the first paragraph more to the point, and contrast with an embedded-in-a-flat-ambient-space in a second paragraph.

I'd recommend trying to read some of Needham's Visual Differential Geometry when working to make relevant articles accessible. There are a lot of clear explanations and nice pictures there. –jacobolus (t) 03:46, 5 July 2024 (UTC)

Maybe this is where I admit that differential geometry was my second least favorite undergraduate mathematics class. Too much focus on symbolic formalisms like Christoffel symbols, too little intuition. I like the material now but I didn't get it then. I should take a look at that book, I'd likely still get something out of it. (Least favorite was plug-and-chug differential equations.) —David Eppstein (talk) 07:06, 5 July 2024 (UTC)

While on the topic of symbols vs. explanations, Petersen's book doi:10.1007/978-0-387-29403-2_1 looks like it has a decent amount of prose explanation and historical discussion. (Disclaimer: I only looked at a few pages.) –jacobolus (t) 16:26, 5 July 2024 (UTC)

@Tazerenix @Jacobolus @David Eppstein I definitely agree with adding applications. Physics, design/engineering, machine learning, and cartography all provide examples of applications. I propose the following lead spliced from Tazerenix's paragraph and the current lead and following Jacobolus's suggestions.

In differential geometry, a Riemannian manifold is a curvy space called a smooth manifold endowed with geometric information allowing many geometric notions such as distance, angles, length, volume, and curvature to be defined. These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside. However, the notion of a Riemannian manifold emphasizes the intrinsic point of view as conceptualized by its namesake Bernhard Riemann, which makes no reference to an ambient space and instead defines geometric notions directly on the abstract manifold by specifying inner products on each tangent space. The tangent space at a point is the vector space of all vectors tangent to the manifold at that point, and it can be thought of as the Euclidean space best approximating the manifold at that point. An inner product is a measuring stick that defines Euclidean geometry on a vector space by specifying the length of each vector and the angles between each two vectors.

The choice of an inner product on each tangent space is called a Riemannian metric (or just a metric), and a Riemannian manifold is defined as a smooth manifold with a Riemannian metric. Riemannian geometry is the study of Riemannian manifolds. The techniques of differential and integral calculus are used to pull geometric data out of a Riemannian metric. For example, the length of a curve can be determined by integrating the infinitesimal measure of distance along the path given by the metric.

Formally, if $M$ is a smooth manifold, a Riemannian metric is a smoothly-varying family $g$ of positive-definite inner products $g_{p}$ on the tangent spaces $T_{p}M$ at each point $p$, and the pair $(M,g)$ is a Riemannian manifold. The requirement that $g$ is smoothly-varying is that for any smooth coordinate chart $(U,x)$ on $M$, the component functions of the metric

$g_{ij}=g\left({\frac {\partial }{\partial x^{i}}},{\frac {\partial }{\partial x^{j}}}\right):U\to \mathbb {R}$

are smooth functions, i.e., they are infinitely differentiable.

Applications include ...

We also have an article Riemannian geometry which is essentially a (relatively short) list of theorems from Riemannian geometry. My thought on how to differentiate this from Riemannian manifold is to have Riemannian manifold be less about big results in the field and more about the structure of a Riemannian manifold and what you can do with it. Mathwriter2718 (talk) 13:21, 5 July 2024 (UTC)

@David Eppstein, Jacobolus, Mathwriter2718, and Tazerenix: That is not an improvement over the version from Tazerenix due to several issues:

1. The term curvy is confusing
2. The reference to embedding belongs in a history section; Riemannian manifold is about intrinsic geometry.
3. The lead contains technical details that really should be defer to later in the article.
4. It does not address an issue raised by Jacobolus: I recommend deferring mention of tangent spaces and Nash embedding theorems past the first paragraph, until such a space as they can be unpacked (briefly but) clearly where mentioned.

I would cut it back to

In differential geometry, a Riemannian manifold is a space called a smooth manifold endowed with geometric information allowing many geometric notions such as distance, angles, length, volume, and curvature to be defined. Although Riemannian geometry has an intrinsic perspective, it was historically motivated by the study of surfaces in Euclidean geometry.

with everything else in subsequent sections. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:11, 5 July 2024 (UTC)

@Chatul I strongly disagree with cutting the lead down to those two sentences. Most critically, it makes no attempt to say what a Riemannian manifold is, instead merely saying a few properties it has. I think we ought to discuss the tangent space here. It can be explained in a non-technical way and it's a fundamental part of any description of a Riemannian manifold. I also think that clarifying embedded spaces vs abstract spaces as quickly as possible is a good idea, because omitting this is guaranteed to cause misunderstanding. That distinction should not merely be relegated to history. I also think including a single sentence mentioning applications in the lead is a good idea.

To make it less technical, my first thought is to shorten:

The techniques of differential and integral calculus are used to pull geometric data out of a Riemannian metric. For example, the length of a curve can be determined by integrating the infinitesimal measure of distance along the path given by the metric.

To:

The techniques of differential and integral calculus are used to pull geometric information, such as lengths of curves, distances between points, and volumes of shapes, out of a Riemannian metric.

We could also move the paragraph starting "Formally" out of the lead, or just the description of smoothness, though I think that the audience for this page includes many people for having a formal description in the lead would be very useful. Mathwriter2718 (talk) 14:42, 5 July 2024 (UTC)

This first paragraph is a bit bloated I think. I would just mention "Riemannian metric" in the first paragraph, and defer discussion of tangent spaces etc. to a subsequent paragraph. –jacobolus (t) 17:35, 6 July 2024 (UTC)

Fwiw, I think tazernix lede is good as is. There's no need to complicate matters with endless debate as to the merits of this or that. Tito Omburo (talk) 17:37, 5 July 2024 (UTC)

However my intention was to start a conversation! I'm sure there are ways of improving my attempt as others have commented on. I think the most essential point is to find just the right first sentence. Everything after that is natural. One needs to find the right word to convey to the reader that Riemannian manifolds can be curved, folded, that they are manifolds, but have the same geometric information as rigid figures from Euclidean geometry, which is the main interaction the lay person or those uneducated in geometry understand. We've had "curvy", "non-Euclidean", "smooth manifold", "space" etc. My attempt tried to rely on peoples lay knowledge of "Euclidean" although even that may be a bit esoteric for the first sentence. Happy for people to keep debating it! Tazerenix (talk) 23:55, 5 July 2024 (UTC)

I think some kind of picture(s) would help a lot, even if it's just showing a funky 2-dimensional surface immersed in Euclidean space. –jacobolus (t) 00:10, 6 July 2024 (UTC)

Aren't there some nice pictures available of what hyperbolic 3-manifolds look like "from within"? Seems like this conveys the idea of "intrinsic geomtery" in a fairly striking way. Tito Omburo (talk) 00:19, 6 July 2024 (UTC)

Such a thing is also neat, but I think it might be confusing to start with. –jacobolus (t) 01:18, 6 July 2024 (UTC)

I would suggest two images: a Klein bottle, since this is a surface which can be smoothly immersed in 3-space but which is not an embedded surface (though here the intrinsic uniformizing geometry is flat!), and an image like File:Order 5 dodecahedral honeycomb.png with words to the effect of: "An observer inside hyperbolic 3-space will see polygons in a hyperbolic tessellation up close as almost Euclidean, while polygons further away become distorted because of the non-Euclidean Riemannian metric." Tito Omburo (talk) 10:37, 6 July 2024 (UTC)

@Tazerenix I'm really glad a discussion about this page is happening. Yet another possibility for a first sentence emphasizes that it is a generalization of Euclidean geometry:

In differential geometry, a Riemannian manifold is a vast generalization of Euclidean geometry to arbitrary smooth manifolds.

Mathwriter2718 (talk) 02:08, 6 July 2024 (UTC)

I don't think leading with "generalization of Euclidean geometry" gives the right impression either. I would make a first paragraph more along the lines of:

"A Riemannian manifold is a geometric space which locally, in the vicinity of each of its points, has the same metrical structure as flat Euclidean space – in the same way that spatial relationships in a small portion of a globe's surface can be modeled using a flat map – including concepts of perpendicularity and angle measure, straightness and curvature, and an infinitesimal definition of distance and volume, based on a formal structure called a Riemannian metric. Using the tools of differential and integral calculus, this local structure can be extended to larger portions of the space, yielding a generalization of Euclidean geometry, Riemannian geometry, in which space might be warped or curved and straight lines are replaced by locally straight curves called geodesics. It is named after Bernhard Riemann, who, building on the work of Carl Gauss, proposed a way of defining and studying such spaces in general."

I'm not sure if "infinitesimal" is the best word – it might be confusing or ambiguous – and neither infinitesimal nor differential (mathematics) seems like quite the right Wikilink to employ, and e.g. differential form may be be unhelpfully advanced for less prepared readers. Do we have a clear lay-accessible article about these general kinds of concepts? Anyway, I'd then defer discussion of more precise definitions of Riemannian metric, tangent space, etc. to after the first paragraph. The second or third paragraph can also discuss the difference between extrinsic vs. intrinsic definitions, embedding theorems, and so on. –jacobolus (t) 21:00, 6 July 2024 (UTC)

We can argue about wordsmithing but I like the general focus of this version on local geometry, and I especially like the suggestion of flat maps of the earth early in the lead as an analogy. —David Eppstein (talk) 22:12, 6 July 2024 (UTC)

(Please everyone feel free to wordsmith to your heart's content.) –jacobolus (t) 22:33, 6 July 2024 (UTC)

I can see why this paragraph feels compelling, but I don't endorse this usage of "locally". Specifically, the first sentences are not true: a Riemannian manifold does not have the same local metric space structure or Riemannian metric structure as flat Euclidean space, and indeed it is impossible to have a map of a part of Earth that preserves these structures. The thing that is true is that Riemannian manifolds look "infinitesimally" like flat Euclidean space. But "locally" should mean on a neighborhood. Riemannian manifolds that look locally like flat Euclidean space are called flat. Mathwriter2718 (talk) 14:29, 7 July 2024 (UTC)

Is there an accurate but legible/accessible way to express that they have the same structure in the limit? –jacobolus (t) 17:10, 7 July 2024 (UTC)

How about A Riemannian manifold is a geometric space which locally, in the vicinity of each of its points, has nearly the same metrical structure as flat Euclidean space – in the same way that spatial relationships in a small portion of a globe's surface can be modeled using a flat map – including concepts of perpendicularity and angle measure, straightness and curvature, That should be sufficiently precise for the lead. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:39, 7 July 2024 (UTC)

I'm afraid the phrasing "locally the same metrical structure as flat Euclidean space" is unsalvageable even if qualifiers are added to it, because it's not nearly true, it's very false. The phrasing "infinitesimally the same geometry as flat Euclidean space" would be true. Mathwriter2718 (talk) 20:59, 7 July 2024 (UTC)

Maybe it would be better to say something like it resembles the plane, and has the same structure in the infinitesimal limit. –jacobolus (t) 22:00, 7 July 2024 (UTC)

I agree with Mathwriter2718 that this isn't accurate. The metrical structure of a sphere, on even the finest scale, has notably different metrical structure from flat Euclidean space: for instance the sectional curvature (as a Riemannian-geometric notion) in any small region of the sphere is exactly one, never getting closer to zero (the curvature of Euclidean space).

The basic fact is this: a Riemannian metric gives each tangent space an inner product, and any inner product space is (up to isometry) the same as a Euclidean space. I can see why some might phrase this as "infinitesimally Euclidean geometry" but I think it's a clunky way to view it and could lead to confusion. Taking a somewhat broader view, "infinitesimally Euclidean geometry" could naturally be formalized by saying that every tangent cone of a Riemannian manifold (viewed as a pure metric space) is isometric to a Euclidean space. That's true, but it fails to distinguish Riemannian manifolds. I think it would be better to simply say exactly what a Riemannian metric is: an inner product on each tangent space. Personally, I believe that would be as simply-put as possible. Gumshoe2 (talk) 21:09, 7 July 2024 (UTC)

"I think it's a clunky way to view it" – It's a sort of hand-wavy view, but it's not detailed enough to be clunky. By comparison, the business about tangent spaces is a very "clunky" way of expressing this idea, a formal definition for a new concept duct taped together from other abstractions previously defined and already at hand. It's not a requirement to define it this way, and most students do not have a clear intuition about the concept of the tangent space for a long time after being introduced to it, but it was convenient for the other proofs people wanted to make.

"sectional curvature (as a Riemannian-geometric notion) in any small region of the sphere is exactly one" – this is not so. The way you "zoom in" on a small portion of the sphere is by expanding the sphere until the portion of interest fills your view (or equivalently, imagine yourself and your natural scale of measurement to be shrinking and shrinking). In the limit as the sphere becomes infinitely large or you become infinitely small, you are left looking at a completely flat surface, indistinguishable in any way from part of a plane. [For a physical example, we don't yet know if the large scale structure of spacetime is flat or not, and we could well imagine the universe being "spherical" or "hyperbolic", but if so the curvature is so slight that it appears flat to within our capacity to measure. The curvature of a spherical, flat, or hyperbolic universe would be very very nearly the same, and you'd need a whopping big length scale to say it had sectional curvature of 1.] –jacobolus (t) 21:40, 7 July 2024 (UTC)

Each of the textbooks I have at hand (Petersen, do Carmo, Kobayashi–Nomizu) define a Riemannian metric as a choice of inner product on each tangent space. What alternative do you have in mind?

I didn't realize you had zooming/rescaling in mind, since the proposed opening paragraph above didn't mention it. If that paragraph is to be used, I think that would have to be clarified. Regardless, I think it is a curious notion to put up front, since even in the most basic examples of Riemannian manifold – namely surfaces in 3-space – this idea of rescaling and recovering a Euclidean space in the limit is not of major importance, nor is it terribly immediate from the actual definitions. (And I don't know of any textbooks where it is emphasized.) The notion of tangent space is more immediate, both in the intuitive visual sense and in the formal setup. (Nor, at least in the formal version of saying that every tangent cone is a Euclidean space, does it even characterize the spaces in question. There are geometric spaces which equally have 'infinitesimally Euclidean geometry' which are not Riemannian manifolds.)

In terms of an opening line, I hardly think it's necessary to mention tangent space and inner product, but something along the lines of tazerenix's, something like

Riemannian manifolds are certain geometric spaces in which Euclidean notions of length and angle are generalized.

seems perfectly appropriate (and standard) to me. Gumshoe2 (talk) 23:02, 7 July 2024 (UTC)

Thanks everyone for your interesting comments in this discussion.

1. From my experience, math undergraduates find the tangent space intuitively clear soon after it is introduced.
2. In my opinion, the definition of a Riemannian metric as an inner product on each tangent space is extremely elegant and not clunky.
3. @Jacobolus you suggest that there is an alternative definition of a Riemannian manifold. I have never heard of an alternative definition, so if one exists, I would be extremely interested.
4. If you "take the limit approaching a point" by choosing smaller and smaller coordinate neighborhoods, you will not approach Euclidean space. But if you zoom in and rescale as you do the limiting process, you will approach Euclidean space. If someone just said "take the limit approaching a point", I would expect that they meant the first construction. The second construction is just as valid, but I think it is more unusual in the math world.

Here is yet another ordered set of words for our collective consideration:

In differential geometry, a Riemannian manifold is a geometric space equipped with, at each point, a copy of the Euclidean space most closely approximating it near that point.

I also like the idea of having an opening line that avoids the notion of tangent space or entirely. Here is an appropriate modification of what I said earlier:

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined.

I still think the lead section should give a formal definition. But maybe no one disagrees with this. Mathwriter2718 (talk) 01:32, 8 July 2024 (UTC)

My concerns that the lead

1. Comply with MOS:LEAD
2. Provide definitions that are understandable by the uninitiated
3. Not be wrong, although vagueness is fine

Either your In differential geometry, a Riemannian manifold is a geometric space equipped with, at each point, a copy of the Euclidean space most closely approximating it near that point. or your In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. seem fine.

I don't see the value of formal definitions in the lead, although they are essential in later sections. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:25, 8 July 2024 (UTC)

"a copy of the Euclidean space most closely approximating it near that point" seems confusing (and possibly meaningless) to me, but I think your second version is good. Ideally there would be a more descriptive label than "geometric space" but I'm not sure what it would be.

If it's possible to make the lead section both accurate and generally accessible, I think it's good to skip formal definitions until sections in the body. Gumshoe2 (talk) 17:41, 10 July 2024 (UTC)

"A copy of the Euclidean space most closely approximating it near that point" is my best attempt to describe a Riemannian metric both intuitively and accurately. I really think "Riemannian metric" should be defined in the lead. The page for Euclidean space defines a Euclidean space as a finite-dimensional real inner product space. Indeed, each tangent space of a Riemannian manifold is a finite-dimensional real inner product space. Now it is hopefully clear why I claim that out of all the finite-dimensional real inner product spaces one could associate with a point of a manifold, the tangent space equipped with the metric at that point is the best approximation. Mathwriter2718 (talk) 19:10, 10 July 2024 (UTC)

I haven't thought very deeply about it but there are surely many ways that the class of Riemannian manifolds might be precisely characterized instead of points quadratic forms in a tangent space. For example, as the limit of some discrete triangular-mesh approximations; as points along with some full description of intrinsic n-dimensional curvature at each point; flipping the embedding theorem around, as something isometric to a sub-manifold of Euclidean n-space; ...; anything you might come up with would surely have its own complications as a definition, and might be inconvenient, but the standard definition (for this or any other class of mathematical objects) is an arbitrary cultural choice.

There are two different kinds of questions the start of an article like this could be trying to answer. (1) What sort of a thing is a Riemannian manifold? how is it different from other objects? what are examples? how does it relate to other concepts it is used with? what can be done with one? etc. (2) How do mathematicians formally define Riemannian manifolds? what other abstract concepts is that definition built on? what theorems can we prove about it and specifically how? and so on.

I don't personally see how to make a first paragraph from the perspective of #2 which is both technically precise at all accessible to people who haven't spent many years of diligent effort learning about a large number of prerequisite abstractions amounting to most of an undergraduate pure math degree. However, if we start (just in a first paragraph or two) with something a bit more handwavy and written in plain language, I think we can give some reasonable approximation of an answer to #1 type questions which can be understood by, say, high school students. So I hope we'll keep trying. –jacobolus (t) 02:40, 8 July 2024 (UTC)

I think it would be good to remove the details of proofs. They are pretty irrelevant for the page and the claims seem to have appropriate textbook citations. (I think I'm guilty of adding at least one of the proofs, some time ago!) Gumshoe2 (talk) 21:14, 7 July 2024 (UTC)

This conversation has slowed down, so I am going to propose yet another lead (not just the first paragraph, but the whole section), attempting to compromise between all of the perspectives I have heard. I think it's really good to at define the terms "Riemannian manifold", "Riemannian metric", and "Riemannian geometry" in the lead. I am also throwing in an image from the ongoing discussion at Talk:Riemannian_manifold#A_couple_of_example_pictures,_not_sure_if_useful; please discuss the image there.

The square with sides identified is a Riemannian manifold called a flat torus (left). Attempting to embedded it in Euclidean space (right) bends and stretches the square in a way that changes the geometry. Thus the intrinsic geometry of a flat torus is different from that of an embedded torus.

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside. However, the idea of a Riemannian manifold emphasizes the intrinsic point of view as conceptualized by its namesake Bernhard Riemann, which defines geometric notions directly on the abstract space itself with no reference to an ambient space.

A Riemannian manifold is defined as a smooth manifold equipped with, at each point, a copy of the Euclidean space most closely approximating it near that point. The techniques of differential and integral calculus are used to pull geometric data out of the Euclidean approximations. Formally, if $M$ is a smooth manifold, a Riemannian metric (or just a metric) $g$ is a smoothly-varying family of inner products on the tangent spaces of $M$, and the pair $(M,g)$ is a Riemannian manifold.

Riemannian geometry is the study of Riemannian manifolds. Applications include physics (especially general relativity and Gauge theory), computer graphics, machine learning, and cartography.

Mathwriter2718 (talk) 13:27, 10 July 2024 (UTC)

The sentences in the first paragraph after the first sentence should be deferred. Putting them there puts emphasis in a misleading direction, and is not really the point of the subject. From the second paragraph, I don't think «smooth manifold equipped with a copy of Euclidean space at each point» is a good explanation for non-experts. It's too abstract and confusing, and doesn't really give an idea why you would want to "equip" a space with a bunch of other spaces (the word "equip" in plain English also has a sense of "put provisions in a backpack" or "pick up a sword" or something). –jacobolus (t) 17:42, 10 July 2024 (UTC)

I feel strongly that we should define "Riemannian metric" in the lead. Is there any way that your views would accommodate this? Mathwriter2718 (talk) 19:04, 10 July 2024 (UTC)

I think this is a definite improvement over the current lead, but I agree with jacobulus' comments. But it's not very clear to me what content an ideal opening paragraph would contain.

Also, I would remove "smoothly-varying." Many introductory textbooks do make this part of the definition, but it is not required and many Riemannian manifolds, especially in Riemannian convergence theory, have less regularity. I also wonder if it would be more clear to say that a Riemannian metric is a "choice of inner product for each tangent space" rather than a "family of inner products on the tangent spaces." Gumshoe2 (talk) 17:52, 10 July 2024 (UTC)

Can you provide an example of an introductory textbook that does not mandate smoothness of the metric? Mathwriter2718 (talk) 18:59, 10 July 2024 (UTC)

I would get rid of "smoothly-varying" from any lede written for a general audience, but it's fine as a general assumption throughout the article (and obviously should be stated explicitly in the body). Someone should probably write a section about generalizations like relaxed smoothness (important for geometric analysis, an example that occurs to me is plane wave vacua) or relaxed boundary conditions (e.g., manifold with boundary/singularities). Tito Omburo (talk) 20:42, 10 July 2024 (UTC)

I agree with this Gumshoe2 (talk) 20:47, 10 July 2024 (UTC)

@Tito Omburo @Gumshoe2 @Jacobolus @Chatul Based on your feedback, I have a new lead for your consideration. I tried to reorder things to emphasize @Jacobolus's perspective #1 (see the discussion a bit above). I still strongly feel that this lead cannot be complete without a description of a Riemannian metric. I don't think this has to be a formal definition, but at this time I think it's the best option. I won't repeat the lead's image to save space.

In differential geometry, a Riemannian manifold, named after German mathematician Bernhard Riemann, is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the sphere, hyperbolic space, ellipsoids, and the flat torus are all examples of Riemannian manifolds.

Riemannian geometry is the study of Riemannian manifolds. Applications include physics (especially general relativity and Gauge theory), computer graphics, machine learning, and cartography.

Formally, if $M$ is a smooth manifold, a Riemannian metric (or just a metric) $g$ is a choice of inner product for each tangent space of $M$. The pair $(M,g)$ is a Riemannian manifold. The techniques of differential and integral calculus are then used to pull geometric data out of the Riemannian metric.

The geometric notions that a Riemannian manifold has could be defined through reference to an ambient Euclidean space which the manifold sits inside. However, the idea of a Riemannian manifold emphasizes the intrinsic point of view, which defines geometric notions directly on the abstract space itself without referencing an ambient space.

Mathwriter2718 (talk) 22:29, 10 July 2024 (UTC)

A couple of tweaks: smooth manifold should be linked, and I would pull the parenthetical remark about whom it is named after (as it distracts from the main point and breaks up the flow of the sentence) to the end of the paragraph rather than placing it first. —David Eppstein (talk) 22:35, 10 July 2024 (UTC)

I think this is pretty good, enough so that I think it would be worth making the edit. My only major comment is that in the second paragraph I think it would be worth noting that Riemannian geometry is also of purely mathematical interest, having applications in other mathematical fields such as geometric topology, algebraic geometry, and statistics, and it has inspired modern developments in group theory and graph theory. (My goal being to avoid the impression that Riemannian manifolds are more of applied than pure interest.) Gumshoe2 (talk) 22:44, 10 July 2024 (UTC)

Non-math major here. I thought both of these versions were good. The only place I held up and wondered was the list of examples. When I read sphere and ellipsoid I see their 3D representation, but I believe the manifold refers to the surface only? Would it be correct to segment the example list into 2D and 3D manifolds? Johnjbarton (talk) 01:04, 11 July 2024 (UTC)

@Johnjbarton what I intended was this:

• for any number n, the n-dimensional Euclidean space,
• for any number n, the n-dimensional sphere, which is, shall we say, the surface of an n 1 dimensional Earth,
• for any number n, the n-dimensional hyperbolic space,
• the 2-dimensional ellipsoid, which can be thought of as a surface in 3-dimensional space,
• the 2-dimensional flat torus.

If what I wrote signals a different image in readers' heads, the text can be modified accordingly. Mathwriter2718 (talk) 01:24, 11 July 2024 (UTC)

Then my suggestion is to give the simple examples and mention in a trailing phrase the general case. eg.

• Examples of Reimannian manifolds include the 2D ellipsoid or sphere, which can be thought as surfaces in 3D space, as well as higher dimensional manifolds such as n-dimensional Euclidean or hyperbolic spaces.

Johnjbarton (talk) 01:45, 11 July 2024 (UTC)

Perhaps include

• for any number n, the n-dimensional hyperellipsoid
• for any number n, the n-dimensional flat torus

Are there any non-orientable Riemann manifolds of interest in Mathematics or Physics? Perhaps Alice universes? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 08:33, 11 July 2024 (UTC)

I believe that the second sentence, These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside., is inappropriate. Manifolds are intrinsic and not dependent on any particular embedding. For most applications there is no natural embedding. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:57, 10 July 2024 (UTC)

The next sentence explicitly states that Riemannian manifolds are intrinsic and not dependent on a particular embedding. The point of these sentences is actually to clear up the misconception that geometric spaces should be thought of as embedded, which many readers will have by default. Mathwriter2718 (talk) 19:01, 10 July 2024 (UTC)

I believe "can be defined through reference..." is accurate, because of the Nash embedding theorem. There may be no canonical embedding but one can still define a Riemannian manifold to be a manifold equipped with a distance and smoothly embedded in some Euclidean space with distance equal to the geodesic distance in that space. It would not be as good a definition as the intrinsic one and it does not match most of the literature but it would still define the same class of objects. The lack of a canonical choice of embedding is not really a problem. All that said we should emphasize the intrinsic approach here both because that's the way our sources treat it and because it's better. —David Eppstein (talk) 02:03, 11 July 2024 (UTC)

Just a thought. It might be natural to change that paragraph to say something in the spirit of:

Any surface in three-dimensional Euclidean space has an automatically induced Riemannian structure. Although Nash proved that every Riemannian manifold arises as a submanifold of some (higher-dimensional) Euclidean space and although some Riemannian manifolds are naturally exhibited or defined as such submanifolds, in many contexts Riemannian metrics are more naturally defined or constructed directly, without reference to any Euclidean structure. For example, natural metrics on Lie groups can be defined by using group theory to transport an inner product on a single tangent space to the entire manifold; many metrics with special curvature properties such as constant scalar curvature metrics or Kähler–Einstein metrics are constructed as direct modifications of more generic metrics using tools from partial differential equations.

It could also be valuable to mention that even as fundamental a Riemannian manifold as hyperbolic space has no known natural isometric embedding into Euclidean space. (Natural meaning that internal metric symmetries are represented by symmetries of the ambient space, as for the sphere.) Gumshoe2 (talk) 03:39, 11 July 2024 (UTC)

How about Any regular surface in three-dimensional Euclidean space has an automatically induced Riemannian structure. Although Nash proved that every Riemannian manifold arises as a submanifold of some (higher-dimensional) Euclidean space and although some Riemannian manifolds are naturally exhibited or defined as such submanifolds, in many contexts Riemannian metrics are more naturally defined or constructed directly, without reference to any Euclidean structure. For example, natural metrics on Lie groups can be defined by using group theory to transport an inner product on a single tangent space to the entire manifold; many metrics with special curvature properties such as constant scalar curvature metrics or Kähler–Einstein metrics are constructed as direct modifications of more generic metrics using tools from partial differential equations.? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 08:33, 11 July 2024 (UTC)

As far as I am aware, "regular surface" and "smooth surface" are synonyms. It's a shame that right now smooth surface redirects to the top of Differential geometry of surfaces and regular surface redirects to the subsection Differential geometry of surfaces#Regular surfaces in Euclidean space, which claims that a regular surface is a "formalization of the notion of a smooth surface", as if smooth surfaces aren't a formally-defined concept.

Anyway, I would not endorse putting that last sentence in the lead, I think it is too vague and too far afield and belongs later in the article body where it could be explained in more detail. But I do like the other parts of it. I suggest this:

Any smooth surface in three-dimensional Euclidean space, such as an ellipsoid or a paraboloid, has an automatically induced Riemannian structure. The same is true for any submanifold of Euclidean space of any dimension. Although Nash proved that every Riemannian manifold arises as a submanifold of Euclidean space, and although some Riemannian manifolds are naturally exhibited or defined in that way, the idea of a Riemannian manifold emphasizes the intrinsic point of view, which defines geometric notions directly on the abstract space itself without referencing an ambient space. In many contexts, Riemannian metrics are more naturally defined or constructed using the intrinsic point of view. For example, there is no known way to place the hyperbolic plane into Euclidean space that perseveres its internal symmetries.

It worries me slightly that we are using the word "submanifold" here to mean variously "submanifold" and "Riemannian submanifold", but I'm not qualified to declare if this is actually confusing or not. If it is, try this:

Any smooth surface in three-dimensional Euclidean space, such as an ellipsoid or a paraboloid, has an automatically induced Riemannian structure. The same is true for any submanifold of Euclidean space of any dimension. Such a submanifold is called a Riemannian submanifold of Euclidean space. Although Nash proved that every Riemannian manifold arises as a Riemannian submanifold of Euclidean space, and although some Riemannian manifolds are naturally exhibited or defined as one, the idea of a Riemannian manifold emphasizes the intrinsic point of view, which defines geometric notions directly on the abstract space itself without referencing an ambient space. In many contexts, Riemannian metrics are more naturally defined or constructed using the intrinsic point of view. For example, there is no known way to realize the hyperbolic plane as a Riemannian submanifold of Euclidean space that perseveres its internal symmetries.

@Gumshoe2 can you provide a citation of the fact that there is no known symmetry-preserving isometric embedding of the hyperbolic plane into Euclidean space? Mathwriter2718 (talk) 17:40, 11 July 2024 (UTC)

The phrase "automatically induced structure" is needlessly confusing for non-experts. It would be better to say something more like, "Any smooth surface in three-dimensional Euclidean space, such as an ellipsoid or a cone, is a Riemannian manifold, inheriting its infinitesimal [?] definition of distance from the ambient space." –jacobolus (t) 18:19, 11 July 2024 (UTC)

I agree that the phrase "automatically induced structure" is confusing for non-experts. Cones in the sense of the page you linked are not smooth manifolds, so I won't replace paraboloid with them. How about this?

Any smooth surface in three-dimensional Euclidean space, such as an ellipsoid or a paraboloid, is a Riemannian manifold with its Riemannian metric coming from the way it sits inside the ambient space.

Mathwriter2718 (talk) 18:59, 11 July 2024 (UTC)

We need to distinguish the intrinsic metric from the Euclidean metric, but I would prefer to talk about geodesic distance than infinitesimal distance. —David Eppstein (talk) 19:00, 11 July 2024 (UTC)

This is only something to distinguish if you're talking about metrics as in metric spaces – there are two natural metric space structures on a surface in R³, one intrinsic and one Euclidean. But metric spaces are currently not mentioned at all in these proposals for the lead, except indirectly in the one mention of "distance." And for metric instead as shorthand for Riemannian metric, there's no ambiguity (there is only one natural Riemannian metric on the surface).

Possibly it could be worth adding a line or two to the lead explicitly about the metric space structure induced by a Riemannian metric, along with a warning about the resulting double/inconsistent meaning of "metric." Gumshoe2 (talk) 19:23, 11 July 2024 (UTC)

The current lead (a big improvement) says:

• A Riemannian metric is not to be confused with the distance function of a metric space, which is also called a metric.

This is not helpful. If you don't know the topic, you will be confused. This sentence also does not summarize the article. The closest thing I could find was:

• The distance function ... called the geodesic distance, is always a pseudometric (a metric that does not separate points), but it may not be a metric.

which is a clear as mud.

IMO the article should have a paragraph explaining the difference and the sentence should summarize the paragraph, not tell us we are confused. Johnjbarton (talk) 03:12, 13 July 2024 (UTC)

I agree that this sentence should be removed from the lead and instead something about it should go in the article body. Mathwriter2718 (talk) 03:29, 13 July 2024 (UTC)

For the purposes of the lead, personally I see no issue with just saying that a surface automatically inherits a Riemannian metric (though I am not attached to "automatically induced structure" in particular) since there are details further down the page. But it is also pretty elementary to just say how it works: the inner products defining the induced Riemannian metric are just given by restricting the inputs of the usual dot product to vectors tangent to the surface. Gumshoe2 (talk) 19:17, 11 July 2024 (UTC)

The best reference I have is (see pages 2-3 in linked pdf):

• Gromov, Misha (2000). "Spaces and questions" (PDF). In Alon, N.; Bourgain, J.; Connes, A.; Gromov, M.; Milman, V. (eds.). Visions in mathematics: GAFA 2000 Special Volume, Part I. Proceedings of the meeting held at Tel Aviv University, Tel Aviv, 25 August – 3 September 1999. Geometric and Functional Analysis. Basel: Birkhäuser. pp. 118–161. doi:10.1007/978-3-0346-0422-2_5. ISBN 978-3-0346-0421-5. MR 1826251. Zbl 1006.53035.

which is less explicit than ideal. Gumshoe2 (talk) 19:36, 11 July 2024 (UTC)

The July 12th lead:

The square with sides identified is a Riemannian manifold called a flat torus (left). Attempting to embedded it in Euclidean space (right) bends and stretches the square in a way that changes the geometry. Thus the intrinsic geometry of a flat torus is different from that of an embedded torus.

In differential geometry, a Riemannian manifold, is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the $n$-sphere, hyperbolic space, and smooth surfaces in three-dimensional space, such as ellipsoids and paraboloids, are all Riemannian manifolds. Riemannian manifolds are named after German mathematician Bernhard Riemann, who first conceptualized them.

Riemannian geometry, the study of Riemannian manifolds, has deep connections to other areas of math, including geometric topology, complex geometry, and algebraic geometry. Applications include physics (especially general relativity and Gauge theory), computer graphics, machine learning, and cartography.

Formally, if $M$ is a smooth manifold, a Riemannian metric (or just a metric) $g$ is a choice of inner product for each tangent space of $M$. The pair $(M,g)$ is a Riemannian manifold. The techniques of differential and integral calculus are then used to pull geometric data out of the Riemannian metric. A Riemannian metric is not to be confused with the distance function of a metric space, which is also called a metric.

Any smooth surface in three-dimensional Euclidean space is a Riemannian manifold with a Riemannian metric coming from the way it sits inside the ambient space. The same is true for any submanifold of Euclidean space of any dimension. Although Nash proved that every Riemannian manifold arises as a submanifold of Euclidean space, and although some Riemannian manifolds are naturally exhibited or defined in that way, the idea of a Riemannian manifold emphasizes the intrinsic point of view, which defines geometric notions directly on the abstract space itself without referencing an ambient space. In many instances, such as for hyperbolic space and projective space, Riemannian metrics are more naturally defined or constructed using the intrinsic point of view. Additionally, many metrics on Lie groups are defined intrinsically by using group actions to transport an inner product on a single tangent space to the entire manifold, and many special metrics such as constant scalar curvature metrics and Kähler–Einstein metrics are constructed intrinsically using tools from partial differential equations.

I personally am quite happy with this. I previously opposed adding the last sentence (suggested by Chatul) because I thought it was too technical, but now I think it's a good example. I did remove a few words adding detail though.

Mathwriter2718 (talk) 14:36, 12 July 2024 (UTC)

I think this introduction is still simultaneously too technical and too vague.

There are many objects which are "geometric space[s] on which many geometric notions such as distance, angles, length, volume, and curvature are defined" but which are not Riemannian manifolds. The examples are helpful, but I think we should also try to make the first paragraph give a bit clearer plain-language impression of what the word means. The later description "choice of inner product for each tangent space of M" doesn't cut it, as many potential readers may not know the meaning of "inner product" or "tangent space".

We should be saying more clearly that the Riemannian metric is an instantaneous/infinitesimal/local/whatever definition of distance and angle, and that by integrating, we can also see larger-scale behavior, with concepts like geodesics along which we measure length, area/volume of shapes, geodesic circles, geodesic polygons, parallel curves/surfaces, ... The phrase "pull geometric data out" is too vague.

The paragraph "Riemannian geometry, the study of Riemannian manifolds, ..." should be moved to the bottom of the lead section.

I'd drop the disclaimer about metric spaces. A Riemannian manifold is a type of metric space, and this is distracting and seems unnecessary here.

The paragraph about embeddings seems too into the weeds and sort of disjointed. Some of this should be saved for the article body. –jacobolus (t) 15:22, 12 July 2024 (UTC)

I don't think that replacing the current definition to say that a Riemannian metric defines "infinitesimal distances" would achieve your goal of making this less technical and less vague. Mathwriter2718 (talk) 15:38, 12 July 2024 (UTC)

My concrete proposal was above, "A Riemannian manifold is a geometric space which locally, in the vicinity of each of its points, has the same metrical structure as flat Euclidean space – in the same way that spatial relationships in a small portion of a globe's surface can be modeled using a flat map – ..." –jacobolus (t) 15:59, 12 July 2024 (UTC)

I still find that proposal highly misleading, and incorrect when taken literally. I don't think it can be used. Gumshoe2 (talk) 16:12, 12 July 2024 (UTC)

"There are many objects which are "geometric space[s] on which many geometric notions such as distance, angles, length, volume, and curvature are defined" but which are not Riemannian manifolds."

What other such objects do you have in mind? But I do agree that it would be ideal to have a more direct way of saying what a Riemannian metric is and not just what it defines. I don't have a non-clunky way to say it at the moment, but I think it would be nearly precise to say that on a smooth manifold you can look at all the possible (smooth) curves, and a Riemannian metric is an internally consistent way of assigning them lengths, along with angles between them when two of them intersect. (The other notions of distance, volume, and curvature are of course secondary.) It could be said that this assignment is based on infinitesimal information, with lengths defined by integration in the same way arclength is computed in standard calculus.

In the end, I think it is impossible to fully meet the combined requirements of: (1) using plain language (no inner product, no tangent space), (2) having a description which uniquely distinguishes the class of Riemannian manifolds, (3) being correct. But I think each one is good to aspire to. Gumshoe2 (talk) 16:29, 12 July 2024 (UTC)

For one thing, there are pseudo-Riemannian manifolds. But also plenty of other more exotic metric spaces can have "many geometric notions ..." defined, including the listed ones.

The essence of a Riemannian manifold is not only that these notions can be defined, but that they are locally the same as Euclidean space. –jacobolus (t) 17:38, 12 July 2024 (UTC)

Pseudo-Riemannian manifolds don't have a distance function; for them, distance is only defined for certain pairs of points. Perhaps there are other kinds of spaces out there which have all of these objects, but I think pretty much any mathematician would see 'geometric space on which distance, angles, length, volume, and curvature are defined' and immediately think 'Riemannian manifold.' Which is why I think it is ok here, if not ideal.

Taken at face value, your description of Riemannian manifolds is not accurate, it only applies to flat Riemannian manifolds. The 'zooming' procedure you described before as what you have in mind also does not pick out Riemannian manifolds in particular, so I don't see any reason to prefer it to the present suggestions. (And I see a good reason to not prefer it, which is that it's nonstandard.) Gumshoe2 (talk) 19:05, 12 July 2024 (UTC)

Pseudo-Riemannian manifolds have a notion of "distance" in the same physical sense that spacetime does, which is frankly the most important and real sense. Distances have to be broken into "timelike" vs. "spacelike" or similar, but that's not really a problem. The most unambiguous formalized concept, of "squared distance", is in fact a much more natural and better one to use than its square root, and is treated as secondary because of historical inertia. Features of Lorentzian geometry and the hyperbolic number system are precisely analogous to those of Euclidean geometry and the "circular" complex number system, and we can certainly talk about angle measure, (timelike or spacelike) distance, "circles", curvature, and so on.

[It's quite a tangent here, but not teaching students about the Lorentzian plane, hyperbolic numbers, etc. starting in high school or early in undergraduate school blinkers them and significantly limits their understanding not only of such spaces but also of the geometry in Euclidean space (etc.) which are intimately intertwined with pseudo-Euclidean concepts and models. Focusing on Riemannian manifolds and Euclidean tangent spaces to the exclusion of pseudo-Riemannian manifolds and pseudo-Euclidean tangent spaces is a serious pedagogical blunder.]

"Taken at face value ... only applies to flat Riemannian manifolds." – My explicit example is of a globe, so your characterization clearly can't be right, but I clearly am expressing the idea in a way which is unclear or confusing to you personally, so we can probably do better. I expect there's enough brainpower in this discussion that we can collectively come up with some description which is accurate enough for your taste while still being clear and accessible. Does anyone have ideas? –jacobolus (t) 19:36, 12 July 2024 (UTC)

Sorry if the above sounds combative/defensive. I just want to make sure we give readers a reasonably clear idea of the purpose and nature of the subject. For example, "tangent space" more or less means "space of infinitesimal motions at a point", and "inner product space" (i.e. finite-dimensional vector space with a positive definite quadratic form) is jargon for "has the same geometry as the space of Euclidean translations". But to a reader who doesn't already know that, those jargon words are not meaningful. –jacobolus (t) 20:00, 12 July 2024 (UTC)

No problem, as long as my own posts here are understood in the same spirit ;)

Within the context of Riemannian manifolds, "locally the same as Euclidean space" is pretty much a meaningful and precise definition of the flat ones. The problem with your description is that it doesn't say anything about the 'zooming in' procedure that you explained earlier as what you have in mind.

But even the 'zooming in' procedure does not characterize Riemannian manifolds, see e.g. either Reifenberg subsets of Euclidean space or certain metric spaces. It is very possible that in some contexts some form of 'approximately Euclidean on zoomed-in scales' does actually characterize Riemannian manifolds (I would find it very interesting if so) but it would be nonstandard and would likely count as original research by wiki standards. (Possibly also by any standards.)

I don't see any way to avoid the actual fact of the matter, which is (in seemingly every standard account) inner products on tangent spaces. It would be great to have a way to say it without jargon, but I think it would be a big mistake to try to do so by reformulating it in some nonstandard/conjectural way. Gumshoe2 (talk) 20:42, 12 July 2024 (UTC)

I've read all of the comments in this thread. You both have some very interesting points, but in the end, I cannot sign off on a version of "locally the same as Euclidean space" because many or most reasonable readers will not understand "locally" to mean with zooming. I think there is a glimmer of hope for this strategy, perhaps one can think of a Riemannian manifold as locally looking like a Euclidean space up to the first order, with the second order giving curvature?

I think such a strategy has a long road to being written up, validated as correct, being more transparent than the current lead, achieving consensus over it, and steering clear of original research. I encourage those who are interested to keep working on it. But right now it seems like there is a consensus among the editors besides @Jacobolus around a lead that is a small perturbation of the current one, and I would really like to make a "version 1" edit of the lead to the live page soon. Mathwriter2718 (talk) 21:13, 12 July 2024 (UTC)

I'd encourage you to make the edit whenever you feel like it. I think we all agree that it's an improvement over the current lead, and we can keep discussing even after an edit.

Just two small things: constant scal metrics should link to Yamabe problem, and it may be good to throw in a mention somewhere that Riemannian manifolds are a special case of both pseudo-Riemannian manifolds and Finsler manifolds. Gumshoe2 (talk) 21:21, 12 July 2024 (UTC)

I think constant scalar curvature metrics deserves its own page. I can get around to writing it eventually. Mathwriter2718 (talk) 01:56, 13 July 2024 (UTC)

I went ahead and made the edit. Mathwriter2718 (talk) 02:33, 13 July 2024 (UTC)

The reason I think explicitly (briefly) mentioning cartography is helpful is that (a) it's a subject much more familiar to a wide range of readers than inner products or tangent spaces, and (b) these concepts and problems concretely arose because Euler, Lagrange, Lambert, Chebyshev, Jacobi, Gauss, etc. were directly working in cartography/geodesy. Map projections were quite directly in mind (not sure about Riemann per se), which is why we ended up with names like "chart", "atlas", and "geodesic".

The point here being that if we "map" a small part of a Riemannian manifold, the flat map is very nearly accurate, and gets more and more accurate as we shrink the area being mapped. So that e.g. a geodesic looks locally like a straight line, a tiny enough circle has π as its ratio of circumference to diameter, a tiny enough geodesic triangle has interior angles almost exactly summing to π/2, and so on. We get closer and closer to Euclidean geometry. The Riemannian metric is a way of formalizing this idea, using the name "tangent space" for the space of infinitesimal motions (or if you prefer, the space of velocities).

While "up to the first order" is more or less synonymous with the formal definition, I don't think it's really that much more accessible. –jacobolus (t) 21:43, 12 July 2024 (UTC)

One way to adjust the sentence might be to say

"In differential geometry, a Riemannian manifold, is a geometric space on which the geometric notions of length and angle, and subsequently distance, volume, and curvature are defined. These notions of distance and angle are specified infinitesimally in the form of a Riemannian metric, and the techniques of differential and integral calculus are used to link this infinitesimal data with notion of lengths, volumes, and curvature as they are commonly understood."

It specifies what a Riemannian manifold is a bit more uniquely, whilst still emphasizing the most important geometric concepts defined on them. Tazerenix (talk) 13:22, 13 July 2024 (UTC)

I like something like that - although in the second sentence I think you mean to switch "length" and "distance". Putting this in terms of the present second paragraph on the page:

Formally, a Riemannian metric (or just a metric) on a smooth manifold is a choice of inner product for each tangent space of the manifold. A Riemannian manifold is a smooth manifold together with a Riemannian metric. The techniques of differential and integral calculus are used to pull geometric data out of the Riemannian metric. For example, integration leads to the Riemannian distance function, whereas differentiation is used to define curvature and parallel transport.

I think it would make sense to edit to:

Formally, a Riemannian metric (or just a metric) on a smooth manifold is a choice of inner product for each tangent space of the manifold. A Riemannian manifold is a smooth manifold together with a Riemannian metric. These inner products represent infinitesimal measures of length and angle. By integration, these infinitesimal measures define measures of surface area and volume, including (non-infinitesimal) lengths of curves. A distance function, giving the structure of a metric space, is constructed from curve lengths using the calculus of variations. By contrast, differential calculus is employed to use the inner products to define curvature and parallel transport. Special curves known as geodesics can be constructed by the calculus of variations used to define the distance function, or as solutions of certain ordinary differential equations constructed from the metric using differential calculus.

I think that with the new reference to surface area and geodesics, this covers all of the major bases in terms of key objects. (Most notably, minimal surfaces are missing, but presently they are not at all present on the page itself.) Happy to take alternative suggestions or further edits. Gumshoe2 (talk) 17:36, 13 July 2024 (UTC)

There are a lot of flabby and unnecessary linking words in there. "By contrast is employed to use to define", for instance. —David Eppstein (talk) 17:53, 13 July 2024 (UTC)

Agreed, maybe "Curvature and parallel transport are constructed by differential calculus from the inner products" is an improvement. I am also not satisfied with the awkwardness of "can be constructed by the calculus of variations used to define the distance function"; my intention was to make clear that it comes from the same calculus of variations problem that defines the distance function, the distance function being the minimal values in the optimization and the geodesics being (locally) the minimizers. Gumshoe2 (talk) 18:07, 13 July 2024 (UTC)

I'm not convinced that calculus of variations is used to define the distance function, though I see where you are coming from. The distance is defined as the infimum of a functional. The calculus of variations is about actually proving that a given function is a local minimum, no? So the calculus of variations would not come up in the definition of distance, but it would come up in a discussion of geodesics.

If you mention geodesics, you might consider briefly explaining that they are "curves of zero intrinsic acceleration" or "the generalization of straight lines from Euclidean geometry" or "the path someone living in the manifold would trace out if they walked directly forward without turning" or something. Mathwriter2718 (talk) 13:48, 14 July 2024 (UTC)

The language "Special curves known as geodesics can be constructed by the calculus of variations used to define the distance function, or as solutions of certain ordinary differential equations constructed from the metric using differential calculus." is way too wordy, confusing, and technical for the lead section. Instead it should say something along the lines of "The analog of a straight line, called a geodesic, locally has no curvature relative to the manifold". A precise description of how to construct geodesics can be deferred to the article body. –jacobolus (t) 15:17, 14 July 2024 (UTC)

@Mathwriter2718:, that's a good point. Maybe calculus of variations does not need to be mentioned in the lead at all. @Jacobolus:, I agree that the language ends up being a bit much. My intention was to match the style of the previous sentences – and in that context I think your version is too little.

In all I would like to be able to concisely communicate that the geodesic condition can be formulated directly in terms of the distance function but also as the solution of a ODE whose coefficients come from the Riemannian metric. The former corresponds directly to "shortest-length path between points" and the latter to "curve of zero acceleration/curvature." Gumshoe2 (talk) 19:07, 14 July 2024 (UTC)

That's a great topic to discuss in the article, but way too down in the weeds for the lead section. –jacobolus (t) 20:06, 14 July 2024 (UTC)

I agree with you that for the lead, it's best to just say geodesics are one of:

- locally distance minimizing curves

- curves with no intrinsic acceleration

without going any further into the weeds. Mathwriter2718 (talk) 23:25, 14 July 2024 (UTC)

@Gumshoe2 you should try showing first the 1st paragraph, then 2 paragraphs, then your whole intended lead section to a non-expert, for example an undergraduate student taking a second-semester calculus or introductory linear algebra class, or an adult friend who is a computer programmer or mechanical engineer. Ideally they should be able to understand the majority of it without needing to do a ton of extra background reading. If they can't clearly make sense of it, then the lead section is too technical and has failed at one of its essential purposes. –jacobolus (t) 20:13, 14 July 2024 (UTC)

I think this lede is really good. Since most contention seems to focus on the third paragraph, how about something like this

A Riemannian metric on a smooth manifold gives a local way (in each tangent space) of measuring lengths. Formally, a Riemannian metric $g$ is a choice of inner product for each tangent space of $M$ (usually assumed to be smooth as well). The pair $(M,g)$ is a Riemannian manifold. Integration of the metric leads to a distance function (in the sense of metric spaces), whereas differentiation of the metric leads to notions of curvature and parallel transport.

--Tito Omburo (talk) 16:22, 12 July 2024 (UTC)

I also like it, along with your edit. But I think it is not even necessary to use any symbols, which I think is preferable when possible. (Formally, a Riemannian metric is a choice of inner product for each tangent space (usually assumed to be smooth as well). The pair of manifold with metric is a Riemannian manifold.) It would also be more accurate to replace "local" in the first sentence with "infinitesimal." Gumshoe2 (talk) 16:34, 12 July 2024 (UTC)

I agree that this lead can easily be phrased to not use any symbols and that that is preferable. Mathwriter2718 (talk) 02:32, 13 July 2024 (UTC)

List of Johnson solids list-article in WP:FL

I invite any member of this WikiProject to review the potential featured list about the article List of Johnson solids in this nomination. This will be the next featured list in WikiProject Mathematics, as well as the first featured list in WikiProject Polyhedra, which may featured in the main Wikipedia someday. Reviewing such as spot-checking the references and additional comments is welcome. Many thanks. Dedhert.Jr (talk) 14:52, 17 July 2024 (UTC)

Problems with Musical isomorphism

In 2021, a talk page user pointed out that the definition of the musical isomorphisms on the page musical isomorphism is needlessly complicated. Indeed, since at least 2020, the text itself begrudgingly admits that the second description it gives is "somewhat more transparent" than the first one it gives:

Let (M, g) be a pseudo-Riemannian manifold. Suppose {e_i} is a moving tangent frame (see also smooth frame) for the tangent bundle TM with, as dual frame (see also dual basis), the moving coframe (a moving tangent frame for the cotangent bundle $\mathrm {T} ^{*}M$; see also coframe) {eⁱ}. Then, locally, we may express the pseudo-Riemannian metric (which is a 2-covariant tensor field that is symmetric and nondegenerate) as g = g_ij eⁱ ⊗ e^j (where we employ the Einstein summation convention).

Given a vector field X = Xⁱ e_i and denoting g_ij Xⁱ = X_j, we define its flat by:

${\begin{aligned}\flat :\mathrm {T} M&\longrightarrow \mathrm {T} ^{*}M\\X&\longmapsto g_{ij}X^{i}\mathbf {e} ^{j}\\&\longmapsto X_{j}\mathbf {e} ^{j}\end{aligned}}$

This is referred to as lowering an index. Using angle bracket notation for the bilinear form defined by g, we obtain the somewhat more transparent relation

$$X^{\flat }(Y)=\langle X,Y\rangle$$

for any vector fields X and Y.

But the problem is actually much more significant than this. Indeed, the definitions as stated are mathematically invalid, as the vector field $X$ is not an element of the tangent bundle $TM$, which consists of individual vectors. Immediately after this is a parallel discussion on the sharp isomorphism, which suffers from exactly the same defects. Mathwriter2718 (talk) 02:59, 11 July 2024 (UTC)

I don't see a major issue, just change "vector field" to "vector" and "covector field" to "covector."

Actually, the whole article is really just about linear algebra in a single vector space with inner product – setting the context as Riemannian metrics and bundles is completely unnecessary. It's kind of a fake generality since the musical isomorphisms on a Riemannian manifold are just defined point by point, and for each point you have a single vector space with inner product in question. It would be just like defining the determinant as taking a map $\Omega \to \mathbb {R} ^{n\times n}$ and returning a map $\Omega \to \mathbb {R}$; it's technically more general than the determinant as a map $\mathbb {R} ^{n\times n}\to \mathbb {R}$ but not in any important way. Gumshoe2 (talk) 03:54, 11 July 2024 (UTC)

I absolutely see where you're coming from, but the phrase "musical isomorphism" really means in the setting of Riemannian metrics and bundles. I'll try today to make the discussion be more clearly the generalization of the linear algebra isomorphism though. Mathwriter2718 (talk) 11:28, 11 July 2024 (UTC)

Related, I would suggest that Flat map and sharp map be deleted or redirected to musical isomorphism. Gumshoe2 (talk) 04:33, 11 July 2024 (UTC)

I definitely support this. Mathwriter2718 (talk) 11:03, 11 July 2024 (UTC)

I have opened a merge proposal at Talk:Musical_isomorphism#Merge_proposal to merge Musical_isomorphism and Raising and lowering indices. Mathwriter2718 (talk) 20:48, 17 July 2024 (UTC)

Number pages

Should pages in the scope of Wikipedia:WikiProject_Numbers be added to this WikiProject? I've seen some apparent inconsistencies. For example, 12 (number) and 13 (number) are not in the Project but 11 (number) and 14 (number) are. Mathwriter2718 (talk) 22:13, 17 July 2024 (UTC)

@Mathwriter2718 I'm not sure whether it is important to include them in WP:WPM, but we do have articles about number theory other than those enumerated numbers. To put it in a plain, if you want to include them, then so be it. Conversely, why can't just include articles such as Prime number, Regular number, 69 (number), Number theory, or any articles that involves number theory in WP:NUMBERS? Dedhert.Jr (talk) 02:59, 18 July 2024 (UTC)

You can add them to WPM if you want. I would generally recommend assigning them "mid" priority. –jacobolus (t) 05:34, 18 July 2024 (UTC)

@Dedhert.Jr @Jacobolus I went ahead and added a lot of the more important ones, though I think it would be a bad idea to add every number 1-1,000 (I think they all have their own page). My opinion is that numbers should be added to this project if and only if they are deemed sufficiently important. Mathwriter2718 (talk) 13:19, 18 July 2024 (UTC)

@Mathwriter2718 But the problem is how many that is sufficiently important in mathematics? Dedhert.Jr (talk) 13:23, 18 July 2024 (UTC)

This is subjective, and I personally think it would be a bad idea to have a long argument about this. If people disagree with my opinions about what articles to add to the Project, they can go ahead and remove or add and I won't contest them. I just hope that any changes are consistent with changes made or not made to other pages. Mathwriter2718 (talk) 13:33, 18 July 2024 (UTC)

If we are trying to be restrictive of how important they are in this project, the only I can think of is are they have a relation to other mathematical branches: 1234 (number) in geometry? But my idea is probably not always good or the best idea, so other opinions are welcome. Dedhert.Jr (talk) 13:47, 18 July 2024 (UTC)

If you want to see the articles I added and the ratings I made, here's all of my Talk page contributions today:

https://en.wikipedia.org/w/index.php?title=Special:Contributions&target=Mathwriter2718&namespace=1&tagfilter=&start=2024-07-18&end=2024-07-18

Note that I revised a few of my ratings later and also that some articles were already in the project and were already rated. This might be a good starting point for someone who wants to look at this question much more carefully than I did. Mathwriter2718 (talk) 14:33, 18 July 2024 (UTC)

Discussion at Talk:Piecewise § Requested move 20 July 2024

 You are invited to join the discussion at Talk:Piecewise § Requested move 20 July 2024, which is within the scope of this WikiProject. 174.92.25.207 (talk) 14:59, 20 July 2024 (UTC)

An article of mine seems to be not appearing on Google

Hello,

I wrote an article Deficiency (statistics) which was accepted but is still somehow hidden to the public since it does not appear on search engines like Google. Why is that? The article is about a term introduced by Lucien Le Cam in a famous paper called "Sufficiency and Approximate Sufficiency" in the Annals of Mathematical Statistics which was the starting point for Le Cam theory and he later extended in a book.--Tensorproduct (talk) 19:57, 4 July 2024 (UTC)

If there are other articles that ought to link to that one but don't, then adding the links may improve the results from Google. Michael Hardy (talk) 00:30, 5 July 2024 (UTC)

@Michael Hardy Thank you for the answer. Also thank you for your contribution to mathematics articles on Wikipedia! I saw your name as the initial author of a lot of articles about infinite-dimensional stochastic analysis. Thank you for your contribution.--Tensorproduct (talk) 20:38, 12 July 2024 (UTC)

It appears on Google for me. MrOllie (talk) 20:49, 12 July 2024 (UTC)

It changed after I commented here.--Tensorproduct (talk) 21:17, 20 July 2024 (UTC)

Image in Estimator article

I posted this at the Statistics project page, but that project seems to be very quiet. Can someone here take a look?

https://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Statistics#Image_in_Estimator_article

. 76.14.122.5 (talk) 20:33, 20 July 2024 (UTC)

I've deleted it from the article and left a message on the talk page of the user who created it. Michael Hardy (talk) 21:51, 20 July 2024 (UTC)

Thank you 76.14.122.5 (talk) 23:32, 20 July 2024 (UTC)

Theory pages vs structure pages

There are many pairs pages in this project of the form (theory of X, X). Examples:

• Ring theory and Ring (mathematics)
• Group theory and Group (mathematics). For this one, the pages explicitly make clear that Group (mathematics) is about "basic notions" and Group theory is the "advanced treatment".
• Riemannian geometry and Riemannian manifold
• Linear algebra and Vector space
• Topology and Topological space
• Module theory and Module (mathematics). This one is a bit different from the others, because Module theory is a redirect to Module (mathematics)!
• Geometry and Geometric space. In this case, it is the second that links to the former.
• Graph theory and Graph (discrete mathematics)
• Set theory and Set (mathematics). This is again apparently supposed to follow the more advanced vs more elementary distinction.

Can we put some guidance, maybe in Wikipedia:Manual of Style/Mathematics, about what content goes in which page, and when to have a redirect? Mathwriter2718 (talk) 17:21, 18 July 2024 (UTC)

Another thing that seems arbitrary (to me) is that for some of these pairs, the two articles will have different Vital article status. Mathwriter2718 (talk) 17:25, 18 July 2024 (UTC)

The vital article list is somewhat arbitrary. If you care strongly and want to comb through the list of vital articles at various levels and re-level or add mathematics items, and come up with a clear proposal that other editors here agree sounds okay, I'm sure it would be possible to make changes. –jacobolus (t) 22:14, 20 July 2024 (UTC)

I looked at the list and I think it's pretty good. When I find something that I think should be changed, I will post it on the relevant vital articles page Wikipedia_talk:Vital_articles/Level/5/STEM. I've posted 3 so far. Mathwriter2718 (talk) 03:41, 21 July 2024 (UTC)

I am allergic to the (probably impossible) task of trying to centrally resolve questions like this, so I will make the sole observation that "Linear algebra and Vector space" is very much unlike the other examples in that linear algebra is vast and in particular consists of many things that few people would call "the theory of vector spaces". --JBL (talk) 17:40, 18 July 2024 (UTC)

@JayBeeEll: Maybe because linear algebra is the theory of linear transformations? Michael Hardy (talk) 20:43, 20 July 2024 (UTC)

Arrow's impossibility theorem

There is a lot of attention on Talk:Arrow's impossibility theorem right now (a GA nomination, my comment, several other comments), and I invite people from this Project to join the discussion. Mathwriter2718 (talk) 14:13, 18 July 2024 (UTC)

The discussion under my post in this talk page has turned into a lengthy discussion between one other editor and myself, and about issues such as this, there should probably be at least a third opinion. Mathwriter2718 (talk) 03:43, 21 July 2024 (UTC)

Guidance on spelling

Some terms have alternate spellings in the literature, e.g., fiber versus fibre. I checked a few article on style, and while they addressed assumptions and symbols, they did not address spelling. Is there an article that addresses alternate spelling of mathematical terms? Should there be? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:30, 23 July 2024 (UTC)

Are there any mathematical examples that aren't just American vs British English? Gumshoe2 (talk) 14:02, 23 July 2024 (UTC)

(edit conflict) See MOS:SPELLING where meter/metre is considered, but not fiber/fibre. D.Lazard (talk) 14:03, 23 July 2024 (UTC)

The most obvious example is Abelian versus Commutative.

Would you consider vielbein versus n-bein to pertain to Mathematics, or only to Physics? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:17, 23 July 2024 (UTC)

An abelian integral is not a commutative integral. The fact that a "commutative group" is the same thing as an abelian group is not a question of spelling, it is a question of terminology. The spelling question is that, commonly, "abelian" is not capitalized (see MOS:SCIMATH). I ignore the origin og this exception to the general rules of capitalization. D.Lazard (talk) 14:56, 23 July 2024 (UTC)

Agreed that abelian/commutative is not a spelling issue. Gumshoe2 (talk) 15:01, 23 July 2024 (UTC)

Perhaps I should have written terminology instead of spelling. And that includes guidance on capitalization.

Yes, abelian, like Gaussian, is one of those terms that has different meanings in different fields. For that matter, so is commutative. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 15:45, 23 July 2024 (UTC)

I think the most important thing is to be consistent within an article. Mathwriter2718 (talk) 17:26, 23 July 2024 (UTC)

Peer review of Algebra

I was hoping to get some feedback on the article Algebra in preparation for an FA nomination. Comments are welcome at Wikipedia:Peer_review/Algebra/archive1. Phlsph7 (talk) 07:42, 25 July 2024 (UTC)

Template:Infobox knot vs Template:Infobox knot theory

Are there good reasons to have two different templates or should these be merged? If the former, what are the situations where one should be used instead of the other? Mathwriter2718 (talk) 13:11, 27 July 2024 (UTC)

I have seen Template:Infobox knot used in some cases for things that are not mathematical knots (or not usually thought of in a mathematical context) (example: Matthew Walker knot), so it would seem to me that this might be the difference. Mathwriter2718 (talk) 13:19, 27 July 2024 (UTC)

mapsto arrow symbol

Does anyone know the history of the ⁠$\mapsto$⁠ symbol, LaTeX \mapsto, usually pronounced "maps to"? We have an article which I just moved from maplet to maps to because the former name seems exceedingly rare and basically unused in mathematical literature, but it's hard to find information about where the symbol comes from or much clear discussion about its nature and use. Our article is currently not great. One book I found in a search claims the symbol was invented by Bourbaki c. 1930 but doesn't give a specific source. –jacobolus (t) 05:39, 28 July 2024 (UTC)

Widest path problem

A user on widest path problem is edit-warring to add a long paragraph on widest-path problem, citing recently published research in preprints and/or dubious journals, claiming a result that was long-known (that the undirected all-pairs version can be solved in quadratic time), and in more recent edits has additionally removed text and sourcing documenting the fact that this was long known [15]. I've hit my revert limit. Additional editors would be helpful. —David Eppstein (talk) 18:23, 28 July 2024 (UTC)

I'm still somewhat new to Wikipedia, so forgive me if this is obvious, but is there not a better option here than actively fighting the edit war until, I suppose, the editor gives up? Can we request for the page to be restricted to autoconfirmed or extended confirmed users? Mathwriter2718 (talk) 19:31, 28 July 2024 (UTC)

I have reported them to WP:3RRN, which will at some point result in their being blocked or the page being protected for a brief period. Anyone is welcome to try to explain things to them on their talk-page; it is often better when that comes from someone not involved (hint hint nudge nudge ;) ). --JBL (talk) 19:39, 28 July 2024 (UTC)

It seems that I was wrong about "for a brief period" -- probably for the best. --JBL (talk) 20:05, 28 July 2024 (UTC)

(Generally speaking, though, people who write this kind of thing while promoting their own recent research are not really very interested in learning about our rules or contributing to Wikipedia in a serious way.) --JBL (talk) 19:55, 28 July 2024 (UTC)

I kind of want to get e.g., fame, citation etc. on a T-shirt. XOR'easter (talk) 21:58, 28 July 2024 (UTC)

Thanks, all, for getting this situation resolved!

Autoconfirmed protection would be an appropriate solution if they return not-logged-in or if sockpuppetry becomes a problem. But those sorts of measures require sufficient evidence of continued misbehavior and I'm too WP:INVOLVED with that article to have done that already myself. In this case, warning them for edit-warring and letting them get blocked when they ignored the warning may have been the easiest solution. —David Eppstein (talk) 20:09, 28 July 2024 (UTC)

Welcome Jean-Pierre Serre

The edit summary of this edit is signed J.-P. Serre. Glad to welcome this new editor, born in 1926. D.Lazard (talk) 13:44, 29 July 2024 (UTC)

That's very exciting! David Hilbert (talk) 20:31, 29 July 2024 (UTC) — Preceding unsigned comment added by Mathwriter2718 (talk • contribs)

My own suspicion is that Serre has been quietly editing Wikipedia from IP accounts for decades. Tito Omburo (talk) 21:24, 29 July 2024 (UTC)

Wikipedia:Featured article review/0.999.../archive2

Would anyone be willing and able to weigh in at this FA review as to whether any major concerns remain? XOR'easter (talk) 21:49, 30 July 2024 (UTC)

I am not sure if I want to weigh in about whether "major concerns remain" in the abstract, but I feel that the article 0.999... is extremely good. I think it hits every important thing it should, and I think the explanations are very good, and it does a good job at correctly discussing the various arguments. I also like the discussion of skepticism in education. I think the "Related questions" section is a bit lackluster, though, and I think that the article might be able to do a better job at sourcing and/or justifying early on the definition of 0.999... as being the smallest number greater than every number in the sequence 0.9, 0.99, 0.999, .... Mathwriter2718 (talk) 15:29, 31 July 2024 (UTC)

Requested move at Talk:Piecewise#Requested move 20 July 2024

There is a requested move discussion at Talk:Piecewise#Requested move 20 July 2024 that may be of interest to members of this WikiProject. ASUKITE 20:11, 31 July 2024 (UTC)

Aug 2024

Wish on making formula editing easier

I submitted a “community wish” on mathematical formulas: meta:Community Wishlist/Wishes/Editing mathematics is too difficult. Jean Abou Samra (talk) 13:45, 30 July 2024 (UTC)

You can use {{tmath}} to save a bit of typing, e.g. {{tmath|x}} means the same as <math>x</math> and either one renders as ⁠$x$⁠, though which one of these is easier to read is somewhat a matter of taste. (This template has an extra advantage that if you put punctuation after the math, you won't get a line break in between.) If you want to specify inline style, you can write e.g. {{tmath|\textstyle \int_1^2 dx/x}} as an alternative to <math display=inline>\int_1^2 dx/x</math> for ⁠$\textstyle \int _{1}^{2}dx/x$⁠. If you need to include an equals sign, either wrap it like {{=}} or explicitly name your template parameter 1 as in {{tmath|y {{=}} x}} or {{tmath|1= y = x}} to produce ⁠$y=x$⁠.

You can ask if you like but special syntax seems extremely unlikely to be implemented. A more plausible thing we could do without platform changes is to find a template name only 2 or 3 letters or symbols. Not sure it would be worth the trouble though. A shortcut something like {{imath|x^2}} for {{tmath|\textstyle x^2}} could be helpful. –jacobolus (t) 18:07, 30 July 2024 (UTC)

Huh! Never heard of this template ever in my life. But the code for writing is apparently somewhat strenuous to me, so I'm comfortable with <math>. Dedhert.Jr (talk) 15:09, 2 August 2024 (UTC)

I appreciate you bolding pointing out flaws in the current math notation system. I think it will take a significant amount of effort to improve it, and certainly the WPM editors should be involved in significant changes.

It's good that you're thinking about ways to shorten the math syntax, but dollar signs for inline math is very unlikely to happen because it would mess up a lot of articles that have dollar signs in them. Mathwriter2718 (talk) 21:20, 30 July 2024 (UTC)

The official LaTeX \( ... \) and \[ ... \] syntax is less problematic, but I think still unlikely to get Wikimedia approval. In general mathematics formatting efforts at Wikimedia have been focused on the vain hope that mathml will eventually work and on doing as little as possible in any other direction. —David Eppstein (talk) 21:39, 30 July 2024 (UTC)

It seems like math editing should be one problem visual editor "solves", or perhaps via a plug-in that automatically converts LaTeX into wiki math formatting. Related, thunderbird email client has math editing in in a separate window where you can use ordinary latex and is then converted into whatever format the email client understands. Tito Omburo (talk) 17:19, 31 July 2024 (UTC)

By the way, @Jean Abou Samra if you ever run into difficulty with math formatting on a specific page, feel free to ask for help here, or drop a note at my talk page. –jacobolus (t) 16:59, 31 July 2024 (UTC)

This is just some general comment. There is a question on what is technically possible, but there is also a question on what Wikimedia/Wikipedia community would want. I have been having a suspicion that the subper implementation of math rendering/editing here might be intentional; i.e., it’s Wikipedia:Broken by design. Surprisingly (and not really surprisingly), not many people are fond of math contents in Wikipedia. So, maybe it is not necessary for Wikipedia community's interest to make math editing easier (at least, I have not seen any real efforts to recruit more new editors to write and edit math articles). See also User:Deltahedron. So, if this theory is correct, the foundation may nominally solicit some comments for improvement but they will never be implemented. (I emphasize I may be wrong about my suspicion.) —- Taku (talk) 17:49, 31 July 2024 (UTC)

"Admits"

Would it be possible to create an entry for "admits" in the glossary of mathematical jargon? There's what looks to me like a plausible definition in this Reddit post, but Reddit is far from being a WP:RS. — The Anome (talk) 10:02, 3 August 2024 (UTC)

The top answers on that Reddit post are more or less correct. Object A admits structure B if structure B could be imposed on object A. I mildly support adding "admits" to glossary of mathematical jargon. "Equipped with" is another good candidate. Mathwriter2718 (talk) 12:00, 3 August 2024 (UTC)

1234 (number)

Tension arise between @David Eppstein and @Radlrb in the article 1234 (number). Previously, both users had already edited war in the article Golden ratio, and one of them was blocked. Now, to think that the main problem of the article is about the content explicitly saying about the "mock rational" property of 1234, and both of them are talking about the property from different perspectives, many members of this WikiProject are welcomed. Dedhert.Jr (talk) 02:31, 15 July 2024 (UTC)

I have a clear-cut case that my addition is worthwhile, as the reference used makes use of the term "schizophrenic" for all its terms. Provided (non-WP:SYNTH) associated properties that tie together, from already published sources (OEIS sum-of-divisors).

I'm not sure why you mention "one of them was blocked" unless you are purpusefully trying to tilt the scales (I see he was your GA arbitrator for Square pyramid, which raises questions here with regard to your impartiality). I am not going to continue debating this with David Eppstein as he is clearly not interested in holding a back-and-forth conversation (as is his history with anyone disagreeing with him, aside from his obvious prejudice as I mentioned), nor will I debate with anyone who blankly denies entries on WP on the basis of breach of specific policies, where nowhere is there a mention of non-addition of properties that directly tie to properties of another number (in light of, distorted "off-topic" removals; like saying that the Golgi apparatus has nothing to do with non-protein synthesis and packaging in a cell, when its in a diverse metabolic environment where even slight temperature changes, for example, lead to differentials in cell metabolism that affect all organelles). This being said, I welcome honest, and intuitive points of view, given the natural goal I have in mind when I contribute here, which is to muster together major properties of numbers, in a manner that links our number articles together into a sort of flowing unit. It's an important and invaluable endeavor! Radlrb (talk) 03:21, 15 July 2024 (UTC)

I'm having trouble following this. On the talk page David Eppstein refers to the "first member of sequence to have a repeated digit in the first five after the decimal" property, but I cannot find this on the page or in the edit history of the page. Based on the edit history it seems like this is instead the contentious content. If so, then I think I agree with David Eppstein – however I find the removed content too confusingly stated to be completely sure. (If it's not a schizophrenic number, then what's the sequence in question?) Gumshoe2 (talk) 03:36, 15 July 2024 (UTC)

Follow the current stated property, for integer parts of square roots of the sequence of numbers 1, 12, 123. Thats what is there right now. And read the title of the source. Radlrb (talk) 03:53, 15 July 2024 (UTC)

So the property is that $\lfloor {\sqrt {1}}\rfloor =1$ and $\lfloor {\sqrt {12}}\rfloor =3$ and $\lfloor {\sqrt {123}}\rfloor =11$ are not composite numbers but $\lfloor {\sqrt {1234}}\rfloor =35$ is? And the first few schizophrenic numbers are 0, 1, 12, 123, 1234, ...? Then I don't understand any of the talk page discussion, and also this property seems extremely arbitrary. And I don't understand why the wikipage presently says "Though not strictly a schizophrenic number in base ten..." when it seems that 1234 is exactly a schizophrenic number. Gumshoe2 (talk) 04:06, 15 July 2024 (UTC)

It's not arbitrary, not any more "arbitrary" than 1234 being the first in its sequence (1, 12, 123, 1234, ...) *not Radlrb (talk) 21:55, 15 July 2024 (UTC)* divisible by their one's digit, which David Eppstein added. The sequence property I added mentions its composite integer part that is also the first term in a self-similar sequence, as it points out; the first term. In fact, its not arbitrary at all, because it shows that this sequence is self-similar like the sequence for odd-indexed schizophrenic numbers, tying them together with this property. Indeed, I also see sqrt1234 as a schizophrenic number and many authors do too, however in the literature, the property of interest of repeating digits in the fractional part of their square roots is most prominent in odd-indexed terms (sqrt1, sqrt123, sqrt12345,...), and these are technically the "strict" schizophrenic numbers. If you ask David, he will tell you that the square root of 1234 is not schizophrenic. Radlrb (talk) 04:15, 15 July 2024 (UTC)

I don't completely follow everything you're saying, but I am confident now in saying that it's a pretty arbitrary property. However I completely agree with you that it's no more arbitrary than the other property you just mentioned – the reference given for it doesn't even suggest that it's notable, it's just mentioned there as an example of a non-solution to some mental puzzle. Gumshoe2 (talk) 04:23, 15 July 2024 (UTC)

Well, if you don't follow what I am saying, then you very likely don't understand the very subject matter we are speaking of, I think. 1234 is not a schizophrenic number, is it's square root, likewise for 123, etc. I am amazed, because I showed there that the arithmetic means of divisors of the following even indexed schizophrenic number (sqrt123456) is twice the integer part of the square root of the sqrt of 1234. Then I showed that the product of the first and forty-fourth super primes is the integer part of the sqrt12345678, the following (fourth) indexed member, where 44 has distinct and important partitions that number 1234. (By the way, none of this is OR or SYNTH, as many claim, these are known facts, I'm just juxtaposing them.) So, I am amazed, that so many people here throw the word "arbitrary" around like it's Christmas. Do you have any idea, of how difficult, and challenging, it is to find synchronicity and sense in mathematics? Be grateful, for the love of our very existence and subsistence, that these facts exist. That you ask, for an infinitude of data, to make sense of a sequence linearly that ties sum-of-divisors, aliquot parts, totients, or triangular numbers, together as I am ligating, so as to then say "okay, maybe I'll buy it", is an affront; these types of data represent an unimaginable blessing, any time they come into form. The unimaginable magnitude of complexity to tie these together, and any set of sufficiently differently defined sequences together, in purely logical form, is so astronomically difficult, that we should STILL not expect to delve into the real deep end of mathematics for another ten thousand years, at the very, very least. So when you just tell me something like what I am telling you is "arbitrary", that's akin to a school child (you, me, a plant, anyone) trying to tell the very Earth, or Sun, in their absolute enormous computational power, anything about anything that exists outside a flat surface in her/his little bedroom, house, or school yard. And im being kind here, there's no telling how complex Mathematics really, really is. There's no living organic-born or ethereal angel in our Universe that has a real-idea of all Math. Thats for the stars to contemplate. Radlrb (talk) 05:18, 15 July 2024 (UTC)

Wow. 100.36.106.199 (talk) 12:10, 15 July 2024 (UTC)

That you ask, for an infinitude of data – I don't need an infinitude of data, but it would be nice to have a reliable source demonstrating that this is considered important by someone other than Wikipedians or OEIS contributors. The OEIS has decent standards for correctness of details but very lax relevance standards for inclusion of new sequences.

when you [tell me something] is "arbitrary", that's akin to tell[ing] the very Earth, or Sun [...]" – let's not get carried away please. –jacobolus (t) 20:29, 23 July 2024 (UTC)

Not getting carried away, we are ants still, trying to understand a landscape of truth far larger than you or I can even conceive, proven every millenium by the next mass discovery that upends everything once conceived. If anything, I was being quite minimalistic. The comparison is more on the order of particles, and entire universes. We're little specs, and if you think you have any true idea of anything, check back in your next ten thousand lifetimes, and then tell us what you've learned. Don't come and tell me anything absolute about anything only after 10,000 years of "civilization". There is a saying that goes more or less, "the more aware you are of how little you know, the wiser you become." I'm sure you've heard of it. It makes sense, because the more open you are to what holes you have in your consciousness, the more keenly you will reach to understand more clearly. Radlrb (talk) 00:34, 28 July 2024 (UTC)

You are welcome to expound about this at whatever length you want on your own blog. It's entirely inappropriate at Wikipedia. –jacobolus (t) 00:58, 28 July 2024 (UTC)

Oh yeah, what policy am I violating here, please enlighten me. I can speak my opinion on shortsightedness that is being displayed here, based on which number properties to include on a number article, to your chagrin. It seems you're also short of an actual response, so you revert to attempting to mute me, which is of course, a weak display of discourse. I can speak my opinion here, period. You're the one who doesn't need to answer, or even read it. Like the rest of what you have already ignored. Radlrb (talk) 04:40, 28 July 2024 (UTC)

This venue is for discussions about issues related to the content or style of mathematics Wikipedia articles which can't be resolved at a specific article talk page or which concern multiple pages. It is not a free-for-all about any Wikipedian's shower thoughts about their communion with the spirit of the universe or whatever you are talking about. Take it to twitter or something; I'm sure your ideas about the unboundedness of existence are perfectly lovely but nobody here cares to read them. –jacobolus (t) 04:48, 28 July 2024 (UTC)

"The integer part of this number's square root is composite" is a rather boring property. If you want to mention schizophrenic numbers, the best thing I can come up with is "1234 appears in a sequence of numbers whose square roots are schizophrenic"; this is at least marginally more interesting than the compositeness of the integer part of the square root. —Kusma (talk) 12:23, 15 July 2024 (UTC)

Sure, in your perspective, since no known “applications” are known, that’s how we define usefulness here, on practical terms alone. Oh I get that; in our mathematical global community, we don’t seek bridges between numbers. Radlrb (talk) 16:25, 15 July 2024 (UTC)

I see he was your GA arbitrator for Square pyramid, which raises questions here with regard to your impartiality Well, in a precise meaning, he reviewed the article Square pyramid regarding the criteria of GA. I did not see anything about my impartiality whenever replying to his comments. The fact that the way you are saying "arbitrator" means I have some dispute with another user, and he gave a solution to alleviate the tension between me and another user? I can't understand what do you mean about that. Perhaps there are some alternative interpretations from your perspective that I could not imagine in my head. Dedhert.Jr (talk) 10:15, 15 July 2024 (UTC)

I used the wrong word, but for other reasons. Radlrb (talk) 16:22, 15 July 2024 (UTC)

I'm sorry, but what other reasons are you referring to? Dedhert.Jr (talk) 15:17, 4 August 2024 (UTC)

I would like to remind everyone that on Wikipedia, we assume good faith and use etiquette and civility when talking to others. Cases of severe incivility are subject to policies on WP:UNCIVIL. Mathwriter2718 (talk) 14:34, 28 July 2024 (UTC)

Non-mathematician here. The article 1234 (number) says:

• Though not strictly a schizophrenic number in base ten, the square root of 1234 is the first in its sequence (of square roots of integers 1, 12, 123, 1234, ...) to have a composite integer part, of 35.

with a ref to a site OEIS.

The ref does not say anything about 1234, it's about "Integer parts of the square roots of the schizophrenic numbers", which 1234 is not. In normal parts of Wikipedia such a sentence would be deleted.

I found the article very unsatisfying. It seems to be mostly a list of all the things one could find using a search on OEIS. That's not knowledge. Johnjbarton (talk) 22:56, 4 August 2024 (UTC)

Has anyone been able to figure out what property is actually being asserted? Like, what is its definition? Tito Omburo (talk) 02:29, 28 July 2024 (UTC)

I have serious concerns about the continued editing of number articles by Radlrb, which appears to involve high degrees of OR and synthesis. We have recently had some back-and-forth at 18 (number), but I think the underlying issue is probably present elsewhere, too. Could anyone take a look? 100.36.106.199 (talk) 09:41, 4 August 2024 (UTC)

My edits do not make statements or clauses of “consequences” from the additions. They compound relevant information together, that is all. If it is such an issue, then why do my edits continue to exist? Maybe it is because it is valuable information, and because it is advancing an encyclopedic understanding of mathematics. I’ve been adding information here for over two years now, in like fashion, and it is definitely a serious improvement to the state of number articles here since say, March 2022. Radlrb (talk) 09:50, 4 August 2024 (UTC)

You're defining WP:SYNTH. Tito Omburo (talk) 12:35, 4 August 2024 (UTC)

Irrelevantly so, since in number theory you will get natural "flow" when points start to amalgamate together. To not juxtapose them is therefore unscholarly and a lie. Take for example additions I made to the article for 19, regarding hexagons:

The number of nodes in regular hexagon with all diagonals drawn is nineteen.

• Distinguishably, the only nontrivial normal magic hexagon is composed of nineteen cells, where every diagonal of consecutive hexagons has sums equal to 38, or twice 19.
• A hexaflexagon is a strip of nineteen alternating triangular faces that can flex into a regular hexagon, such that any two of six colorings on triangles can be oriented to align on opposite sides of the folded figure.
• Nineteen is also the number of one-sided hexiamonds, meaning there are nineteen ways of arranging six equiangular triangular polyforms edge-to-edge on the plane without turn-overs (and where holes are allowed).

Yes, these all make connections together for the sake of 19 as it expresses symmetries in a hexagon, in different ways. However, they clearly belong together. WP:SYNTH is therefore clearly not constructive to an encyclopedic representation of hexagonal symmetry and 19, regardless of whether someone else said it directly or not. The same applies for my other additions, of which they number more than 8,000 edits. Who else on Wikipedia has done more than 1000 edits to number articles here, and who has begun to generate a clearly needed template for the development of a "number article" here, beyond lower subheadings?

Can we please stop this nonsense now, you both and anyone else "fearing and concerned" about what I am doing here know very well, that I am a benefitting force, rather than a limiting one. Respectfully, and thank you. Radlrb (talk) 13:27, 4 August 2024 (UTC)

Tito is not complaining about juxtaposition, which is different than WP:SYNTH, see WP:SYNTHNOTJUXTAPOSITION. Tito is complaining about including facts in an article that are not stated in a source.

The fact that some of your edits were not reverted immediately is not evidence that they are high-quality. Wikipedia is run by volunteers and many of your edits won't be reviewed for a long time. I looked at some of your edits to other pages and I think that some of them are genuine improvements that the members of WPM would be thankful for, and some of them contain large amounts of irrelevant information. Instead of getting into a big argument about this, we could see it as an opportunity to grow and engage with the community. Mathwriter2718 (talk) 13:43, 4 August 2024 (UTC)

I agree with this 100%. 100.36.106.199 (talk) 13:52, 4 August 2024 (UTC)

99.9999% or more of my edits have not been reverted, so in all likelihood, the converse is what is true. More so, people do revert edits of vandalism to number pages very quickly, take a look yourself at just about any number page. Radlrb (talk) 14:13, 4 August 2024 (UTC)

No one is accusing your edits of being vandalism. Mathwriter2718 (talk) 14:21, 4 August 2024 (UTC)

I know my edits are not vandalism, however showing that vandalism actively gets reverted also demonstrates that number article pages are being constantly monitored and vetted. Radlrb (talk) 14:33, 4 August 2024 (UTC)

No, it does not, it shows that people patrol things like WP:recent changes specifically to prevent vandalism. 100.36.106.199 (talk) 14:36, 4 August 2024 (UTC)

Nope, it shows people are watching. Two years and half, its been. Radlrb (talk) 14:47, 4 August 2024 (UTC)

Many Wikipedia changes which are nonsense, factually inaccurate, original research, push a POV, use an un-encyclopedic tone, etc. persist in Wikipedia for extended periods – decades sometimes. This happens because volunteer effort is finite and it's easy to slip under the radar, not because these changes would stand up to close scrutiny. [Note: the same is also an issue with every other kind of published work, including newspaper articles, peer-reviewed papers, scholarly monographs, textbooks, ...] –jacobolus (t) 15:40, 4 August 2024 (UTC)

Not accurate, since we know that my additions have been watched for quite some time, and if you look at page views, the're has been a substantial increment of views, at least by 1,000 views or more since I started editing, for small number pages. So the idea that it has gone unnoticed is a flawed narrative. It's definitely been notices for quite some time, and those in Wikiproject Numbers have also monitored developments, as seen in the Talk page. Radlrb (talk) 16:37, 4 August 2024 (UTC)

Some of your additions remain a long time because it requires a certain amount of mathematical expertise to understand that they are off-topic or otherwise not an improvement. Very few editor-volunteers can do that, but nearly anyone can see that adding "farts!" to an article is not an improvement, so simple vandalism like that is (usually) quickly reverted by a larger community of recent-page patrollers. -- Beland (talk) 21:52, 4 August 2024 (UTC)

Some of your edits to 18 (number) (specifically, the ones I reverted) are bad because they violate WP:SYNTH. I do not think you are intentionally making bad edits. However, when someone explains to you that your edits are bad, you should try to understand the objection and change the way you edit. Will you do that? Have you read WP:SYNTH? Do you understand how it applies to the edit I reverted? 100.36.106.199 (talk) 14:31, 4 August 2024 (UTC)

I don't have to change my editing behavior when I disagree with your position, and when most editors vetting the pages have let the information stand. I don't see an issue, I only see 10 or so people disagreeing, which is an overwhelming minority opinion. Radlrb (talk) 14:35, 4 August 2024 (UTC)

To be clear: you agree that perhaps 10 different people have told you that there are problems with your edits, and you are committed to not changing the way that you edit despite this? 100.36.106.199 (talk) 14:37, 4 August 2024 (UTC)

That's right. I don't expect support to arrive, since what I am doing is pushing through a barrier that shouldn't exist, and a policy that is derogatory and unapplicable here in this case. Also, because I know I have silent support, and I have proof of it, as I already mentioned: my edits have stood the test of time. Also, I have added brilliant material, so I know I am doing the right thing, regardless of immature pedantic views. You know, as with many peoples, black folk were unnallowed to do many things in America, against "laws" inhumane to them. They broke free, and are breaking free more every day, teaching us along the way to not hold back against unfair and limiting barricades. In like manner, I am unafraid of breaking this Wiki "law", I'll tell you that, because I am enlightening our Wiki community, and you are not going with the flow of things, by pushing this. Radlrb (talk) 14:43, 4 August 2024 (UTC)

Unfortunately WP:ANI is semi-protected at the moment, so I cannot report you there until that expires. You can look forward to that when the semi-protection expires. It's too bad, because you're not a total crackpot or hopelessly incompetent, but Wikipedia has policies for good reasons, and your belief in your personal superiority is, uh, not very compelling. 100.36.106.199 (talk) 15:15, 4 August 2024 (UTC)

"you're not a total crackpot or hopelessly incompetent". I do not think of myself above anyone, and I welcome others to join me in this loving work that I continue to bring forth. Radlrb (talk) 15:24, 4 August 2024 (UTC)

What would it take to convince you that the consensus is that some of your edits should be reverted? If 10 people telling you so isn't enough, what about 100 or 1,000? What if half of your edits were in fact reverted by various editors? If you'd like, I can start reverting your edits. For what its worth, Wikipedia has a policy WP:DETCON about how to determine consensus, which essentially says that in this instance, discussions on this page are what determine consensus. Mathwriter2718 (talk) 15:18, 4 August 2024 (UTC)

If someone wants to report these funny discussions in WP:ANI. I think I can help. Dedhert.Jr (talk) 15:20, 4 August 2024 (UTC)

I'll do that. Mathwriter2718 (talk) 15:23, 4 August 2024 (UTC)

Reported. Dedhert.Jr (talk) 15:30, 4 August 2024 (UTC)

Go right ahead! Let's get to it once and for all. My work has already been done: vet the information I have added, and it stood the test. People are genuinely interested in my inputs. I don't know how any of the votes would go, however, it is definitely worth witnessing. What you do with the information from here on forth, is another matter entirely, if I get blocked, banned, or whatever. Many good-doers have gone to jail for their efforts. I did my job. Oh, and you will eventually be grateful. Radlrb (talk) 15:31, 4 August 2024 (UTC)

You keep claiming that all of your "work" is improving the pages, and that some mysterious "other people" support you, yet no-one else here has actually observed any of these approving people. I have removed a number of your contributions which I think (my opinion, just like your opinion) are not appropriate. For example, the strange diagram now on Talk:2; I have just removed again, and request other people here to consider this example. Imaginatorium (talk) 17:47, 4 August 2024 (UTC)

You should not assume that because 1000 people read an edit and of the 9 people who commented upon it, they all opposed it, means that 991 people approve of the edit. It's more realistic to assume the silent majority breaks down similarly to the people who are actually speaking up. In other words, if 1 editor (the author) is in favor and 9 are against, if the editors are at all a representative sample of readers, probably 90% of the people who read the edit disapproved of it. It's just that not everyone files a complaint every time they see something wrong on Wikipedia. In fact, the vast majority do not. I generally assume that if two editors tell me a change I've made is bad and no one else replies to the talk page discussion, then it is in fact an undesirable change. If it's only one editor and I have strong feelings I'm right, I'll ask for a third opinion. If I think the two editors are not representative of broader editor opinion, I'll ask at a WikiProject or RFC, but that's really for extraordinary circumstances, and only after trying to resolve the disagreement through discussion. If ten editors tell me I've made a bad edit and no one else replies to the request for opinions, then clearly consensus is against my edit, and it'll be removed no matter how right I think I am, and at that point it's time to move on to something else. The discussion part is very important; not everyone is really paying attention at first or has really thought through all the consequences of an opinion (including me). But at some point once a question has gotten a fair shake, the supermajority of discussion participants rule. -- Beland (talk) 22:03, 4 August 2024 (UTC)

By the way, since you like arithmetic: I have reverted, today, two of your edits. Since you have only ever made 8532 edits to Wikipedia, that means that your estimate of your error rate (you said less than 1 in 1000000) is off by at least 2.4 decimal orders of magnitude. 100.36.106.199 (talk) 14:34, 4 August 2024 (UTC)

lol, I did add two extra 9s, didn't I Radlrb (talk) 14:36, 4 August 2024 (UTC)

References

Suspected mistake

Perhaps someone who is familiar with continued fractions (and/or "generalized continued fractions") and maybe also "infinite series" ... could take a look at this recently added section in a "Talk:" page :

Talk:List of things named after Leonhard Euler#Suspected mistake ("finite" vs. "infinite")

OR: ... (in case it has been 'archived', or something...) one may "instead" look here:

Talk:List of things named after Leonhard Euler&oldid=1238883601#Suspected mistake ("finite" vs. "infinite"

Thank you, Mike Schwartz (talk) 06:02, 6 August 2024 (UTC)

Template:Polytopes

I'd bring this up on Template talk:Polytopes, but that hasn't had activity in a decade, so I though I'd start here. WP:BIDIRECTIONAL indicates that in most cases that for a template like Template:Polytopes, pages that link to the template should be the same as those that the template links to. Template:Polytopes is *massively* off from that, see https://templatetransclusioncheck.toolforge.org/index.php?lang=en&name=Template:Polytopes . The ones that are linked to that don't use the template are mostly Lie groups, and there are a *lot* of Polytopes that have the template, but aren't part of it... Naraht (talk) 18:55, 6 August 2024 (UTC)

Help make number articles more accessible!

See: Wikipedia talk:WikiProject Numbers#Help remove WP:CRUFT on number articles! Allan Nonymous (talk) 20:40, 6 August 2024 (UTC)

Mathematics glossaries

Given that Wikipedia:WikiProject Glossaries is inactive, do we want to do anything with the mathematics and logic glossaries? A few possibilities:

1. These glossaries are a bad use of our editors' time. Remove them from this WikiProject.
2. These glossaries are not very important to us, but they should still all be added to this WikiProject as low-priority.
3. It is useful to have some glossaries, and we should clean up the existing organization insofar as it is insufficient and spend some editor time improving these.
4. Glossaries are be an important way for us to organize our articles, and we should spend significant time on them.
5. Some of these glossaries are important and we should spend time on them, and others are really not important and we can safely ignore them.

I'm wondering where others stand on this. I would consider myself either a 2er or a 3er. If some of you are 3ers or 4ers, I can propose a clean-up to the existing organization. Also note the existence of Category:Outlines of mathematics and logic and Category:Mathematics-related lists. Mathwriter2718 (talk) 00:57, 22 July 2024 (UTC)

I definitely find some of the glossaries to be important, for at least two reasons. First and most importantly, they provide wikilink targets for terminology that may not have or deserve its own separate article. But also, by putting the terminology for a subfield in a single place, they give readers a broad overview of the terminology and can be a helpful warning about certain pieces of ambiguous terminology. In particular I think those justifications are all valid for the glossary I have put the most effort into, glossary of graph theory. But I don't think your questions can be answered as you have formulated them, at least not by me, because I don't have the comprehensive knowledge about all our glossaries that would enable me to answer universally-quantified questions about them.

As for wastes of editors' time: I think you are wasting your time casting around for content to destroy. Find something more constructive to do. —David Eppstein (talk) 01:14, 22 July 2024 (UTC)

@David Eppstein I am sorry that I gave off the impression that I am "casting around for content to destroy". To be honest, I am kind of shocked by your accusation, and I don't really know where it is coming from. Mathwriter2718 (talk) 02:28, 22 July 2024 (UTC)

Perhaps you found my inclusion of position 1 offensive, but I do not support position 1, and position 1 does not call for "destroying content". Mathwriter2718 (talk) 02:30, 22 July 2024 (UTC)

After looking again at @Jacobolus's comment, maybe I was unclear: by 1's "remove from this project", I meant "remove the WPM template from their talk page", not delete the page. I only brought this up because some of the math glossary pages are do not have the WPM template, and I was trying to ask if this was intentional before I went ahead and added them to WPM. That was what really prompted me to make this post. Mathwriter2718 (talk) 02:57, 22 July 2024 (UTC)

There is no reason to remove the WPM template. If it is missing from one or another of these pages feel free to add it. –jacobolus (t) 08:35, 22 July 2024 (UTC)

Hey, everyone here is a volunteer. We should respect what other people choose to spend their time on, even if it's not interesting to us. Mathwriter2718 was not proposing the deletion of any content, merely trying to get a sense whether this WikiProject wanted to adopt some additional pages. -- Beland (talk) 17:06, 7 August 2024 (UTC)

These glossary pages all have very few page views. Feel free to work on improving them if you want to, or else leave them alone. They aren't particularly important to Wikipedia as a project or WPM just because they are so rarely seen. But they also aren't hurting anything. There's no reason to remove them. –jacobolus (t) 02:20, 22 July 2024 (UTC)

As someone who edits the glossaries articles a lot, I think the glossaries should have a place in Wikipedia. To add to what David said, the glossaries often contain red links and red links are useful and important. I don’t know about view counts of the glossaries but they shouldn’t matter much; in fact, in Wikipedia, we don’t pursue views or likes (gasp) and that should be a good thing. What I am less sure about are lists of topics or outline articles; they seem to cover essentially the same ground as that by the glossaries. So, we can argue there is some redundancy, which itself is not a problem but the less redundant the content is the easier we can maintain it. —- Taku (talk) 06:25, 22 July 2024 (UTC)

I had a look on category:Glossaries of mathematics. Most of them are glossaries of "terminology of some area of mathematics". Such glossaries are very useful, especially for areas that have a large terminology that is commonly used without being redefined and for areas, such as graph theory, where the number of variants make correct linking difficult. Some general glossaries seem also essential, such as Glossary of mathematical jargon and Glossary of mathematical symbols, for which many individual entries cannot be the subject of specific articles. The only mathematical glossary that is problematic seems Glossary of areas of mathematics, per WP:INDISCRIMINATE, and also because the linear order of a glossary hides the complex graph of the relationships between areas of mathematics, better renderes with categories.

On the other hand, most articles in Category:Outlines of mathematics and logic are misleading because they oversimplify their object and give a biased information by omitting important aspects and giving too much importance to minor aspects. IMO, most articles entitled "Outline of someAreaOfMathematics" or "List of topics in someAreaOfMathematics" should be transformed into a redirect to someAreaOfMathematics. D.Lazard (talk) 09:50, 22 July 2024 (UTC)

Thanks for mentioning Category:Glossaries of mathematics, I hadn't seen that. I updated Wikipedia:Contents/Glossaries/Mathematics and logic to be consistent with it. I went ahead and added all of the pages in that category (that weren't already) to WPM.

It seems to me like the following glossaries ought to exist (but don't currently):

• Analysis (real and complex),
• Combinatorics,
• Differential equations and dynamics (which would include both ODE and PDE),
• Geometric topology,
• Logic (or model theory, if logic overlaps too much with set theory, for which a glossary already exists),
• Number theory.

Mathwriter2718 (talk) 13:23, 22 July 2024 (UTC)

We have Glossary of algebraic topology, which should cover geometric topology. On the other hand, I am quite surprised to find out that we don’t have glossary of number theory and glossary of complex analysis (we do have Glossary of arithmetic and diophantine geometry, but that one would arguably have a limited scope.) —- Taku (talk) 15:10, 22 July 2024 (UTC)

I have just started glossary of real and complex analysis; seems no-brainer. —- Taku (talk) 07:52, 23 July 2024 (UTC)

Excellent, thank you. That really is a no-brainer, as is Glossary of number theory, which I will start today. In my opinion, Glossary of algebraic topology should be renamed to Glossary of algebraic and geometric topology and geometric topology terms should be added to it. I also think it would make sense to rename Glossary of topology to Glossary of general topology or Glossary of point-set topology. Mathwriter2718 (talk) 11:24, 23 July 2024 (UTC)

Why not make Glossary of geometric topology a separate article? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:04, 23 July 2024 (UTC)

I would support this too. I don't feel strongly either way. Mathwriter2718 (talk) 13:18, 23 July 2024 (UTC)

I personally feel geometric topology is a subfield of algebraic topology, and it’s usually easier to maintain fewer articles. But I don’t have a strong opinion on the matter. I second on a move of glossary of topology; in fact, I will just go ahead and do now. —- Taku (talk) 14:12, 23 July 2024 (UTC)

I definitely disagree that geometric topology is a subfield of algebraic topology. Mathwriter2718 (talk) 14:16, 23 July 2024 (UTC)

Well, it probably depends on how you define algebraic topology. Do you consider Poincaré conjecture belongs to algebraic topology or geometric topology? For me, it’s a result in algebraic topology more specifically in geometric topology. I do not see it does not belong to algebraic topology; that’s weird (weird because Poincaré is a sort of results you tell laypersons when you explain algebraic topology). That’s what I mean by a subfield. Taku (talk) 15:41, 23 July 2024 (UTC)

Dynkin diagram dark mode

Dark mode seems to break the {{Dynkin}} template. E.g., . -- Tito Omburo (talk) 18:38, 7 August 2024 (UTC)

Verified both with the dark mode gadget (under gadgets in preferences) and with the dark mode appearance menu item (in Vector2020, the goggle icon in the upper top right). In both cases the yellow dots stay yellow dots but all the lines and annotations become invisible. —David Eppstein (talk) 19:02, 7 August 2024 (UTC)

I do not understand the technical things in Wikipedia. But are there other ways to change black to white lines during the use of dark-mode gadgets? Relatedly, I mean, the gadget is beneficial in reducing the amount of light that comes into one's eyes when reading an article. But for some reason, this gadget is already problematic, including PNG vector images, where the background of an image occasionally shows fully dark color with some distorted uncomfortable white dots near the black lines (see image on Square pyramid, or the GIF in Pentagonal pyramid#In polyhedron). I think this is already explained in an essay or whatever it is. Dedhert.Jr (talk) 02:46, 8 August 2024 (UTC)

RfD

Can somebody help me list a new redirect for discussion about Elongated tetragonal disphenoid? There is a discussion the redirect should be deleted, but the result is the wrong venue. Now I have no idea how do I handle this technical thing.

• Wikipedia:Articles for deletion/Elongated tetragonal disphenoid

Dedhert.Jr (talk) 08:21, 1 August 2024 (UTC)

If you install the Twinkle tool (see instructions at this link), it allows you to conveniently create an RfD (and any other deletion discussion). Once installed, go to the redirect page, press on 'TW' next to the star and click on XfD. You can then input your reasoning and submit the RfD; Twinkle will create the discussion for you. Sgubaldo (talk) 10:07, 1 August 2024 (UTC)

Are there other ways to propose RfD instead of using Twinkle? This tool seems risky. Dedhert.Jr (talk) 04:13, 2 August 2024 (UTC)

Have you seen WP:RFDHOWTO? Mathwriter2718 (talk) 12:00, 2 August 2024 (UTC)

I have seen that, but still got stuck. This is unlike WP:AfD inputting which article you would like to delete. The RfD, according to me, is somewhat the next harder level technical to propose an article. Dedhert.Jr (talk) 15:40, 4 August 2024 (UTC)

I listed it at Redirects for discussion here. Felix QW (talk) 08:25, 7 August 2024 (UTC)

Many thanks. Dedhert.Jr (talk) 03:56, 8 August 2024 (UTC)

Cleaned up the article 7

Hi, I just went through the mathematical facts on the article 7 with a bit of a blowtorch and removed a lot of trivial, not well connected to the number 7, or inaccessible mathematical facts about the number. I might go through other articles like this but I wanted to first get feedback here. Allan Nonymous (talk) 15:55, 5 August 2024 (UTC)

Looks good. A lot of our number articles have been accumulating a similar amount of cruft, thanks in part to the efforts of one editor in particular. One small critique: I would be inclined to restore the fact about 7 being the most likely roll for a pair of six sided dice. Tito Omburo (talk) 16:05, 5 August 2024 (UTC)

Definitely a good fact to restore. Mathwriter2718 (talk) 16:32, 5 August 2024 (UTC)

It's still there. XOR'easter (talk) 16:43, 5 August 2024 (UTC)

That looks like a good trim overall. I might quibble on the details later, but it seems mostly fine. XOR'easter (talk) 17:43, 5 August 2024 (UTC)

An edit removing that much material deserves a thorough review to ensure there is not any rescueable content that was deleted. Maybe we can even update the guidelines to specify what kind of facts are considered interesting enough to include and what is cruft, considering how much work there is to do on the number pages. @Dedhert.Jr asked about such a guideline in Wikipedia_talk:WikiProject_Numbers#Interesting_properties. Mathwriter2718 (talk) 17:51, 5 August 2024 (UTC)

I 100% agree, feel free to go in and add back (in a more clear and concise way) some of the facts deleted if there is a consensus to do so. Allan Nonymous (talk) 19:34, 5 August 2024 (UTC)

I, for one, am happy to see cruft removed from our number articles. I was working on that for a while but kind of gave up after Wikipedia:Articles for deletion/198 (number) (2nd nomination) last year. But although many of the listed mathematical properties in these articles are crufty and uninteresting, I think a bigger cause of cruft is the use of numbers as identifiers rather than for their numeric value (for instance as numbers of highways, bus lines, etc), which to my mind should go on separate disambiguation pages rather than on articles about the numbers themselves. —David Eppstein (talk) 19:42, 5 August 2024 (UTC)

Note: following the positive feedback here, I have gone through other number articles, especially (shudders) 744 (Number). Frankly, I think its fine time we write up a WP:NOTOEIS policy to prevent so many of these "xth number with y property" entries. Allan Nonymous (talk) 19:46, 5 August 2024 (UTC)

Perhaps it is time for WP:NOTOEIS, though I don't have enough experience with number pages to know if this is actually necessary.

The most obvious content for removal is of the form "number x is associated with number y, and number y has property a" on pages for number x. See https://en.wikipedia.org/w/index.php?title=744_(number)&diff=1238550872&oldid=1230509719 for an example. Even if both statements are valid on their own, the fact that number y has property a should still typically not be on the page for number x.

Statements of the form "number x has property a" are, in my opinion, valid if and only if property a is sufficiently interesting, as are statements of the form "number x is the yth number with property a". It's not clear to me that mentioning that it is the yth is usually any more helpful than just saying "number x has property a", unless y is very small. For example, the page for 45 should probably say that 45 is a triangle number, but I can't convince myself that saying it is the 9th triangle number is any more helpful. On the other hand, maybe the page for 3 should say that 3 is the first non-even prime. Mathwriter2718 (talk) 20:04, 5 August 2024 (UTC)

Perhaps a guideline might say that OEIS is a reliable source but it cannot be used to establish notability of a fact. Mathwriter2718 (talk) 20:09, 5 August 2024 (UTC)

My personal inclination is that a number appearing in an OEIS entry is only worth mentioning if the sequence is "nice", "core" (of central importance to some topic), or "hard" (which often means that it comes from an unsolved problem). Because the source is reliable but intentionally rather indiscriminate, we should focus our attention on the subset of it that is marked as more interesting than the rest. Or, in other words, we should follow the source when it comes to emphasis. XOR'easter (talk) 20:17, 5 August 2024 (UTC)

We might get almost the same effect by only mentioning properties or sequences that have bluelinked Wikipedia articles. —David Eppstein (talk) 20:24, 5 August 2024 (UTC)

Yes, that sounds plausible. XOR'easter (talk) 20:37, 5 August 2024 (UTC)

I think OEIS needs to be treated with caution, essentially as a WP:PRIMARY source. Tito Omburo (talk) 20:54, 5 August 2024 (UTC)

See the discussion now at Wikipedia talk:What Wikipedia is not#WP:NOTOEIS. XOR'easter (talk) 21:05, 5 August 2024 (UTC)

Regarding this problem being related to OEIS, do we have to check again whether OEIS is questionably reliable? This was discussed when I was reviewing 69 (number) to become GA. Maybe, just maybe, just in case, some points of view can be included to support the new additional guidelines we have discussed right now. Dedhert.Jr (talk) 02:12, 6 August 2024 (UTC)

In my view, OEIS is entirely reliable; its edits go through a very strict hierarchy of multiple reviewers, much like a peer-reviewed journal. This process has led it to be much less error-prone than many other sources such as Wikipedia or (worse) MathWorld. What it does not provide is depth of coverage of individual numbers, such as would be needed for WP:GNG-based notability. And because the choice to include a sequence is WP:ROUTINE, it does not tell us much about the notability of individual sequences. —David Eppstein (talk) 17:06, 6 August 2024 (UTC)

I agree with this. XOR'easter (talk) 17:26, 6 August 2024 (UTC)

I think OEIS is reliable (though not a good indicator of notability). Mathwriter2718 (talk) 17:28, 6 August 2024 (UTC)

There is a related discussion (also opened by @Allan Nonymous) at Wikipedia_talk:WikiProject_Numbers#Help_remove_WP:CRUFT_on_number_articles!. Mathwriter2718 (talk) 15:39, 7 August 2024 (UTC)

The article 7 has a long but nowhere near complete section (previously titled "History", which I moved to 7 § Numeral shape) about the way the glyph is drawn in various countries and historical periods. This seems off topic or at least out of scope for an article about the number 7 per se. Should there be dedicated articles about individual numerals and the history of their visual representation in various written number systems? (While we are at it, {{Infobox number}} is an egregious waste of space.) –jacobolus (t) 03:37, 6 August 2024 (UTC)

I think it makes sense to have a section about how 7 is drawn in the article for 7. Mathwriter2718 (talk) 10:53, 6 August 2024 (UTC)

If I may stick my nose in here: user @Allan Nonymous seems to be edit warring on a number of number pages. Reviewing the edit history for number one, I see the removal of all interesting and spicey mathematical facts, leaving behind a bland, tasteless and boring section on math. Whatever your views on cruft may be, the reality is that math is widely misunderstood in Western Culture, often taken to be "boring". Most of us here have the opposite experience: we know how interesting, exciting and even mind-boggling it is. To take the numbers articles, and remove everything that is mathematically interesting and exciting from them just reinforces the ugly stereotype that "math is boring". Let's not do this. 67.198.37.16 (talk) 19:06, 7 August 2024 (UTC)

Oh, foo. I now see that some of this is related to the histrionics from User:Radlrb, above, in the discussion about number 1234. While not a fan of histrionics, there are the unresolved questions of "what makes mathematics interesting?" and "how should enthusiastic compilations of facts about numbers be treated in Wikipedia?" For example, looking at the dozens (hundreds?) of articles on Lie algebra theory, we see that they are often extensive compendiums of factoids and trivia, but we have no problem with that content. We enjoy things like Jacques's titilating Tits buildings. But the trivia and factoids added & removed for 1234? Not so much, it seems. Part of me wants to encourage amateur enthusiasts. A different part of me says "take it to youtube if you think it's interesting." Beats me. 67.198.37.16 (talk) 19:56, 7 August 2024 (UTC)

I'm not sure about Lie algebra pages, but I routinely find mathematical articles on Wikipedia that are very short on context, history, and basic explanation but have long lists of obscure trivial formulas etc. I for one would be very happy to see some of that cruft cleaned up and the space used for material that would be reasonably found in a well written survey paper. –jacobolus (t) 02:14, 8 August 2024 (UTC)

Obscure factoids are fine if there exist reliable secondary sources. But for a lot of these number edits, the only source for some property is OEIS, and often it's a "second order" property that requires combining two OEIS entries, or counting the number of things in an OEIS entry. OEIS is a primary source, and this kind of original research is expressly forbidden (and specifically called out at WP:PRIMARY). Tito Omburo (talk) 13:15, 8 August 2024 (UTC)

I agree with you that the most pressing problem is not obscurity but OR. I think the introduction of the term "cruft" to these discussions might have lead us to focus in the wrong direction. Mathwriter2718 (talk) 14:13, 8 August 2024 (UTC)

To take the numbers articles, and remove everything that is mathematically interesting and exciting from them just reinforces the ugly stereotype that "math is boring". Let's not do this. Yep. Please don't throw the baby out with the bathwater. I'm more than happy to go through anything at 1 which is deemed unsuitable but this was GA quality content. Polyamorph (talk) 23:38, 7 August 2024 (UTC)

but this was GA quality content Meh! Still lack of sources. Demoted to C-class per both WP:QUALITY and this assessment project. Dedhert.Jr (talk) 02:30, 8 August 2024 (UTC)

I'm talking about some of the prose I added, not the article as a whole. Polyamorph (talk) 04:33, 8 August 2024 (UTC)

Optimisation under uncertainty

I've noticed that we have a few articles related to it (Stochastic optimization, Robust optimization) but there is no article which gives a general overview of the topic. Do you think it would make sense to create it? Would it be better to describe methods like chance constraints programming in a that article or to add them to Stochastic optimization? Alaexis_¿question? 16:01, 3 August 2024 (UTC)

I've created an article about chance constrained programming for a start, I'd be grateful if someone could review it. Alaexis_¿question? 07:23, 10 August 2024 (UTC)

Presently, it is too abstract to make sense to me. Please, add at least one simple example and show how it fits the abstract model. JRSpriggs (talk) 12:54, 10 August 2024 (UTC)

Thanks for the feedback, I'll try to add something over the next few days. Alaexis_¿question? 19:46, 10 August 2024 (UTC)

Does this project cover numeral systems?

I was having a similar discussion on Wikipedia talk:WikiProject Numbers, but they didn’t have a clear answer yet –it would be great if someone could make it’s more clear. Legendarycool (talk) 22:41, 19 August 2024 (UTC)

If you run into conflict or some other difficulty in articles about numeral systems, you can certainly bring discussion here for more eyes. Is there something specific you are interested in / working on? –jacobolus (t) 00:54, 20 August 2024 (UTC)

No nothing at the moment, just for future reference. Legendarycool (talk) 02:02, 20 August 2024 (UTC)

TFL List of Johnson solids

Participants of this member are allowed to give opinions on whether the article List of Johnson solids is submitted on a given date. Dedhert.Jr (talk) 05:05, 20 August 2024 (UTC)

Template:Equation in andriod dark mode

A couple of users complain that equations in boxes are not viewable on Android in dark mode. The highlighting of the box is a nice-to-have. Is there any workaround short of removing the template? Johnjbarton (talk) 14:55, 14 August 2024 (UTC)

Oh, turns out the template is "Equation box 1" (ugh) and there are some hints about dark mode issues. Johnjbarton (talk) 15:20, 14 August 2024 (UTC)

I partly fixed this issue, but it turns out this template is mainly used in physics articles. Johnjbarton (talk) 18:10, 15 August 2024 (UTC)

Another problem is {{Dynkin}}. Tito Omburo (talk) 16:40, 20 August 2024 (UTC)

Skolem's Paradox

Hello WikiProject Mathematics. Recently I noticed that the article Skolem's paradox had very few inline citations, so I decided to fix the refs and tweak some things. Now I've been working on it enough that I'd like to take it to GA review, but I would really appreciate if anyone could read through it first, especially someone with the knowledge to verify the "The result and its implications" section. I think that the first "formal" explanation of the paradox in that section is a bit weak. Thanks, Pagliaccious (talk) 01:20, 21 August 2024 (UTC)

Requested move at Talk:Hilbert system#Requested move 20 August 2024

There is a requested move discussion at Talk:Hilbert system#Requested move 20 August 2024 that may be of interest to members of this WikiProject. Rotideypoc41352 (talk · contribs) 21:54, 21 August 2024 (UTC)

Uncited and vague statement at Trigonometric functions

This line in Trigonometric functions is tagged for temporal vagueness and needing a reference: The modern trend in mathematics is to build geometry from calculus rather than the converse. Is this remark actually true, and if so, is it worth saying in that spot? It seems to me that talking of a singular "trend" in mathematics is likely to be unsupportable. If one is doing coordinate geometry, one might found it upon properties of the real numbers as developed in real analysis, which is the sophisticated version of/groundwork for/elective taken after calculus. But to a reader for whom geometry is a prereq to calculus, this statement is probably rather puzzling. XOR'easter (talk) 23:21, 21 August 2024 (UTC)

This seems more or less right, but may be unnecessary here, and could be significantly elaborated. Our description both here and at trigonometry and history of trigonometry is extremely incomplete. As for when this occurred, as concerns trigonometry per se this approach more or less originates with Euler, but picked up steam with Fourier series and then efforts to make them more rigorous in the 19th century, and by studies of elliptic functions, &c. With respect to geometry more generally, I'd also say this is a trend, with pure mathematicians treating geometry as founded in analysis (and its offshoots of topology and set theory), more and more over time starting in the 18th century but since the 20th century almost completely. You could extend this general trend earlier if comparing the gradual substitution of coordinates and analytic geometry in preference to Greek definitions and "synthetic" methods. –jacobolus (t) 00:11, 22 August 2024 (UTC)

I've given it a go, but I think the article needs some organizing. Also, there is no mention of asymptotes. Tito Omburo (talk) 01:14, 22 August 2024 (UTC)

I'm not sure the gesture toward G. H. Hardy is any more helpful to readers than the previous vague handwave about trends away from geometry. I'd just cut those prefatory sentences and discuss the broader context more thoroughly in the history section and in history of trigonometry.

This and related articles could definitely use organizing. There could also be separate articles about tangent (trigonometry) and secant (trigonometry) to go along with sine and cosine, which would leave more room for discussing more specific history, applications, etc. –jacobolus (t) 05:06, 22 August 2024 (UTC)

A problem with the previous vagueness is that it was an unreferenced point of view. Also, the assertion that there are "two ways" to define the trigonometric functions was flat out wrong. Hardy lists four, not including the first one described in the article (which I found in Bartle and Sherbert). Tito Omburo (talk) 09:58, 22 August 2024 (UTC)

A minor point: I don't understand why there's so much name-dropping/attribution in your addition. One can write "there is a problem with geometry as a definition.[ref: hardy] there are mutliple modern approaches to fix this: (1)(2)(3)(4).[refs:hardy, bartle-sherbert]" What is added by announcing at the beginning of these sentences that the references at the end of the sentence are written by Hardy and by Bartle--Sherbert? --JBL (talk) 17:54, 22 August 2024 (UTC)

I'm not married to the wording, but it seems like this is the basic content and sources that should be there. Tito Omburo (talk) 20:31, 22 August 2024 (UTC)

This discussion might better be moved to talk:trigonometric functions, but @Tito Omburo you should give a source for "amplitude function", "method of amplitudes", etc. These are extremely rare names I have never heard of after spending many hundreds of hours researching the specific topic of the trigonometric half-tangent, and can't find any mention of in a google scholar search. –jacobolus (t) 21:45, 22 August 2024 (UTC)

It's just the amplitude of $x iy$, but I'll get rid of the neologism. I thought I had seen this in Bourbaki's real variables, but now it seems I was mistaken. Tito Omburo (talk) 22:26, 22 August 2024 (UTC)

"Build geometry from calculus"? What is being referred to here? Michael Hardy (talk) 02:35, 22 August 2024 (UTC)

I'd say that The modern trend in mathematics is to build Euclidean geometry from calculus rather than the converse. is generally true, but that the more general statement is false. I'm having trouble coming up with a replacement that is both accurate and concise enough to be in the lead. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:12, 22 August 2024 (UTC)

This statement is basically true from the perspective of a differential geometer, but not from the perspective of an algebraic geometer. I think this statement should be expanded upon or removed because it is just way too vague to be helpful. In the context of trig, it might be more helpful to say that nowadays people define trig functions using calculus and then define angles using trig functions. Mathwriter2718 (talk) 13:39, 22 August 2024 (UTC)

Convex polyhedron

The article Convex polyhedron is currently under the article's redirection Convex polytope. Our articles have several type of convex polyhedrons: Platonic solid, Archimedean solid, Catalan solid, deltahedron, Johnson solid, and many more. The article convex polyhedron should have redirected into Polyhedron#Convex polyhedra. It seems convex polytope describes the generalization concept. Dedhert.Jr (talk) 09:15, 23 August 2024 (UTC)

I'll do this change, since readers interested in convex polyhedra need not know dimensions higher than 3. D.Lazard (talk) 09:25, 23 August 2024 (UTC)

"Multiplicity of a restricted root" listed at Redirects for discussion

The redirect Multiplicity of a restricted root has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 August 21 § Multiplicity of a restricted root until a consensus is reached. 136.152.209.125 (talk) 04:24, 24 August 2024 (UTC)

Rhombic icosahedron and Springer

The Springer source [16] states that it is false in our Wikipedia that rhombic icosahedron is the dual polyhedron of a pentagonal gyrobicupola. I am surprised this fact still exists nowadays. Any thoughts? Dedhert.Jr (talk) 11:13, 26 August 2024 (UTC)

The Springer source is correct. The rhombic icosahedron has adjacent degree-5 and degree-3 vertices, so the dual should have adjacent pentagons and triangles, as shown in the figure in the Springer source. The pentagonal gyrobicupola has the correct numbers of faces of each type but incorrect adjacencies; its pentagons and triangles are not adjacent. I will remove this mistake from our article. —David Eppstein (talk) 17:22, 26 August 2024 (UTC)

Sep 2024

Updates to "Math theorem" Templates: Improved style and new proof parameters

Currently, there are two templates for inserting formatted theorems and proofs into articles: {{Math theorem}} and {{Math proof}} In many cases, however, the proof of a theorem directly follows the theorem. The formatting when juxtaposing these templates is not great, however:

Theorem — My theorem statement.

Proof

My proof statement.

I have written a modified version of {{Math theorem}} (see {{Math theorem/sandbox}}, at [this revision]) to improve the formatting by incorporating the proof as a new parameter for {{Math theorem}}, and also bringing the default formatting of theorems in line with typical math texts:

Theorem. My theorem statement.

Proof. My proof statement.∎

Please join the conversation at Template talk:Math theorem there if you have opinions about the proposed change. The-erinaceous-one (talk) 04:50, 2 September 2024 (UTC)

Can you give examples of articles where you think this template should be used? Personally I find that most of the time ordinary paragraphs are sufficient for theorem statements and proofs (in some articles where authors put theorems in flashy boxes, sometimes with color, etc., I have found the decorations more distracting than helpful). Proofs are helpful in particular in articles that are directly about a theorem or a few theorems, or occasionally in articles where a particular theorem is fundamentally important to the topic, but in cases I'm thinking of collapsing the proofs would defeat the point of including them. Most of the rest of the time I'd skip the proofs altogether (proofs in external resources can be linked from footnotes, or if a proof seems distracting but necessary, it could be put in a footnote in full). –jacobolus (t) 06:35, 2 September 2024 (UTC)

I envision the new version of the template replacing the current {{Math theorem}} template and also being used anywhere else that a formal theorem statement could be useful. As you noted, many pages currently display theorems and proofs in boxes, which I agree are undesirable. Editors might sometimes intentionally add boxes around theorems and proofs, but I think in many cases they simply use {{Math theorem}} because they assume it is the "standard" Wikipedia formatting of theorems. By updating the template, we would improve the formatting across all of those pages that use it and discourage editors from doing ad-hoc formatting of theorems (e.g., boxes and colors).

Regarding the formatting of proofs, I'm not married to the idea of making the proofs collapsed by default, or, in fact collapsible by default. We could choose the default to not make proofs collapsible and then allow editors to enable it using a parameter flag. I am also looking into adding another parameter that allows displaying the proof in a footnote, although I personally find this a worse option than a collapsible box since it requires readers to scroll up and down if they want to see the theorem while reading the proof.

One example of a page that would benefit from a nicely formatted Theorem template is Liouville's theorem (Hamiltonian). Despite the name of the page including "theorem", there is not a formal statement of the theorem. The closest thing it has is

The distribution function is constant along any trajectory in phase space.

but this doesn't state the formal assumptions of the theorem. The-erinaceous-one (talk) 22:58, 2 September 2024 (UTC)

I was looking around for an example of a proof in the footnote, but didn't find one quickly. Here's what I have tried for the {{Math theorem}} template.

Theorem. Mathy mathy math.

The-erinaceous-one (talk) 23:27, 2 September 2024 (UTC)

I would recommend against replacing the previous template, since authors who used it were intending the behavior as provided at the time, not an entirely different appearance chosen by someone else later. I also disagree that Liouville's theorem (Hamiltonian) would benefit from having parts of it wrapped in boxes or reformatted. Ordinary paragraphs are working fine there. In my opinion you should make a new template under a new name if you want it, and then adopt it on pages you write yourself or do significant work on, but should leave other pages alone. Aside: your sandbox version probably has some kind of malformed HTML which causes it to render outside of a colon-indented talk page response (which uses a definition list element). –jacobolus (t) 23:44, 2 September 2024 (UTC)

It looks like the existing template does not work well in lists either. [Edit: I placed an example here, but it broke our ability to use the "reply" editor]. The-erinaceous-one (talk) 00:07, 3 September 2024 (UTC)

Regarding Liouville's theorem (Hamiltonian), I think a weakness of that page is that it is difficult to figure out what "the theorem" actually says. First you have to search through the page to find the quoted text I copied above (which is not clearly labeled as the theorem). Then, you have to reconstruct and/or guess what the assumptions of the theorem are from the rest of the article. The-erinaceous-one (talk) 00:13, 3 September 2024 (UTC)

In other words, it's a typical explanation of something that physicists call a theorem. XOR'easter (talk) 02:31, 3 September 2024 (UTC)

Skimming through links at Special:WhatLinksHere/Template:Math theorem and Special:WhatLinksHere/Template:Math proof, these templates aren't really all that widely used, and in my opinion most of the articles where they are used would be improved by avoiding the templates (and sometimes taking out the proofs). YMMV. –jacobolus (t) 06:51, 2 September 2024 (UTC)

Their usage might not be ubiquitous, but 400 pages is not insignificant and improving the available template(s) would improve those pages and making nicely formatted theorems and proofs easier. Regardless, the {{Math theorem}} template already exists and is used, so the question is whether the proposed changes would be improvements---not whether we should completely stop using it. The-erinaceous-one (talk) 23:01, 2 September 2024 (UTC)

Also, many of the pages I've opened up use the templates multiple times, so the total number of uses is well over 400. The-erinaceous-one (talk) 00:34, 3 September 2024 (UTC)

Yeah, if it were up to me at least half of those would not have any such template. But it's disruptive to make changes like this at large scale. People should feel free to use this list as inspiration for finding articles which could be improved, including by removing the templates. –jacobolus (t) 01:45, 3 September 2024 (UTC)

I agree with @jacobolus that we don't want to put too much emphasis on proofs. Many articles would actually benefit from removing some of their proofs. This has been discussed multiple times on WPM. From the Proofs section of MOS:MATH: A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result. In many cases it would be more beneficial to work on replacing the proofs with some suitable references to reputable sources instead of incorporating them into some new template. PatrickR2 (talk) 03:19, 3 September 2024 (UTC)

Even without the issue of incorporating proofs or not, I often find the current template (and the new template) which wraps the result in a "template box" to be distracting and annoying. In articles that discuss multiple results, it gives undue weight to those that happen to have an official name of "Theorem of Such-and-such" compared with those results that don't. That unnecessarily breaks the flow of exposition. Better use something less intrusive like "Theorem of such-and-such: statement ..." in the text itself. One case where the template could be justified is an article or section dedicated to a single theorem. But most of the time, the use of the template seems misguided to me. PatrickR2 (talk) 03:28, 3 September 2024 (UTC)

References

There are two different matters: how to update the current theorem template and whether its use is appropriate. I commented on the first in the talk page of the template and so here I comment on the second. As someone who actually likes using the template (and the one who actually imported the template from French Wikipedia), I think it depends on how it is used within an article. I agree in some instances, boxes can be jarring especially if there are too many of them. On the other hand, emphasizing a statement in some way is a good idea in some other instances. The axiom of choice articles gives a good example in my opinion: since the article is about a single statement. (As the proof template, I have never used it personally but apparently some people like it) —- Taku (talk) 08:26, 3 September 2024 (UTC)

Square bipyramid proposal to split

Discussion on splitting article the square bipyramid is ongoing. See Talk:Octahedron#Create a square bipyramid or regular octahedron article. More opinions are welcome. Dedhert.Jr (talk) 11:08, 4 September 2024 (UTC)

Help needed on several elementary articles

Farkle Griffen made many edits on several elementary articles including Variable (mathematics), Mathematical object, Indeterminate (variable) and several others. Generally, these article are of low quality, but IMO, most of their edits are disimprovements, as consisting generally of misinterpretations of randomly chosen sources. One of their typical edit is to change the first sentence of Variable (mathematics) from "In mathematics, a variable is a symbol, typically a letter that is used for naming a mathematical object, often a number" to "In mathematics, a variable is a symbol, typically a letter, that holds a place for constants, often numbers".

I must stop to revert them, because WP:3RR, and because of the lack of third party input, I cannot open an ANI thread for disruptive editing (this appears as content dispure).

So, I need some help. D.Lazard (talk) 18:36, 5 September 2024 (UTC)

Mathematical object seems broadly improved. Variable and indeterminate seem tricky to me. There's at least one way these are different, in that variables usually have a domain, while indeterminates are purely formal symbols. (E.g., random variable, real variable, etc.) But many people in casual discourse make no such distinction. Tito Omburo (talk) 18:53, 5 September 2024 (UTC)

Eigenmode vs. eigenmodes (redirects)

Currently,

• eigenmode redirects to Eigenvalues and eigenvectors, and
• eigenmodes redirects to Normal mode.

This is obviously confusing, because eigenmodes ([[eigenmode]]s) and eigenmodes ([[eigenmodes]]) are different link destinations.

Suggestion: the plural redirect [[eigenmodes]] should point to Eigenvalues and eigenvectors, just like the singular version. Thoughts?  — sbb (talk) 03:30, 5 September 2024 (UTC)

The word “mode” (with or with prefix) does not appear at Eigenvalues and eigenvectors; should it? 100.36.106.199 (talk) 10:36, 5 September 2024 (UTC)

I believe that the best way forwards is to look at all of the articles on eigenfunction, eigenmode, eigenstate, eigenvector and normal mode collectively, then discuss what to merge and what to redirect. As part of this, the redirects for singular and plural should be brought into alignment with each other after looking at what links to what.

My first take is that eigenfunctions and eigenvectors should be in the same article, but I could make a case for keeping them separate. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:52, 5 September 2024 (UTC)

Clearly the target of any of these links should not depend on whether it is plural or not. That's easy to fix.

I think Eigenfunction should be kept separate from Eigenvalues and eigenvectors, since the latter article is necessarily focused on linear endomorphisms in general, whereas the former should be focused on the specific application to function spaces. It's fine to leave a summary in Eigenvalues and eigenvectors § Eigenvalues and eigenfunctions of differential operators pointing to Eigenfunction as a main article. –jacobolus (t) 17:25, 5 September 2024 (UTC)

A mode is a standing wave. See eg https://www.feynmanlectures.caltech.edu/I_49.html#Ch49-S5

In mathematical models of wave systems these standing waves appear as "eigenfunctions", also called "eigenvectors" in some representations. A mode, a wave concept, is not a synonym for "eigenfunction", a mathematical concept.

Absent a significant reliable reference, "eigenmode" should be deleted. The word is redundant by repeating itself. Similarly "eigenmodes". Without a reference having these pages is misinformation. Johnjbarton (talk) 15:34, 5 September 2024 (UTC)

According to Eigenmode expansion, eigenmode is a specific term-of-art for solutions of the Maxwell equation along a waveguide. This usage seems to be consistent with many of the hits in a cursory Google scholar search. Tito Omburo (talk) 17:19, 5 September 2024 (UTC)

Thanks, but I disagree with your characterization based on the three sources in that page. None of these references define "eigenmode" and as far as I can tell they only use the word as a modifier as in "eigenmode propagation algorithm".

The solutions to Maxwell's equations along a waveguide seems to be just "modes". Jackson discusses "wave guides" in section 8.3 and says:

• "There will be a spectrum of eigenvalues and corresponding solutions which form an orthonormal set. These different solutions are called the modes of the waveguide.

Here is a review of quantum optics that uses the word 'mode' many times, but 'eigenmode' rarely and inconsistently.

• Fabre, Claude, and Nicolas Treps. "Modes and states in quantum optics." Reviews of Modern Physics 92.3 (2020): 035005.

My guess is that "eigenmode" has a specific technical meaning like you say. But what meaning?

Based on what we know so far, "eigenmode" should redirect to Eigenmode expansion since at least the word is used there. Johnjbarton (talk) 19:38, 5 September 2024 (UTC)

Ok I think I found a review that sorts this out at least for radio waves:

• Huang, Shaode, Jin Pan, and Yuyue Luo. "Study on the relationships between eigenmodes, natural modes, and characteristic modes of perfectly electric conducting bodies." International Journal of Antennas and Propagation 2018.1 (2018): 8735635.
  • Eigenmode expansion method (EEM) [3], singularity expansion method (SEM) [4], and characteristic mode analysis (CMA) [5] are three common modal analysis methods in electromagnetic engineering. The three modal analysis methods result in three different kinds of modes generally, that is, eigenmodes, natural modes, and characteristic modes, respectively.

Based on this reference (and thus restricted to the corresponding field), "eigenmode" is not a synonym for "eigenvector" or "normal mode", but a specialized term related to the "eigenmode expansion method". Johnjbarton (talk) 19:57, 5 September 2024 (UTC)

The edit history for the eigenmode redirect shows that it used to point to Normal mode, but the latest (Oct 2022) edit by Constant314 (talk · contribs) states "Eigenmode is much more general that normal mode. When modes are mapped onto a vector space, a mode becomes a vector. Hence, eigenmode and eigenvector are nearly the same thing", and was changed to point to Eigenvalues and eigenvectors.

I can't comment on whether or not the edit comment is correct, but that was the rationale/statement.  — sbb (talk) 23:22, 5 September 2024 (UTC)

Just some random , unauthoritative thoughts.

• An eigenmode is a mode (whatever that is) that can be mapped onto an eigenvector. More specifically, the numbers that describe the mode can be the components of an eigenvector. Doing that allows the machinery of linear transformations to be used to analyze the mode. Casually speaking, we may say that an eigenmode is a type of eigenvector. Of course, speaking more formally, we mean that the numbers that describe the eigenmode are treated as components of eigenvectors. Again, speaking casually, we say that an eigenmode is an eigenvector, but we do not say that (all) eigenvectors are eigenmodes.

• An electromagnetic field mode is any configuration of the electromagnetic field that satisfies Maxwell’s equations, the constitutive equations, and the boundary values. Solution and mode are used interchangeably. I have not heard the term eigen-solution.

• Mode is not restricted to mean an electromagnetic field mode.

• The voltages and currents of multi-conductor transmission lines are analyzed by the use of eigenmodes.

• It is not an eigenvector unless it is associated with a linear transformation which has an input vector and an output vector.

• The Eigenmode expansion article seems underdeveloped and focused on waveguides. There are no in-line citations in the body of the article. Of the three citations, two are used to establish the name and the other establishes that the method is useful. The external link leads to a not found page. The term eigenmode has been in use since the 1950’s and predats any of the references. I hesitate to redirect anything to this article.

• The Eigenvalues and eigenvectors article is more fully developed. It does not contain the word “eigenmode”, but it does contain “vibrational modes” and maps them to eigenvectors. I have no problem with redirecting eigenmode to Eigenvalues and eigenvectors. Eigenmode is a much broader subject than is covered by the Eigenmode expansion article.

Constant314 (talk) 17:00, 6 September 2024 (UTC)

As far as I know, the level of development of an article is not a criteria for redirects nor are unauthoritative thoughts. My unauthoratative take is that 'eigenmode' is used in different ways in different subfields and mostly as an informal synonym for 'mode' because that does not sound fancy enough.

I have provided a reference that identifies "eigenmode" as a type of "mode". This particular type of mode is discussed in sources listed in eigenmode expansion. So far these are the only source we have that discusses "eigenmode" directly. (Many sources use 'eigenmode' in the sense of 'eigenmode expansion'.) Asserting that 'eigenmode' is a much broader subject and predates the 1950s doesn't really help us here. We can't verify you ;-).

Even with a source that shows 'eigenmode' is an 'eigenvector' representation of a mode, I still do not agree that this redirect to eigenvalues and eigenvectors makes sense. A specialized, modified noun should redirect to the noun, not the adjective. Moreover, all the sources indicate that 'eigenmode' is associated with physics and engineering, not mathematics as topic.

A reasonable alternative to eigenmode expansion could be a redirect to normal mode. Johnjbarton (talk) 17:32, 6 September 2024 (UTC)

I don't think normal mode is a candidate. It is clearly talking about resonances at a fixed frequency. The eigenmodes of a waveguide have a continuous frequency spectrum. Further, it describes a mode as a standing wave. The eigenmodes of waveguides are traveling waves. Constant314 (talk) 21:37, 6 September 2024 (UTC)

Yes, I agree. I think normal mode should be renamed "Mechanical mode" or similar. What if we merge transverse mode and longitudinal mode into eg "Waveguide modes" and add a short section on "eigenmodes"? Johnjbarton (talk) 23:14, 6 September 2024 (UTC)

Of course! We also have Mode (electromagnetism). Bah. Johnjbarton (talk) 23:32, 6 September 2024 (UTC)

I share your frustration. Wikipedia has never been accused of being overly organized. I did not take part in the seminal conversations that established Wikipedia culture, but it seems to have settled to this: verifiability takes priority over completeness which takes priority over avoiding redundancy. You are welcome to reorganize, but don't lose anything. Sound also has longitudinal modes, transverse modes (in solids), and waveguides. You cannot just absorb those into Mode (electromagnetism) or Waveguide modes. However, both of those could use an expanded section on transverse and longitudinal modes. Constant314 (talk) 03:22, 7 September 2024 (UTC)

Redundancy is totally fine in my opinion (and by Wikipedia convention), as long as (1) each subject is encyclopedic ("notable"), (2) the scope of each article is reasonably clear and not entirely overlapping, and the article is reasonably complete and balanced within that scope without putting undue weight on minor aspects of the topic or fringe viewpoints, (3) each article is moderately self-contained and accessible, not dependent on text in other articles, (4) related articles are each correct, don't contradict each-other, reflect the consensus of reliable sources, (5) related articles link to each-other so that readers can find the information they are looking for, and maybe some others I'm not thinking of. With that said though, also feel free to reorganize material by moving it from one article to another, merging articles together, splitting them apart, etc. if a different high-level inter-article organization seems clearer. –jacobolus (t) 04:07, 7 September 2024 (UTC)

I updated Mode (electromagnetism) and included a sentence about eigenmode with the two refs I found. Johnjbarton (talk) 00:51, 8 September 2024 (UTC)

I just made an enquiry at the Teahouse about subpages. Seems that it is not allowed. I was referred to Wikipedia:Splitting. Noit sure if that helps. It looks like your main interest is the eigenmode redirect. Perhaps he should create an eigenmode stub which could point the reader to all the appropriate targets along with some commentary. Does that sound like a good idea? Or, even simple, create an eigenmode dab page. I may go ahead and do that.Constant314 (talk) 18:32, 8 September 2024 (UTC)

I essentially used the page Mode (electromagnetism) for the disambiguation purpose. I think that should be the target for the redirect unless we find a lot more sources and content. We could add an anchor to the paragraph. Johnjbarton (talk) 18:55, 8 September 2024 (UTC)

I am good with that. Eigenmodes is probably a little more general than that, but Mode (electromagnetism) is a probably a good redirect target. You have my support to make the change. I presume that include both eigenmode and eigenmodes. Constant314 (talk) 19:18, 8 September 2024 (UTC)

Thanks,  Done Johnjbarton (talk) 19:39, 8 September 2024 (UTC)

 Courtesy link: Wikipedia:Teahouse § Adding a subpage to an existing article—  jlwoodwa (talk) 20:46, 8 September 2024 (UTC)

Derivative article, again

Sorry, but can someone explain what does the IP say about the numerous references? The IP is known as the former professor, said by itself. Dedhert.Jr (talk) 00:45, 8 September 2024 (UTC)

Just looks like a rant to me, not a real edit request -- there is no concrete proposal to change any particular text to any other particular text that I can see. --JBL (talk) 00:57, 8 September 2024 (UTC)

They do have a point that the Gonnick source is wildly inappropriate. Tito Omburo (talk) 01:30, 8 September 2024 (UTC)

What's inappropriate about it? (Maybe, this discussion should be happening over there.) --JBL (talk) 17:48, 8 September 2024 (UTC)

Wikipedia articles should be based on scholarly sources, not comic books. Tito Omburo (talk) 19:40, 8 September 2024 (UTC)

It's a scholarly source in the format of a comic book. Gonick's three volumes on algebra, geometry, and calculus are each serious about what they cover and don't shy away from hard material; any one of them could be a course textbook. Sure, it makes sense to have multiple citations when a point has been addressed at multiple levels, but I don't see the point of removing citations just because the books they point to are less turgid than average. XOR'easter (talk) 20:58, 8 September 2024 (UTC)

We should probably round out our comic-book references by also citing Prof. E. McSquared's Calculus Primer: Expanded Intergalactic Version. –jacobolus (t) 21:04, 8 September 2024 (UTC)

Tangentially, that seems like a book it might be possible to write an article about, though the reviews I've found so far have been on the short side. XOR'easter (talk) 21:22, 8 September 2024 (UTC)

I'm quite happy with people making the topic entertaining if they're reasonably accurate. But some people think maths has to be po-faced and turgid so I guess another source should be provided as well to cater for them or this complaint will come up again. NadVolum (talk) 20:34, 8 September 2024 (UTC)

This footnote in Kelley comes to mind as an example of humor in a textbook. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:34, 9 September 2024 (UTC)

The sidenotes in Concrete Mathematics are a hoot. note: "What is a proof? 'One half of one percent pure alcohol.'" // "The ∑ sign occurs more than 1000 times in this book, so we should be sure that we know exactly what it means." note: "That's nothing. You should see how many times ∑ appears in The Illiad." // "... now [mathematicians] also have both floor and ceiling [notations]." note: "Next week we're getting walls." // "And the intervals [α..β) and (α..β], which contain just one endpoint, are defined similarly and called half-open." note: "(Or, by pessimists, half-closed.)" // etc. –jacobolus (t) 05:17, 10 September 2024 (UTC)

Not a textbook, but there's also the famous quip about Gauss

References

Category:Pyramids (geometry)

Sorry, but are icosahedral pyramids and gyroelongated square pyramid considered to be part of Category:Pyramids (geometry)? The pyramids are supposed to be a polyhedron in which triangular faces meet their common apex and connect the polygonal base in three dimensions. How are these both supposed to get along with the category, just because they are relatedly constructed by pyramids? I hope someone can explain me before the next edit warring happens again. Dedhert.Jr (talk) 13:01, 12 September 2024 (UTC)

Page move to Piecewise function

After some discussion at Talk:Piecewise_function#Requested_move_20_July_2024, the page Piecewise was moved to Piecewise function. I still consider this decision nonsensical, and the new title highly confusing. For this reason, I'd like to draw your attention to the move. If nobody else has a problem with it, I'll shut up. - Jochen Burghardt (talk) 18:05, 25 August 2024 (UTC)

In addition, a separate(!) DAB page Piecewise property has been created, which links most of its entries (like "Piecewise continuous") back to Piecewise function, where they are explained more or less satisfactorily. According to Piecewise_function#See_also, "Piecewise property" is a generalization of "Piecewise function"! - Jochen Burghardt (talk) 18:05, 25 August 2024 (UTC)

According to WP:NOUN the title should be a noun. For example, instead of "French", articles are titled "French language" or "French people". — Rgdboer (talk) 20:08, 25 August 2024 (UTC)

Or "piecewise property". The problem with "piecewise function" is not grammatical; it is that many of the things defined piecewise are not exactly functions. See e.g. piecewise linear manifold. —David Eppstein (talk) 20:27, 25 August 2024 (UTC)

I'd move Piecewise property to Piecewise, which if someone wants could be upgraded to a "broad-concept article", and leave a separate article at piecewise function, which should ideally contain quite a bit more discussion of piecewise polynomial "splines", piecewise parametric curves as used in CAD/CAM, and so on. –jacobolus (t) –jacobolus (t) 21:33, 25 August 2024 (UTC)

My point is that there is no such thing as a piecewise function. Every function can be defined using if . then . else . endif (linearizing 2dim math terminology), and every function can be defined without it. This is stated correctly in the 2nd lead sentence. In order to subsume also e.g. piecewise linear manifold, what about "Piecewise definition"? - Jochen Burghardt (talk) 21:52, 25 August 2024 (UTC)

every function can be defined without it While this is maybe true in a very narrow pedantic sense, the concept of a "piecewise function" has a clear, obvious, and useful meaning (which is why it is used in practice), and there are valuable things to say about it as a concept which would not be relevant to an article about "every function". –jacobolus (t) 09:27, 26 August 2024 (UTC)

Given a function by its domain, range, and graph, you can check whether it is piecewise linear, piecewise continuous, etc. (provided additional restrictions to domain and range are met). However, I doubt that you can check whether it is piecewise (without any property); I even don't know what that could mean. Moreover, different properties can require different domain decompositions, e.g. $f:\mathbb {R} \to \mathbb {R} ,x\mapsto \min\{1,x^{2}\}$ is piecewise differentiable (use $(-\infty ,1]$, $(-1, 1)$, $[1, \infty )$) and piecewise monotonic (use $(-\infty ,0]$, $(0, \infty )$). Also note the absence of any case distinction from this definition.

What we can say, however, is what a piecewise definition is (one that has an outermost case distinction on a domain decomposition into finitely many intervals). Based on this, we can define a function to be piecewise xxx if is has some piecewise definition such that each piece satisfies xxx (this is what the article does). Possible, this can also be generalized from total to partial orders to subsume also David Eppstein's piecewise linear manifold example. - Jochen Burghardt (talk) 13:22, 28 August 2024 (UTC)

Okay, but "take a function and determine whether it is 'piecewise'" is not really something anyone cares much about. Instead, people are interested in proving properties about functions defined or known to be definable in pieces (usually each piece of some specific type, such as constant, polynomial, rational, a linear combination of given basis functions, continuous with bounded derivative, ...), because such functions are extremely common in all sorts of practical applications. Calling these "piecewise functions" is common and well understood (Google scholar turns up 37k results for that phrase – much more common than alternatives I can find, so a good title following WP:COMMONNAME). Deciding that "there is no such thing as a piecewise function" is in my view a semantic quibble that kind of misses the point. –jacobolus (t) 15:54, 28 August 2024 (UTC)

I agree that the term “piecewise property” seems problematic since, unlike continuity or differentiability, it’s not something a function can have or not. “Piecewise-linear” is a property that a space or a function, etc. can have but that’s different. Since other editors have made the same point, I have started a move proposal: “piecewise property” -> “piecewise” at talk:Piecewise_property#Requested_move_26_August_2024. —- Taku (talk) 08:16, 26 August 2024 (UTC)

What about Piecewise-defined property? Surely we agree that a given definition of a property can be piecewise (or not)? The piecewise functions of calculus are perhaps piecewise elementary functions, for example. 100.36.106.199 (talk) 10:37, 28 August 2024 (UTC)

I've been an advocate of piecewise-defined, as grammatically preferable to the other options. Tito Omburo (talk) 10:57, 28 August 2024 (UTC)

Or, if it must be a noun, piecewise definition. —David Eppstein (talk) 17:49, 28 August 2024 (UTC)

1 for piecewise definition; that seems to get best at the correct concept. Piecewiseness is not a property of functions, but it is a property of definitions. --Trovatore (talk) 19:26, 28 August 2024 (UTC)

Sounds good to me, for the general concept article. Tito Omburo (talk) 19:42, 28 August 2024 (UTC)

Piecewise definition sounds good to me, too. XOR'easter (talk) 02:19, 29 August 2024 (UTC)

Sounds good to me, too. - Jochen Burghardt (talk) 11:52, 29 August 2024 (UTC)

Sure, let's do it. 100.36.106.199 (talk) 16:15, 29 August 2024 (UTC)

Definitely piecewise definition should be the title, and I'm surprised it isn't already. It is the definition, rather than the function itself, that is piecwise. Michael Hardy (talk) 05:50, 13 September 2024 (UTC)

Balinese numerals

The page for Balinese numerals lacks and graphical representation of the numerals so if someone could find some it would be appreciated. Legendarycool (talk) 23:17, 14 September 2024 (UTC)

Unicode mathematical letters block

Hi. Unicode has a Mathematical Alphanumeric Symbols block. For purposes of editing Wiktionary, I'm wondering which of these have set meanings that require their own entries, and which are simply letter variants. For example, using bold letters for vectors is a generic convention, but bold "𝐚" is just a variable without any set meaning, and it can therefore be made a redirect either to 'a' or to a page defining bold variables as vectors. However, ℋ is specifically the Hamiltonian and ℍ (and maybe 𝐇?) are the quaternions, so those should be defined individually.

The Unicode block is too large for me to expect a detailed answer here, but do you know of a reference that might guide me?

I understand that some of the mathematical symbols in Unicode are spurious, or are ad hoc conventions from some source that aren't followed by the mathematical community in general, but it would be nice to define the ones where there is some consensus. (And if there are conflicting consensuses, that's fine, we can always have multiple definitions.)

Again, this is for Wiktionary, but I thought here would be the place to ask. — kwami (talk) 06:54, 12 September 2024 (UTC)

You should definitely not use the unicode ℍ. Use <math>\mathbb{H}</math> instead, giving $\mathbb {H}$. See MOS:BBB. I suspect the same guidance should apply to many of the special unicode mathematics characters. For instance, if it's going to appear in a mathematical equation, the Hamiltonian symbol should probably be <math>\mathcal{H}</math>, ${\mathcal {H}}$, which looks nothing like the unicode to me, so if you mixed the two readers would likely be very confused. —David Eppstein (talk) 07:53, 12 September 2024 (UTC)

For WP, sure, but this is for the purpose of defining the Unicode character.

If the Unicode character doesn't match the <math> display that's supposed to be the same thing, that's presumably an issue with the fonts you have installed: the font called by your browser for a specific Unicode character is different from the font/style called by <math> function. Ideally they should look the same, but there's generally going to be some discrepancy between what we would like the text to look like and what the reader will actually see, unless we post PDF's. Regardless, the underlying data structure will have a use that we would like to define, and AFAIK we can't use <math> to generate entries for Wiktionary. — kwami (talk) 08:19, 12 September 2024 (UTC)

@Kwamikagami Are you sure this is a valuable project? In actual practice, professional mathematicians never use Unicode for mathematical symbols. They almost universally use a variant of Tex/Latex when formatting symbols and equations, corresponding to the <math> tags in wikipedia. PatrickR2 (talk) 19:25, 14 September 2024 (UTC)

Unicode is widely used in mathematical programming, e.g., Lean. And also in domains like industrial mathematics. Tito Omburo (talk) 19:34, 14 September 2024 (UTC)

It seems that in some cases \mathscr is used to display the Hamiltonian symbol. SilverMatsu (talk) 05:47, 15 September 2024 (UTC)

From that thread, if there's a demonstrable contrast between script and calligraphic letters, let me know and we can see about getting them into Unicode. But that may be resolved now - as described at Mathematical Alphanumeric Symbols, there are roundhand and chancery variants of the script letters, which might cover what that thread was calling script vs calligraphic variants. — kwami (talk) 06:34, 15 September 2024 (UTC)

mathscr does not work in the lobotomized version of LaTeX provided by Wikimedia. —David Eppstein (talk) 07:06, 15 September 2024 (UTC)

Ref spam check?

Could someone with more spare minutes than me take a look at this new user's contributions? They have a strong whiff of this to me but I don't have time to properly check. Thanks. JBL (talk) 19:33, 21 September 2024 (UTC)

It looks like this user is in the Albert-László Barabási school of network science. He's a real researcher but also known for some rather exaggerated or pseudo-scientific claims, see e.g. [17]. A textbook on random graphs like Bollobas' will be a vastly more reliable reference than any paper of Barabási's, or most papers in the 'network science' field. When it comes to wiki articles on network science itself, it's ok to use Barabasi's work as a reference. I would avoid it otherwise. Gumshoe2 (talk) 20:17, 21 September 2024 (UTC)

Ok, thanks -- I'm inclined to revert their edits (and have just done so at Graph (discrete mathematics), where they seemed particularly dubious (spammy, NPOV-noncompliant)). --JBL (talk) 20:16, 22 September 2024 (UTC)

That looks like a good revert. The added material was, at best, off-topic. Also, the source removed here was from 2002, pretty much the height of the "scale-free networks" hype era and before the people in that field were adequately scrupulous about things like testing whether a straight-ish line on a log-log plot really is a power law. XOR'easter (talk) 23:21, 22 September 2024 (UTC)

Review of the section "Universal algebra" of the article "Algebra"

The article Algebra is currently a candidate for featured article status. I was hoping to get some more feedback from reviewers. In particular, the 3 paragraphs of the section "Algebra#Universal algebra" need to be assessed for accuracy as the other parts of the article have already been reviewed. The nomination page can be found at Wikipedia:Featured article candidates/Algebra/archive1. Thanks for your time. Phlsph7 (talk) 07:51, 26 September 2024 (UTC)

MAA Reviews broke our links

503 pages currently link to URLs of the form maa.org/press/maa-reviews/*. Many if not all of these appear to be broken. www.maa.org needs to be changed to old.maa.org, as for example here. And sometimes maa.org needs an old. inserted before it, as for example here. Hopefully there is an automated tool that can be deployed for this. XOR'easter (talk) 08:30, 23 September 2024 (UTC)

Seems like a lot of MAA links are broken (not just reviews), but the reviews have the feature that they are recoverable. Now slightly below 500 (although some of those the search finds already have archived versions linked, which both means that for them the situation isn't too bad and that one should be a little careful with an automated fix). --JBL (talk) 00:28, 27 September 2024 (UTC)

At least we have a simple fix for these ones. I have yet to find a working replacement for the broken American Physical Society Fellow archive, to which we have many links. —David Eppstein (talk) 01:45, 27 September 2024 (UTC)

Which things that should not be included in mathematics articles?

In the article four-dimensional space, two users were edit-warring for whether to add video games about four-dimensional objects. The first reversion was because of the WP:BALANCE, and the replying showed a short summary, followed by blanks. Two video games that were added were the Miegakure and 4D Miner.

• https://en.wikipedia.org/w/index.php?title=Four-dimensional_space&action=history

Dedhert.Jr (talk) 09:39, 27 September 2024 (UTC)

I think it would be fine to add some content about 4D video games, but there should be secondary sourcing that puts it into context, not just a random selection of games that happen to have 4D elements. Ideally, the lead section of List of four-dimensional games should contain an introduction into the concept. A shorter version of that would then make sense in the four-dimensional space article. —Kusma (talk) 09:54, 27 September 2024 (UTC)

Are there any reliable sources at list of four-dimensional games? I think it needs to be in much better shape before it is worth summarizing at four-dimensional space. —David Eppstein (talk) 17:53, 27 September 2024 (UTC)

I don't have a problem with mentioning 4-dimensional video games in an article about 4-dimensional space, e.g. in the art section. It's probably not worth putting an extensive discussion there though; maybe more detail could fit at Fourth dimension in art or the like. Any material added to the 4-dimensional space article needs to be concise, supported by sources, and a neutral summary of the subject. –jacobolus (t) 22:01, 27 September 2024 (UTC)

A tip for fixing very old svg files

If (as I just did at File:Lattice in R2.svg) you encounter a really old svg illustration that is mysteriously missing much of its content, try looking for attributes like "xlink:href" in its source code. This attribute used to be used for referring to named objects defined elsewhere in an svg file, but it has been deprecated since 2018 or so when svg 2 was released. Some time in the last year the Wikimedia svg code was updated and stopped handling these. The fix is to replace "xlink:href" by "href". —David Eppstein (talk) 06:51, 27 September 2024 (UTC)

Hello David Eppstein. I happened to be reading Wikipedia:SVG help today, which suggests to exclusively use "xlink:href" rather than "href". This is completely outside of my area of expertise, but perhaps it would be worth updating this help page if Wikimedia has deprecated this. Kind regards, Pagliaccious (talk) 22:11, 27 September 2024 (UTC)

It's the SVG standard that deprecated it; Wikimedia is belatedly following suit. xlink:href also doesn't work in Chrome and in Adobe Illustrator; I don't know how long that has been the case. —David Eppstein (talk) 22:14, 27 September 2024 (UTC)

WikiFunctions in infobox

@Monkelogus has taken it upon themselves to add a link to the respective WikiFunctions function on {{Infobox logical connective}}. While I think this is viable in some form, I just wanted to poll for consensus as to whether we want this kind of presentation. I also have potential quibbles with how it's been placed near the top of the infobox, not consistent with how we generally link to sister sites. Remsense ‥ 论 23:57, 27 September 2024 (UTC)

Sorry, I'm still new to template editing. Maybe linking the wikifunctions like what they do for Apple pie cookbook is a better idea. Monkelogus (talk) 00:09, 28 September 2024 (UTC)

The webpage wikifunctions.org/wiki/Z10237 ("Boolean inequality") per se seems pretty useless to me. YMMV. –jacobolus (t) 00:35, 28 September 2024 (UTC)

It's pretty true that it's kinda useless. I think I'm gonna remove them shortly. However, stuff like SHA-2 and is prime number functions might be much more helpful, when the other alternatives are some random online tools. Monkelogus (talk) 00:37, 28 September 2024 (UTC)

I removed the wikifunctions in Infobox logical connective template. Monkelogus (talk) 00:40, 28 September 2024 (UTC)

Links to Wikifunctions in mathematical articles

Monkelogus has added links to Wikifunctions at the top of several mathematical articles. IMO this must be avoided, and I reverted this, because such a link belongs to sections External links, or to a section describing the linked algorithm, if such a section exists.

Having had a look to one of these links, I found it not understandable for our common readers. IMO such links must be added only if really useful.

IMO, we must elaborate rules saying when and where Wikifunctions must be linked to. D.Lazard (talk) 08:51, 28 September 2024 (UTC)

That's definitely an "External links" thingamabob, not a "top of article" thingamabob. XOR'easter (talk) 10:31, 28 September 2024 (UTC)

I added most of them at the "see also" section, but I agree that right now wikifunctions is extremely buggy and should only be added when it's needed. Monkelogus (talk) 16:29, 28 September 2024 (UTC)

Big traffic spike to Triangle

Apparently there were some kind of puzzles or codes in the recently released Book of Bill (related to the childrens' TV cartoon Gravity Falls) whose answers included "Triangle" and "Eye of Providence", with the result that those pages have seen massive view spikes. Triangle went from a norm of about 800–900 views per day up to 500,000 views yesterday, and possibly more today.

If anyone wants to have improvements to a mathematical page widely seen, Triangle could use some love.

(I added {{talk page header}} to Talk:Triangle hoping it would forestall some of the graffiti being directed there. Are there other good ways to deal with giant traffic spikes like this?) –jacobolus (t) 22:49, 11 August 2024 (UTC)

@Jacobolus Triangle was used to be FA. If anyone wants to improve, especially to revive it, I think I can help, but I need a lot of work. Some advices or comments may be required. Whether the goal is to become GA or FA, that implies the article is suitably referenced and on-topic. Dedhert.Jr (talk) 00:58, 12 August 2024 (UTC)

To be honest I don't care much about GA or FA, but it would be nice if the article were better sourced and more complete. –jacobolus (t) 01:01, 12 August 2024 (UTC)

Okay. I have made it on my sandbox, and the progress is on the way. For someone who would like to give comments or advice for improvement only, ask me on my talk page. Dedhert.Jr (talk) 03:56, 12 August 2024 (UTC)

I have some problems while expanding the article. In the case of non-planar triangles, I found out that there are other triangles as in hyperbolic triangle and spherical triangle. However, I also found out that hyperbolic triangles can be constructed by a so-called Thurston triangle [18]. It also contains the area of a hyperbolic triangle by using Gauss–Bonnet theorem, but according to which it is a geodesic triangle. Dedhert.Jr (talk) 11:38, 14 August 2024 (UTC)

It's unfortunate that we don't yet have an article spherical triangle, and that spherical trigonometry and spherical geometry are so incomplete. These and the many related topics which are currently red links or redirects are on my long-term todo list, but fixing even a few of them properly is a large daunting job and it's hard to get started. I'd eventually like to make a substantial number of diagrams similar to those at Lexell's theorem, but each one takes at least an hour of fiddling, sometimes several. Anyhow, both spherical triangles and hyperbolic triangles are types of geodesic triangles, with edges that are geodesics of their respective spaces.

What your linked article calls the "Thurston model" of hyperbolic space is a discrete (infinite) polyhedron analogous to the regular icosahedron as a model of a sphere. The vertices are those of the order-7 triangular tiling; if you wanted you could put them all on one branch of a 2-sheet hyperboloid in 3-dimensional Minkowski space of signature (2, 1), and then the flat faces would be space-like triangles in the ambient Minkowski space. You could project from the hyperbolic plane onto those triangles, e.g. using the Gnomonic projection, or you can draw shapes directly in the space of the polyhedron. You could do something similar with any other kind of polyhedron. I don't think the article triangle needs to spend much if any time discussing triangles drawn the surfaces of polyhedra. –jacobolus (t) 18:07, 14 August 2024 (UTC)

Another problem: Do you think the conditions about the importance of similarity and congruence sections should be trimmed away? Not something beneficially useful including the article on triangles in general; HL and HA theorem may be included in Right triangle instead. The same reason for the similarity of triangles via trigonometric functions. However, one exception that I include is its relation with trigonometric function, defining their functions as a ratio between both sides in a right triangle, and then including the law of sines and cosines as well. Dedhert.Jr (talk) 05:43, 15 August 2024 (UTC)

Another problem: The article Triangulation (geometry) is somewhat short and unsourced in some areas. Do you think this article should be expanded, or rather redirected to the section of the article Triangle? Dedhert.Jr (talk) 05:43, 15 August 2024 (UTC)

Triangulation (geometry) should definitely be its own article, and does not make sense to redirect. But feel free to dramatically expand it. It's a large topic about which whole books have been written. –jacobolus (t) 16:03, 15 August 2024 (UTC)

Ahh, I think something is missing here. Can somebody remind me, or give me more ideas to expand more in my sandbox? I could think of removing "triangles in construction" as in the Flatiron Building and truss; most of these topics are supposed to be triangular prism and isosceles triangle, respectively. The same reason for calculating the median, circumscribed and inscribed triangles, and many more, since they do have their own articles. Dedhert.Jr (talk) 05:43, 15 August 2024 (UTC)

"Triangles in construction" isn't the best section title or scope, but there should definitely be at least a section about how triangles are the only polygon which is rigid when the side lengths are fixed but the sides can rotate independently about the vertices; this is why triangles are the fundamental shape used in a truss, explains why a 4-bar linkage is the most basic type (a "3-bar linkage" can't move), is a reason triangulation works in surveying, and so on.

There should probably separately be a discussion of the use of triangles as common decorative elements etc. –jacobolus (t) 16:02, 15 August 2024 (UTC)

Triangles are definitely not the unique basis for rigid linkages; see Laman graph. The utility graph $K_{3,3}$ is I think the simplest triangle-free rigid graph (in 2d). —David Eppstein (talk) 18:04, 15 August 2024 (UTC)

That's an interesting subject well worth discussing in Laman graph or structural rigidity, but the utilities graph isn't a polygon, and isn't really relevant to the point that the triangle's rigidity is the reason for many of its practical applications. Edit: Maybe Triangle § Rigidity would be a good top-level heading for Triangle. –jacobolus (t) 19:56, 15 August 2024 (UTC)

@Jacobolus. Okay. I would probably do more research and apply them to my sandbox. One problem here is I still cannot find the sources about the rigidity of a triangle and its tessellation with a hexagon. Dedhert.Jr (talk) 05:55, 16 August 2024 (UTC)

Completion

@jacobolus. The article is done for refactoring and rewriting. But some sources may needed to complete the article. Do you have any comments about something is missing or superfluous in the article? Let me know. Dedhert.Jr (talk) 07:48, 17 August 2024 (UTC)

Thanks for putting in the time and energy. XOR'easter (talk) 21:18, 19 August 2024 (UTC)

I've made a smattering of edits to fix small prose matters and fill in some citations. It's still a little under-referenced, so anyone else who'd like to jump in and work on that should feel more than welcome. XOR'easter (talk) 23:30, 19 August 2024 (UTC)

I appreciate your work, as well as the compliments. Still have problems, however, especially with the sources of Heath's book The Thirteen Books. The first book's Definition 20 describes the isosceles triangle definition according to Euclid, but I think this is a mismatch with the given page in Isosceles triangle, or it is hidden in the Greek writings. Pinging @David Eppstein for further explanation. There is a similar reason for Heath's footnotes being more numerous. Dedhert.Jr (talk) 02:51, 20 August 2024 (UTC)

Maybe I'm misreading your comment: do you mean there is a mismatch in Euclid's definition, or just with the formatting of the reference? If the former, you should read the Usiskin & Griffin source from both articles. There are two different and incompatible ways of classifying shapes:

• In exclusive classification, all cases must be disjoint: each shape can have only one type
• In inclusive classification, special cases are subsets of more general cases

As our isosceles triangle article states, Euclid uses an exclusive classification, in which isosceles triangles must have exactly two equal sides and in which equilateral triangles are not isosceles. Many other sources use an inclusive classification in which equilateral triangles are special cases of isosceles triangles. But both remain in use.

Using an inclusive classification and allowing classes to be subsets of each other can be more flexible and avoids unnecessary case analysis. For instance, when Euclid proves a theorem about isosceles triangles, he would have to prove the same theorem again for equilateral triangles, because the givens from the first theorem would not match the definition needed for the second theorem. And when does a special case become separate from the general case? Maybe isosceles right triangles aren't isosceles triangles, because they are in a different special case class?

The same issue comes up even more strongly for quadrilaterals, where one may reasonably ask whether parallelograms are trapezoids, whether rectangles or rhombi are parallelograms, and whether squares are rectangles or rhombi. And then one must reconcile this classification with cyclic quadrilaterals, tangential quadrilaterals, orthodiagonal quadrilaterals, kites, bicyclic quadrilaterals, etc. In the isosceles triangle case, either definition was easy enough to write, but for many of these other cases of quadrilaterals, the inclusive definitions are easy to write (it's a quadrilateral for which a specific constraint is true) and the exclusive definitions are much messier (the constraint is true but also some other constraints that would cause it to be a more specific special case are all false).

Most of the time we use inclusive classification in our Wikipedia articles, but this distinction should be explained. And it's important that this choice be made in a principled way rather than randomly and inconsistently from one article to another because of the sources you happened to read when you were working on the article.

If I'm misinterpreting and this was all purely about page numbers then sorry for the off-topic rant. The important part of the Euclid reference is "Book 1, definition 20". —David Eppstein (talk) 04:25, 20 August 2024 (UTC)

@David Eppstein What I meant is in the article Isosceles triangle, you cited Euclid's definition on page 187 [Heath (1956), p. 187, Definition 20.] But I cannot find that definition on that page. What I meant about Greek letters is, even though I found the "Definition 20" on a different page, I will never find that the definition, and it is possibly written in Greek language. This is why I leave this to you since you are the nominator of that GA. and I have no clue about the article's expansion back of the day. Anyway, thank you for your explanation above. Dedhert.Jr (talk) 05:12, 20 August 2024 (UTC)

I can check my copy the next time I'm in the office. Are you sure you're looking at Vol.1 of the Dover three-volume edition? There are a lot of different reprints of Heath's translation. If you're reading it in Greek then I think you have a different one; I would have referred to an English translation. —David Eppstein (talk) 05:33, 20 August 2024 (UTC)

@David Eppstein I have searched it on Heath's citation, which I pointed out in the recent replies. As far as I'm concerned, the page describes the Greek language as the definition and English is probably the further explanation and comments. Look at the page 292 that I linked here [19]. Dedhert.Jr (talk) 05:45, 20 August 2024 (UTC)

"Heath's citation" is ambiguous. There are many reprints of Heath's translation of Euclid. Again, are you sure you're looking at Vol.1 of the Dover three-volume edition? The link you give is to Book 7 in Vol.2, not to Book 1 in Vol.1. —David Eppstein (talk) 06:09, 20 August 2024 (UTC)

@David Eppstein Sorry but that source is already linked as a reference or works cited in the Isosceles triangle, see the references:

• Heath, Thomas L. (1956) [1925]. The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). New York: Dover Publications. ISBN 0-486-60088-2.

Dedhert.Jr (talk) 10:16, 20 August 2024 (UTC)

Apparently the incorrect link is the fault of User:InternetArchiveBot: [20]. Reported: T372925. —David Eppstein (talk) 17:25, 20 August 2024 (UTC)

Ideally we should be citing the Cambridge University Press 2nd edition from 1926, which was later reprinted by Dover, and including a link to a scan of the appropriate page with every reference. Unfortunately the internet archive only has a scan of volume 3, and many of their scans of dover reprints are blocked or need to be "checked out" (though they shouldn't be, since the copyright is still 1926, and expired). HathiTrust has a scan of vol 2 (and vol. 3). –jacobolus (t) 15:49, 20 August 2024 (UTC)

What we need in this case is vol.1. —David Eppstein (talk) 17:31, 20 August 2024 (UTC)

Is this it? Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal. XOR'easter (talk) 17:49, 20 August 2024 (UTC)

Yes. And the page number matches, answering Dedhert.Jr's question. —David Eppstein (talk) 18:00, 20 August 2024 (UTC)

Well, the article is down to a handful of uncited statements. I'm not sure that all of them need to be kept in the text. I can try to scrape together the time to work on it more, but maybe someone else would rather take a swing at it. XOR'easter (talk) 18:33, 23 August 2024 (UTC)

It seems that most of the areas are sourced, only some of the "citation needed"-tags and untagged areas are the remaining problems. Yet, is there anything that can include other related topics of a triangle here? Dedhert.Jr (talk) 01:16, 28 August 2024 (UTC)

One more thing: Do you think the article about triangles should include their appearances on some higher-dimensional objects such as polyhedrons, tesselations, etc.? I suppose these things would rather be included in some specific triangles: Isosceles triangles appears on five Catalan solids, infinitely pyramids and bipyramids; Equilateral triangle appears on deltahedron, fractal triangles as in Sierpinski triangles, and so on. Bipyramids and pyramids may be included in the article as isosceles triangles, but they are right (their height is exactly perpendicular to their base), not in the case of arbitrary triangles in obtuse case. Dedhert.Jr (talk) 09:45, 12 September 2024 (UTC)

Yes, it would be entirely reasonable to add such material to triangle, if you want to. It would also be reasonable to discuss topics involving a bunch of triangles stuck together as in Delaunay triangulation, Triangulated irregular network, and Triangle mesh. And there are plenty of other triangle-related topics that are currently unmentioned or barely mentioned that could be discussed. –jacobolus (t) 19:47, 12 September 2024 (UTC)

Okay. Let me think about that. Dedhert.Jr (talk) 14:10, 14 September 2024 (UTC)

Oh, but what about other appearances of triangles in real life, as in architecture, science, etc.? I mean, if we are talking about WP:ONEDOWN, this will target the elementary students. Some unexpected arrangements of sections may perplexe most users, and this leads to the same questions about excluding them in the general triangle, but rather including them in some specific type of triangles. Dedhert.Jr (talk) 15:29, 29 September 2024 (UTC)

Articles about big lists of open problems

Does Wikipedia allow for creation of articles about big lists of open problems, such as Yau's problems or Arnold's problems? Or maybe it's better to create separate articles for each problem? These two examples of big lists of problems seem to have strong influences in mathematics research today, in geometry and dynamical systems at least. DuqueLL (talk) 19:09, 29 September 2024 (UTC)

There are certainly multiple articles about Hilbert's problems, because there are multiple in-depth secondary sources (multiple entire books!) about those problems. That's what such an article or list needs: multiple secondary sources, like anything else, per WP:GNG. —David Eppstein (talk) 19:15, 29 September 2024 (UTC)

Thank you. I think Arnold's Problems (the book) meets WP:GNG (many reviews and highly-cited). So, I'll try to create Arnold's Problems instead of Arnold's problems. DuqueLL (talk) 19:43, 29 September 2024 (UTC)

Actually, I'm not sure there are "many reviews". I've created a draft: Draft:Arnold's Problems. I'll try to find more reviews. DuqueLL (talk) 19:54, 29 September 2024 (UTC)

I found two more and added them to the draft page. I think that's enough to meet the relevant standard. XOR'easter (talk) 22:47, 29 September 2024 (UTC)

Thank you so much! I will create the article about this book then! DuqueLL (talk) 22:56, 29 September 2024 (UTC)

It was also reviewed in MR and ZBL. Those don't usually contribute to notability (because their choice to review mathematics books is routine) and the MR reviewer (of the 2000 Russian version) is the same as the later Intelligencer reviewer, but they might still be useful in providing content for an article. —David Eppstein (talk) 23:09, 29 September 2024 (UTC)

Thank you again!! DuqueLL (talk) 23:11, 29 September 2024 (UTC)

I would suspect that either Yau or Arnold's problems could, on the merits, be justified as a standalone page. However they are both rather long (Yau's 1982 list has 120 problems and his separate 1993 list has 100, and there seem to be a comparable number of Arnold problems), it may not be easy to write a useful page for either. Gumshoe2 (talk) 21:01, 29 September 2024 (UTC)

Thanks to everyone! I've submitted it to review. English is not my native language, so maybe the English could be improved and I don't know, but anyways it looks like a very good start! DuqueLL (talk) 00:56, 30 September 2024 (UTC)

It looked ready enough, so I went ahead and moved it into article space. XOR'easter (talk) 01:32, 30 September 2024 (UTC)

Oh, and we do have the page List of unsolved problems in mathematics. XOR'easter (talk) 01:40, 30 September 2024 (UTC)

Oct 2024

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