Wikipedia talk:WikiProject Mathematics/Archive/2023/Jan

Tensor versus tensor field

There is a Tensor article and also a Tensor field article. The Tensor article contains a good deal of material on tensor fields. The two articles should either be cleanly separated into separate articles or merged; I'm not sure which option is better. Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:06, 23 December 2022 (UTC)

I think I would lean to a merge, or more precisely that the main tensor article should be primarily about tensor fields. It would be reasonable to have a subsidiary article on the sparer concept from abstract algebra. --Trovatore (talk) 22:57, 23 December 2022 (UTC)

I lean against a merge. Based on my experience both on Wikipedia and in the real world, the material covered by the current Tensor article is difficult and confusing for a lot of people, even without bringing in a bunch of calculus and other stuff needed for tensor fields. If we rewrote Tensor to be primarily about tensor fields, then I would want there to still be an article (maybe named Tensor at a point, but hopefully something much better!) that covers the current material well. Mgnbar (talk) 23:19, 23 December 2022 (UTC)

Tensors are algebraic entities in their own right: the name Tensor at a point is inappropriate for anything but tensors on the tangent space at a point of a differentiable manifold. Tensor (algebra) would be more appropriate. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:52, 25 December 2022 (UTC)

Under no circumstances should the Tensor article be changed to be primarily about tensor fields. Tensors are used in many contexts which are not "evaluate a tensor field at a point on a manifold" including in: functional analysis, abstract algebra, multilinear algebra, etc.

As much as physicists who don't know the proper words for mathematical objects might disagree, the notion of tensor field is different and secondary to the notion of tensor.

The two articles should be properly separated. Tazerenix (talk) 01:21, 24 December 2022 (UTC)

I believe that, despite the existence of a Tensor field article, Tensor is currently mostly about tensor fields, which I believe should be corrected. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:52, 25 December 2022 (UTC)

Your belief is one thing, the reality is another thing. The section Tensor#Definitition has 5 subsections, and only the last one is about tensor fields. In this section, a tensor field is defined as a function whose components are tensors, or equivalently as a tensor-valued function (so, a tensor field cannot be correctly defined without the primary concept of a tensor). So, tensor fields is a (very important) application of tensors, but there are other important applications that have nothing to do with tensor fields. One of these important applications is the use of the rank of a tensor in computational complexity theory, in particular for matrix multiplication. Another fundamental application of tensors, which is independent from any tensor field, is geometric algebra.

I do not know what supports your belief that "Tensor is currently mostly about tensor fields". Either, you have read only the article introduction, or the content of the introduction and the article are biased by the knowledge and the preferences of the authors of the article. In any case, the merge that you suggest is a mathematical nonsense. D.Lazard (talk) 14:44, 25 December 2022 (UTC)

The problem is that Tensor#applications et al give applications of Tensor fields. Also, your belief that I support a merge is bizarre, and, in fact, what I support is moving the tensor-field examples to Tensor field. I mention a merge only because it would be better than having two different articles giving examples of tensor fields; that's why I wrote cleanly separated. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:15, 25 December 2022 (UTC)

OK D.Lazard (talk) 21:26, 25 December 2022 (UTC)

better than having two different articles giving examples of tensor fields Why is this a problem? It seems entirely fine to me if both of these articles give examples of tensor fields, as long as the prose is clear about it. (The problem here IMO is the bullet list format for the "Other examples from physics" section, which is rigid and hard to modify or extend, makes it difficult to group different examples together or provide unified context, etc.) –jacobolus (t) 21:07, 27 December 2022 (UTC)

At a minimum, shouldn't the tensor article give substantially more examples of thensors than of tensor fields? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:14, 28 December 2022 (UTC)

Why don’t you add some more examples then? –jacobolus (t) 04:48, 29 December 2022 (UTC)

It seems to me that the origin of the notion of tensor is almost inextricably connected with tensor fields. The name "tensor" comes from the stress tensor in a substance, which is pretty much always going to be a field, and the first serious usages beyond that were in differential geometry and general relativity.

On the other hand the purely algebraic notion is hard to separate out as its own thing. As I understand it, an algebraic tensor is a linear transformation from a vector space to another vector space, particularly when the domain and range are tensor products of simpler spaces. We have articles on linear transformations and tensor products. Shouldn't the main content on algebraic tensors be at tensor product rather than at tensor? What is there really to say about algebraic tensors that wouldn't fit naturally at tensor product? --Trovatore (talk) 22:57, 2 January 2023 (UTC)

Tensor

@Alexmov: has been repeatedly vandalizing Tensor, replacing standard terminology with infantile expressions, e.g. "Multidimenional maps" with " M-way array". Please help. JRSpriggs (talk) 17:44, 22 December 2022 (UTC)

I'll keep an eye on Tensor and revert/warn/block as needed.

Perhaps a knowledgeable editor could review Multilinear principal component analysis as well; a recent edit by Alexmov removed 2k including several types/applications of MPCA.

CRGreathouse (t | c) 18:31, 22 December 2022 (UTC)

It's counterproductive to refer to well-intentioned edits as vandalism (even when, as here, they are obvious disimprovements). --JBL (talk) 22:10, 22 December 2022 (UTC)

Pinging @JayBeeEll: @JRSpriggs:@CRGreathouse::

@JRSpriggs: is vandelising well informed corrections to Tensor, and gaslighting everyone by decreeing those corrections as vandelism or juvenille without any evidence or argument. I've explained that "Multidimensional arrays" are an informal terminology that refers to multi-way array or M-way arrays. Using Profesor Scrotum's terminolgy to which JRSpriggs reverts creates confusion. For example, saying that a 3 dimensional vector is a 1 dimensional array with 3 dimensions creates confusion. Do you see the problem with this informal terminology? Please help. Alexmov (talk) 17:44, 22 December 2022 (UTC)

Pinging @JayBeeEll: @JRSpriggs:@CRGreathouse:

These are not disimprovements. They are correct and well-established terminpology in CS/ML. See

• J.B. Kruskal. Rank, decomposition, and uniqueness for 3-way and n-way arrays. In R. Coppi and S. Bolasco, editors, Multiway Data Analysis, pages 7–18, Amsterdam, 1989. North Holland.
• DeLathauwer etal or https://alterlab.org/teaching/BME6780/papers patents/De_Lathauwer_2000.pdf
• Kolda and Bader, https://www.kolda.net/publication/TensorReview.pdf

The terminology dimensionality, order and mode are closely related but refer to different properties.

In CS/ML, the information of a 3 dimensional vector is stored (as opposed to represented) in a 1-way array data structure with 3 dimensions. Saying that 3 dimensional vecor is a 1 dimensional array with 3 dimensions or even 3 number creates unnecessary confusion. Here is an example of the words order, mode and dimension used for tensors and the words M-way and dimension used for arrays:

• The information of a 3rd order tensor, ${\mathcal {A}}$, of dimensionality $I_{1}\times I_{2}\times I_{3}$ is stored in 3-way array array with the same dimensions. The dimensionality of the 2nd mode of the third-order tensor ${\mathcal {A}}$ is $I_{2}$.
• The word rank in physics was normally used to refer to the order of a tensor, but it is my understanding that rank is being used in physics the same way it is being used in mathematics.

Alexmov (talk) 18:34, 22 December 2022 (UTC)

My view is that the CS/ML usages are not what the main tensor article is or should be mostly about, and those fields should not unduly influence the terminology. It's a convenient word for computer scientists but it's not exactly the same concept. A tensor is not an array; it's a linear transformation between vector spaces that don't necessarily have a preferred basis. We should emphasize the "coordinate-free" approach, and I don't quite see how that applies to ML; in my limited experience ML models have a coordinate system defined by the problem. --Trovatore (talk) 22:43, 23 December 2022 (UTC)

I agree with you 100%!!! JRSpriggs completely misrepresented the edit I was trying to make. Alexmov (talk) 20:25, 1 January 2023 (UTC)

CS/ML was a "slip of the toungue", I meant computational mathematics. I used articles from statistics, psychometrics, economerics and chemometrics that go back to 1960s to substantiate the terminology change. Alexmov (talk) 23:49, 2 January 2023 (UTC)

Just because computer scientists discovered the concept of a tensor in the last 10 years and invented all their own names for the terminology doesn't mean we should go rewrite a century of mathematical language to use their new words. Tazerenix (talk) 01:18, 24 December 2022 (UTC)

I was referring to about 40 years worth of in statistics, psychometrics, economerics and chemometrics. CS/ML was a "slip of he toungue", I meant computational mathematics. Alexmov (talk) 12:44, 1 January 2023 (UTC)

Your statement does not address the issue under discussion. The second sentence in the section called Multidimensional Array is using the phrase "a vector in an n-dimensional space is represented by a one-dimensional array with n components" uses two discrepant definitions of the word dimensional. I argue that it needs to be edited and I had suggested a compromise similar to the one used in Kruskal's work which uses replace "multidimensional array" with "multiway array (multidimensional array)".

• (4326 citations) Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3), 279–311. https://doi.org/10.1007/BF02289464
• (1815 citations) Joseph B. Kruskal, (1977) Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear Algebra and its Applications, Volume 18, Issue 2, 1977, Pages 95-138,ISSN 0024-3795, https://doi.org/10.1016/0024-3795(77)90069-6

Alexmov (talk) 12:57, 1 January 2023 (UTC)

Multidimensional arrays are useful things. Basis-free tensors are also useful things. But they are not the same thing, and the mathematical tensor article should not be converted into something about multidimensional arrays by editors who do not appreciate the distinction. —David Eppstein (talk) 05:40, 25 December 2022 (UTC)

Your statement does not address the issue under discussion.

The second sentence in the section called Multidimensional Array is using the phrase "a vector in an n-dimensional space is represented by a one-dimensional array with n components" uses two different definitions of the word dimensional. Mgnbar thought that it needs to be edited. I suggested a compromise similar to the one used in Kruskal's work which uses replace "multidimensional array" with "multiway array (multidimensional array)".

• (4326 citations) Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3), 279–311. https://doi.org/10.1007/BF02289464
• (1815 citations) Joseph B. Kruskal, (1977) Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear Algebra and its Applications, Volume 18, Issue 2, 1977, Pages 95-138,ISSN 0024-3795, https://doi.org/10.1016/0024-3795(77)90069-6

Alexmov (talk) 12:51, 1 January 2023 (UTC)

I have edited the article, and, now, the two meanings of "dimension" are linked. D.Lazard (talk) 13:08, 1 January 2023 (UTC)

To be clear JRSpriggs has misrepresented the edit I was trying to make to the second sentence in the Multidimensional Array Section.

• In statistics, psychometrics, econometrics, and chemometrics, which have been working on tensor factor analysis since the 1960s, the term "multidimensional array" was deprecated in favor of the term "multiway array" since it clashes with the traditional mathematical meaning of multidimensional. At one point, I suggested Kruskal's compromise which could fix the dual use of the word dimensional and keeps both terms. Six (6) instances of "multidimensional array" could be replaced with "multiway array (multidimensional array)". Thus, deprecating the term multidimensional. Alexmov (talk) 19:52, 1 January 2023 (UTC)

Poincaré lemma

Hi all,

I don't know if this matter has been discussed before (if so, let me know) but I am thinking of splitting off the materials on Poincaré lemma from Closed and exact differential forms to its own article. I think the result is important enough for a separate article. Also, it is a bit awkward to have a discussion of relative Poincare lemma or del-bar Poincare lemma (Grothendieck?) in the closed and exact article. What do the others think? If there is no objection, I will carry out the splitting. -- Taku (talk) 14:04, 8 January 2023 (UTC)

I agree it should probably be its own article. Tazerenix (talk) 20:46, 8 January 2023 (UTC)

It's certainly important historically, but in the context of Homology theory it's a trivial result, since De Rham cohomology satisfies the Eilenberg–Steenrod axioms and an open ball in Rⁿ is simply connected. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:51, 9 January 2023 (UTC)

The result is certainly not trivial. It is required to prove that de Rham satisfies the axioms in the first place. Axioms/universal properties do not specify existence!! Tazerenix (talk) 23:06, 10 January 2023 (UTC)

References

Well, it still requires that we prove the homotopy invariance of de Rham cohomology (to know the axioms are satisfied). That basically amounts to proving Poincaré lemma, since a typical proof is a proof of the homotopy invariance by constructing a homotopy operator (e.g., by integration along fibers.) —- Taku (talk) 10:07, 10 January 2023 (UTC)

Twice more

Would a few of you please check User:WhatamIdoing/Sandbox 3 (permalink) and comment here if anything needs to be fixed? I hope this will help editors who are trying to figure out whether "doubling" is the same as "a 200% increase". WhatamIdoing (talk) 04:02, 12 January 2023 (UTC)

It is better for everyone to avoid this kind of ambiguity in Wiki articles, because there are many readers who will be confused and interpret it to mean the wrong thing. –jacobolus (t) 04:21, 12 January 2023 (UTC)

By the way, this is not the best venue for this question. You may want to try Wikipedia:Reference desk/Mathematics instead. –jacobolus (t) 04:25, 12 January 2023 (UTC)

Question about volume

I'm trying to improve this very-broad but extremely important article about the volume, that volume with liters. While at least I have a clue on how to improve the history and measurement section, I have absolutely no idea on how to rewrite the calculation section to make it more encyclopedic. Do you have any ideas on how to do so? CactiStaccingCrane (talk) 13:26, 12 January 2023 (UTC)

I suggest removing the formulae of volumes of geometric shapes. There is already a link to List of formulas in elementary geometry and each shape has its own article anyway — Martin (MSGJ · talk) 14:16, 12 January 2023 (UTC)

@MSGJ Done, and I've moved the image montage to that list instead. CactiStaccingCrane (talk) 14:40, 12 January 2023 (UTC)

This seems like a regression. Calculating the volume of various shapes seems entirely in scope for the article as it stands (though perhaps a separate volume (mathematics) article would be helpful. The page List of formulas in elementary geometry is frankly terrible, with very unclear purpose and scope. –jacobolus (t) 18:38, 12 January 2023 (UTC)

Would mension of Measure theory be TMI? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 19:51, 12 January 2023 (UTC)

RD nomination for Yuri Manin

In case anyone here is interested: Wikipedia:In the news/Candidates#RD: Yuri Manin. — MarkH₂₁^talk 22:20, 12 January 2023 (UTC)

Also, Wikipedia:In the news/Candidates#RD:Mikio Sato. Mikio Sato might benefit from the attention of more algebraic analysis sources. — MarkH₂₁^talk 15:45, 14 January 2023 (UTC)

Regarding lists of properties/examples in mathematics articles

I have a disagreement with editor Mgkrupa regarding the article Dense-in-itself, but it's a more general issue actually. In the previous version (https://en.wikipedia.org/w/index.php?title=Dense-in-itself&oldid=1131194770) the list of properties were presented in a bullet format. Mgkrupa changed it to this (https://en.wikipedia.org/w/index.php?title=Dense-in-itself&oldid=1132822549), which I have since reverted. His comment was " Reorganized, reworded, and copy editing". Apart from the fact that I don't agree with his particular reorganization of the topics in the article, which we can ignore here, I'd like to focus on the use of lists here. Mgkrupa says in Talk:Dense-in-itself that bullet lists are not encyclopedic and goes against Wikipedia's manual of style, and that it violates MOS:LISTBULLET and Wikipedia:Manual of Style/Lists.

I'd like to ask guidance from the community on this topic. In many articles (in topology for example, which I am more familiar with: Baire space, Countably compact space, etc) we need to present a list of properties or examples, mostly independent of each other, and each of them one line with maybe an accompanying reference. In my opinion, presenting lists of properties/examples in such a context with a bullet list makes it more readable, not less. It allows to scan down the list and quickly find what one is interested in. Compare with Mgkrupa's change above where most of the properties were lumped into a single paragraph, where one now needs to parse a whole paragraph in detail to find something. I am also not saying that we should use bullet lists everywhere. If some properties/examples are more involved and necessitate more explanation, having a separate paragraph for each is perfectly fine. Would appreciate reading other people's opinion. PatrickR2 (talk) 02:26, 12 January 2023 (UTC)

Wikipedia is a large and heterogeneous enough place that you aren't going to find agreement about a subject like this. Personally I think bullet lists should be avoided in this kind of situation. In my view bullet lists are best as either (a) directly encoding something that is obviously a collection of (small) homogeneous items where there is little chance any of the specific items needs additional commentary or expansion, or (b) a temporary lazy placeholder on the way to a proper write-up in prose, to be abandoned at the earliest convenience.

I strongly dislike lists of properties (and similar situations) because once started they are almost impossible to displace as a means of organization and difficult to extend or reorganize without doing a complete rewrite. Very often the elements of a seemingly disparate list of trivia turn out to have some kind of internal interrelationships, groups with shared context, variation in size/complexity, and so on, but these either don't get added because they don't fit in the list format, or they get encoded awkwardly e.g. by adding extra bullets that don't actually belong on equal footing with the rest, adding additional levels of hierarchy, including material in only one bullet that properly belongs in multiple, or redundantly duplicating the same material across multiple bullets. From a technical perspective I dislike mediawiki markup lists (from asterisks) because adding block quotations, block formulas, images, etc. doesn't really work very well with them, requiring various obscure and finicky workarounds.

By comparison, sections, paragraphs and sentences are extremely malleable and can fit whatever narrative structure is appropriate for the content.

On the flip side, one advantage that grab-bag bullet lists do have is that they make it very easy for people to throw extra items into the end of the list without thinking very hard. But this is a mixed blessing, as it can lead to a bloated disorganized mess. –jacobolus (t) 03:21, 12 January 2023 (UTC)

I am well aware of your points, and am personally very careful to avoid the lists of pitfalls you mention when I edit an article that I care about, listing the items in a logically reasonable progression as much as possible, avoiding redundancies, etc, etc. And yes, as you mentioned, not everybody is so careful and it is easy to misuse. But I stand by my point in the particular instances I have listed, that it makes it a lot easier to find information in those contexts. You can also find a disorganized mess, full of redundancies, trivia added in a haphazard way, etc when using paragraphs if people are not careful (I have seen it and could point to examples if necessary). For example, are you really advocating to get rid of the bullets in the Baire space article and replace them with a separate paragraph for each bullet? I am not convinced that would be an improvement. PatrickR2 (talk) 06:54, 12 January 2023 (UTC)

The Baire space article dramatically overuses bullet lists (more or less consists entirely of bullet lists), but since it’s not that far removed from a stub (the "start" class assessment seems fair), I would consider the lists to be more or less placeholders until someone comes along who wants to expand it into a more fully fleshed article with a more reader-friendly narrative structure.

The article currently doesn’t provide much motivation, history, or context, and is so technical that it is almost completely inaccessible to someone who isn’t already a mathematical expert. The individual bullet list items are bare-bones factual statements without explaining why anyone thought those were interesting things to investigate or why anyone should care. They aren’t organized or structured in any way, even though there are surely natural groupings and relationships between them.

The current list-heavy format in my opinion makes it hard to expand or reorganize those sections without doing a complete rewrite, but if someone knows a lot and cares about Baire spaces they should still give it a shot. Personally I am not very knowledgeable about or interested in this subject, so I’ll stay out of it.

YMMV. –jacobolus (t) 07:48, 12 January 2023 (UTC)

To me, a bulleted list like the one currently in dense-in-itself is an outline for how an article should be structured, but is not in itself something that should be considered part of a finished article. Bulleted lists can be used in more-complete articles, but only sparingly; it is not a good idea to have a section that consists only of a bulleted list, and bulleted lists work better when the bullets themselves are more fleshed out rather than bare factoids. MOS:USEPROSE is good advice. As for Baire space, the numbered list in the "definitions" section looks ok to me, but would be better as a bulleted list because the numbers are meaningless: it gives a list of alternatives to be compared to each other that would be too cumbersome to fit into a single sentence. However, the organization of "properties" and "examples" as long undigested lists of bullets is just bad. Find some way of grouping these into related subsets of properties and examples and make a prose paragraph for each subset.

To put it more briefly: Bulleted lists are a good way of formatting multiple things that are explicitly supposed to be parallel to each other, like the multiple equivalent definitions in Baire space. They are not a good way of organizing a non-parallel sequence of disconnected ideas, like the instance in dense-in-itself and the definitions and examples sections of Baire space. —David Eppstein (talk) 08:31, 12 January 2023 (UTC)

FYI, don't confuse Baire space, which is a more specialized topic of less interest to a general public, with the article Baire category theorem, which contains more motivation and applications to other fields of mathematics. For those who care about these things, the Baire space article has a lot of information specifically about that, all backed up with references, which anyone interested can use to dig further. And if they don't care about the topic, that's does not hurt anyone. PatrickR2 (talk) 08:43, 12 January 2023 (UTC)

Quoting PatrickR2:

"when I edit an article that I care about, listing the items in a logically reasonable progression as much as possible"

In at least some (but not all) instances, PatrickR2 and I fundamentally disagree on whether or not a list is appropriate. Consider the article "Separated sets" for instance. On 12 January 2023, PatrickR2 started the following discussion in its talk page Talk:Separated sets:

"Why did you change the staggered formatting of the various properties in the Definitions section? It was really nice to visually indicate that each property was a strengthening of the previous ones."

The staggered format that PatrickR2 was referring is the can be found in the 6 February 2022 version of that article. I've reproduced below a truncated version of the relevant part:

There are various ways in which two subsets of a topological space X can be considered to be separated.

• A and B are disjoint if their [...]
  • A and B are separated in X if each is [...]
  • A and B are separated by neighbourhoods if there are [...]
    • A and B are separated by closed neighbourhoods if there is a [...]
      • A and B are separated by a function if there exists [...]
        • A and B are precisely separated by a function if there exists [...]

/endquote Now, the list above is indeed ordered "in a logically reasonable progression" but I consider that "staggered" format inappropriate for any Wikipedia article and so I "flattened it" to this (I think that the bullet points need to be gotten rid of entirely and turned into paragraphs but that'll have to wait for a future edit). In that discussion, I stated that bullet lists are "not encyclopedic and goes against Wikipedia's manual of style" (I also said this in Talk:Dense-in-itself) Patrick disagreed, stating that

"If it was a regular bullet list, I would agree with you. But the previous layout was more than a simple list. It was also intuitively conveying in a visual manner the relationship between the properties."

I fundamentally disagree (side note: this was not always the case though since for a long time, I would frequently make lists; I stopped after being told to/why and I'm glad that I did because I've since found that avoiding lists has forced an improvement in the quality of my contributions). This disagreement has spread to several articles so far (Nowhere dense set, Dense-in-itself, and Separated sets). I don't want it have this conversation over and over again so I too would like to know where the community stands on this issue. Mgkrupa 21:02, 12 January 2023 (UTC)

Perhaps the logical relationships between the different ways sets can be separated might be indicated with a diagram instead of a hierarchical bullet list. –jacobolus (t) 18:01, 13 January 2023 (UTC)

I agree strongly with Mgkrupa in the particular instance of Separated sets. I just took 5 minutes to convert the first bullet point into prose (it was not terribly difficult). I also agree with jacobolus that these containment relations are well suited to being represented by a diagram. --JBL (talk) 19:25, 13 January 2023 (UTC)

Now I've done half of them (also adding one citation, and tweaking for MOS:MATH#TONE). Someone with more than one topology textbook on their shelf (i.e., not me) should be able to finish easily, I would think. --JBL (talk) 20:12, 13 January 2023 (UTC)

I have removed the remaining bullets. Also added a sentence at the top saying that various properties are presented in increasing order, each stronger than the previous one, so there should be no need for an extra diagram. (In addition, the point that each property is stronger than the previous one was already reiterated in every paragraph anyway.) PatrickR2 (talk) 19:44, 14 January 2023 (UTC)

Thank you! --JBL (talk) 00:51, 16 January 2023 (UTC)

Already much better! Mgkrupa 00:19, 18 January 2023 (UTC)

Thanks for the feedback. I'll make some changes to the Baire space article. PatrickR2 (talk) 20:42, 12 January 2023 (UTC)

Dispute resolution: Monty Hall problem proof

There's a dispute at the Monty Hall problem article about how best to present a proof solving the problem using Bayesian statistics. We're hoping interested editors can help us decide between two options. Thank you. GabeTucker (talk) 18:29, 19 January 2023 (UTC)

Hello

Hello, I am an Iranian. I am fluent in languages ​​such as English-Arabic. I can improve many articles. I want to contribute to this project. How is the working environment of this project? Mohammad.Hosein.J.Shia (talk) 10:06, 20 January 2023 (UTC)

The answer is in User talk:Mohammad.Hosein.J.Shia#Welcome. D.Lazard (talk) 14:19, 20 January 2023 (UTC)

Welcome. Take a peek at WP:MOS, start making small changes and progress to larger changes as you get more comfortable with the tools and customs. Don't be afraid to ask for help should you feel the need. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:03, 20 January 2023 (UTC)

Unreviewed Featured articles year-end summary

Restoring older Featured articles to standard:

year-end 2022 summary

Unreviewed featured articles/2020 (URFA/2020) is a systematic approach to reviewing older Featured articles (FAs) to ensure they still meet the FA standards. A January 2022 Signpost article called "Forgotten Featured" explored the effort.

Progress is recorded at the monthly stats page. Through 2022, with 4,526 very old (from the 2004–2009 period) and old (2010–2015) FAs initially needing review:

• 357 FAs were delisted at Featured article review (FAR).
• 222 FAs were kept at FAR or deemed "satisfactory" by three URFA reviewers, with hundreds more being marked as "satisfactory", but awaiting three reviews.
• FAs needing review were reduced from 77% of total FAs at the end of 2020 to 64% at the end of 2022.

Of the FAs kept, deemed satisfactory by three reviewers, or delisted, about 60% had prior review between 2004 and 2007; another 20% dated to the period from 2008–2009; and another 20% to 2010–2015. Roughly two-thirds of the old FAs reviewed have retained FA status or been marked "satisfactory", while two-thirds of the very old FAs have been defeatured.

Entering its third year, URFA is working to help maintain FA standards; FAs are being restored not only via FAR, but also via improvements initiated after articles are reviewed and talk pages are noticed. Since the Featured Article Save Award (FASA) was added to the FAR process a year ago, 38 FAs were restored to FA status by editors other than the original FAC nominator. Ten FAs restored to status have been listed at WP:MILLION, recognizing articles with annual readership over a million pageviews, and many have been rerun as Today's featured article, helping increase mainpage diversity.

Examples of 2022 "FAR saves" of very old featured articles

Solar System 2007 FA J. K. Rowling 2007 FA June 26, 2022 TFA Antarctica 2006 FA Joan of Arc 2006 FA Speed of light 2010 FA

All received a Million Award

But there remain almost 4,000 old and very old FAs to be reviewed. Some topic areas and WikiProjects have been more proactive than others in restoring or maintaining their old FAs. As seen in the chart below, the following have very high ratios of FAs kept to those delisted (ordered from highest ratio):

• Biology
• Physics and astronomy
• Warfare
• Video gaming

and others have a good ratio of kept to delisted FAs:

• Literature and theatre
• Engineering and technology
• Religion, mysticism and mythology
• Media
• Geology and geophysics

... so kudos to those editors who pitched in to help maintain older FAs !

FAs reviewed at URFA/2020 through 2022 by content area

FAs reviewed at URFA/2020 from November 21, 2020 to December 31, 2022 (VO, O) Topic area Delisted Kept Total Reviewed Ratio Kept to Delisted (overall 0.62) Remaining to review for 2004–7 promotions Art, architecture and archaeology 10 6 16 0.60 19 Biology 13 41 54 3.15 67 Business, economics and finance 6 1 7 0.17 2 Chemistry and mineralogy 2 1 3 0.50 7 Computing 4 1 5 0.25 0 Culture and society 9 1 10 0.11 8 Education 22 1 23 0.05 3 Engineering and technology 3 3 6 1.00 5 Food and drink 2 0 2 0.00 3 Geography and places 40 6 46 0.15 22 Geology and geophysics 3 2 5 0.67 1 Health and medicine 8 3 11 0.38 5 Heraldry, honors, and vexillology 11 1 12 0.09 6 History 27 14 41 0.52 38 Language and linguistics 3 0 3 0.00 3 Law 11 1 12 0.09 3 Literature and theatre 13 14 27 1.08 24 Mathematics 1 2 3 2.00 3 Media 14 10 24 0.71 40 Meteorology 15 6 21 0.40 31 Music 27 8 35 0.30 55 Philosophy and psychology 0 1 1 – 2 Physics and astronomy 3 7 10 2.33 24 Politics and government 19 4 23 0.21 9 Religion, mysticism and mythology 14 14 28 1.00 8 Royalty and nobility 10 6 16 0.60 44 Sport and recreation 32 12 44 0.38 39 Transport 8 2 10 0.25 11 Video gaming 3 5 8 1.67 23 Warfare 26 49 75 1.88 31 Total 359 Note A 222 Note B 581 0.62 536 Noting some minor differences in tallies: A URFA/2020 archives show 357, which does not include those delisted which were featured after 2015; FAR archives show 358, so tally is off by at least one, not worth looking for. B FAR archives show 63 kept at FAR since URFA started at end of Nov 2020. URFA/2020 shows 61 Kept at FAR, meaning two kept were outside of scope of URFA/2020. Total URFA/2020 Keeps (Kept at FAR plus those with three Satisfactory marks) is 150 72 = 222.

But looking only at the oldest FAs (from the 2004–2007 period), there are 12 content areas with more than 20 FAs still needing review: Biology, Music, Royalty and nobility, Media, Sport and recreation, History, Warfare, Meteorology, Physics and astronomy, Literature and theatre, Video gaming, and Geography and places. In the coming weeks, URFA/2020 editors will be posting lists to individual WikiProjects with the goal of getting these oldest-of-the-old FAs reviewed during 2023.

Ideas for how you can help are listed below and at the Signpost article.

• Review a 2004 to 2007 FA. With three "Satisfactory" marks, article can be moved to the FAR not needed section.
• Review "your" articles: Did you nominate a featured article between 2004 and 2015 that you have continuously maintained? Check these articles, update as needed, and mark them as 'Satisfactory' at URFA/2020. A continuously maintained FA is a good predictor that standards are still met, and with two more "Satisfactory" marks, "your" articles can be listed as "FAR not needed". If they no longer meet the FA standards, please begin the FAR process by posting your concerns on the article's talk page.
• Review articles that already have one "Satisfactory" mark: more FAs can be indicated as "FAR not needed" if other reviewers will have a look at those already indicated as maintained by the original nominator. If you find issues, you can enter them at the talk page.
• Fix an existing featured article: Choose an article at URFA/2020 or FAR and bring it back to FA standards. Enlist the help of the original nominator, frequent FA reviewers, WikiProjects listed on the talk page, or editors that have written similar topics. When the article returns to FA standards, please mark it as 'Satisfactory' at URFA/2020 or note your progress in the article's FAR.
• Review and nominate an article to FAR that has been 'noticed' of a FAR needed but issues raised on talk have not been addressed. Sometimes nominating at FAR draws additional editors to help improve the article that would otherwise not look at it.

More regular URFA and FAR reviewers will help assure that FAs continue to represent examples of Wikipedia's best work. If you have any questions or feedback, please visit Wikipedia talk:Unreviewed featured articles/2020/4Q2022.

FAs last reviewed from 2004 to 2007 of interest to this WikiProject

If you review an article on this list, please add commentary at the article talk page, with a section heading == [[URFA/2020]] review== and also add either Notes or Noticed to WP:URFA/2020A, per the instructions at WP:URFA/2020. Comments added here may be swept up in archives and lost, and more editors will see comments on article talk. SandyGeorgia (Talk) 21:29, 20 January 2023 (UTC)

1. 1 − 2 3 − 4 ⋯
2. Archimedes
3. Georg Cantor

"Consider" is a command; Is this appropriate for an encyclopedia?

There are probably too many mathematical topics to fix this, but language such as this seems to violate WP:HOWTO.— Vchimpanzee • talk • contributions • 22:39, 2 January 2023 (UTC)

Can you point to an example? PatrickR2 (talk) 22:42, 2 January 2023 (UTC)

I was afraid you'd ask that. It's not in my history for some reason. Now I don't remember.— Vchimpanzee • talk • contributions • 22:53, 2 January 2023 (UTC)

There is a similar situation on Abel–Plana formula. "Let" is used at the beginning of a section. Is this acceptable?— Vchimpanzee • talk • contributions • 23:05, 2 January 2023 (UTC)

The section of the article titled Abel–Plana formula that begins with "Let" in fact begins with this:

Let $f$ be holomorphic on $\Re (z)\geq 0$, such that $f(0)=0$, $f(z)=O(|z|^{k})$ and for $\operatorname {arg} (z)\in (-\beta ,\beta )$, $f(z)=O(|z|^{-1-\delta })$.

That is obviously not anything at all like a "How to". To think that it is is to construe a standard and universally known figure of speech literally. The purpose of the word "let" is to specify the notational conventions used in the succeeding text and some of the hypotheses of the theorem whose conclusion will follow. Michael Hardy (talk) 01:03, 8 January 2023 (UTC)

MOS:MATH#TONE is the relevant style guideline, FWIW. --JBL (talk) 23:08, 2 January 2023 (UTC)

That seems to support a change, but there are probably a lot of places where this is wrong.— Vchimpanzee • talk • contributions • 23:17, 2 January 2023 (UTC)

Note that 'Let' and Consider that' are two of its examples, so obviously it is easy to see that they should be changed where seen and not if and only if each case has been debated! ;-) NadVolum (talk) 23:52, 2 January 2023 (UTC)

The examples given in MOS:MATH#TONE may describe an appropriate method for avoiding sentences like "Define X to be ..." in cases where the subsequent usage of X is simple enough that the definition can be crammed into the next sentence. But the effect of this replacement is to make sentences longer and more complicated, unnecessarily making them worse with regard to WP:TECHNICAL. This is worse when both the definition of X and the usage of it are themselves more complicated than the examples given. I think the cure is worse than the disease. To be concrete, here's an example from Malfatti circles, a Good Article.

• Current text: Given a triangle ABC and its three Malfatti circles, let D, E, and F be the points where two of the circles touch each other, opposite vertices A, B, and C respectively. Then the three lines AD, BE, and CF meet in a single triangle center known as the first Ajima–Malfatti point. (This is actually simplified from the actual text of the article, in which the second sentence is even longer.)
• Changed to match the examples in MOS:MATH#TONE: Given a triangle ABC and its three Malfatti circles, if D, E, and F are the points where two of the circles touch each other, opposite vertices A, B, and C respectively, then the three lines AD, BE, and CF meet in a single triangle center known as the first Ajima–Malfatti point.

That changed sentence is far too long and convoluted, and its overall structure is much harder to follow. Removing the imperative is not an improvement. Using a larger number of shorter sentences is usually better than avoiding imperative. There is nothing wrong with imperative sentences, and much wrong with blanket prohibitions against them. Additionally, this point of grammar has nothing to do with WP:NOTHOWTO, which is bad advice about never having content that describes algorithms rather than bad advice about never using imperative grammar. —David Eppstein (talk) 00:40, 3 January 2023 (UTC)

I 100% agree here with David Eppstein: the cure is far worse than the disease here, and the guidelines are misapplied or simply wrong. - CRGreathouse (t | c) 06:33, 3 January 2023 (UTC)

Can we get some kind of RFC started to amend MOS:MATH#TONE? Insisting on replacing language like "π is a mathematical constant" with language like "The letter π denotes a mathematical constant" seems like a recipe for boring, borderline unreadable prose. If anything, we should aim to do replacements in the opposite direction wherever possible. –jacobolus (t) 07:32, 3 January 2023 (UTC)

That example is intended to illustrate the principle that sentences should not begin with mathematical notation. That is a fine principle, that is observed in most math writing. It is almost totally independent of the "let"/"consider" issue that we are currently discussing. Mgnbar (talk) 08:33, 3 January 2023 (UTC)

Yeah I think the examples there are poor. For example, Let H be the corresponding subgroup of G. H is then finite. can be equally well fixed by rewriting it as Let H be the corresponding subgroup of G. Then H is finite. -- the problem has nothing to do with "let", and this is confused by the text. The others are similar. --JBL (talk) 19:59, 3 January 2023 (UTC)

No, this has nothing to do with WP:NOTHOWTO. This kind of construction is ubiquitous in mathematical writing, and is not at all the same as a recipe or instruction manual. –jacobolus (t) 07:26, 3 January 2023 (UTC)

I agree with this. --JBL (talk) 20:08, 3 January 2023 (UTC)

I agree entirely with you, and also with David Eppstein above. PatrickR2 (talk) 02:14, 4 January 2023 (UTC)

No, imperatives of the form "Let $N$ be an integer..." do not violate WP:NOTHOWTO. The imperative "Consider that..." is only poor form in so far as it can be superfluous syllables, like the often-eliminable "Note that...". XOR'easter (talk) 15:23, 3 January 2023 (UTC)

I'm glad I got the discussion started. I may have pointed to the wrong policy, but it seemed like these articles were violating something. Now that I see what others think, it may not be a problem.— Vchimpanzee • talk • contributions • 22:58, 3 January 2023 (UTC)

Mathematical writing necessarily involves introducing many new labels, definitions, notations, and structures, often as a hypothetical. There aren’t really any ways to do this that don’t end up sounding sort of forced/formal, and a bit awkward/unfamiliar to people who don’t commonly read mathematical writing. These imperative “Let ...” constructions come straight out of Euclid, and are if anything a way of removing a recipe-like action. Instead of saying “Draw an arbitrary triangle on your paper and label the vertices A, B, and C”, we invoke an abstract triangle out of thin air: “Let ABC be a triangle ...”. –jacobolus (t) 04:34, 4 January 2023 (UTC)

Currently, "Let" is a disambiguation page, but is there a page on wikipedia that explains "Let (mathematical topics)" ? --SilverMatsu (talk) 17:54, 22 January 2023 (UTC)

Let expression also discusses the mathematical grammatical use of "let". --{{u|Mark viking}} {Talk} 18:35, 22 January 2023 (UTC)

MOS:MATH

Pulling out something not related to this discussion: I think this old version of the relevant section was superior in many ways to the current version. (The major edits to that section were in this batch of edits by Magyar25, followed by the mid-section addition of a see-also template by Matthiaspaul.) I propose to revert the section on Writing style in mathematics to the earlier version. (I have not looked at the changes to other sections of MOS:MATH in the same batch of edits; hopefully they are better?) --JBL (talk) 20:06, 3 January 2023 (UTC)

That version may be better but they're both pretty bad IMO. A major rewrite is in order, if someone has the energy for it. - CRGreathouse (t | c) 14:45, 9 January 2023 (UTC)

"top priority" assessment in this wikiproject

This Wikiproject's priority/importance assessment seems to be somewhat variable/arbitrary. Has there been any effort by anyone to look through the lists of Top, High, and possibly Mid importance categories and figure out if they match anyone's gut feeling about relative importance of topics? As an example, here is the list of current "Top" importance mathematicians: Archimedes, Michael Atiyah, Georg Cantor, Shiing-Shen Chern, Paul Erdős, Euclid, Leonhard Euler, Kurt Gödel, Alexander Grothendieck, Jacques Hadamard, Felix Hausdorff, David Hilbert, Donald Knuth, Henri Lebesgue, Benoit Mandelbrot, James Clerk Maxwell, Isaac Newton, Henri Poincaré, Pythagoras, Srinivasa Ramanujan, Bernhard Riemann, Bertrand Russell, Jean-Pierre Serre, Alan Turing, Karl Weierstrass, André Weil. This seems to be a somewhat idiosyncratic list, missing many of the most famous and influential mathematicians in history and including some who seem to me to be less important.

I just added Carl Friedrich Gauss, René Descartes, Apollonius of Perga, Brahmagupta, John von Neumann, Aryabhata, Joseph-Louis Lagrange, Joseph Fourier, Gottfried Wilhelm Leibniz, Muhammad ibn Musa al-Khwarizmi, Emmy Noether, John Napier, Pierre de Fermat, Augustin-Louis Cauchy, Ptolemy, William Rowan Hamilton, Blaise Pascal, Andrey Kolmogorov, but I am sure there are many more who belong in this list that I am not thinking of off the top of my head. –jacobolus (t) 02:15, 22 January 2023 (UTC)

Perhaps the priority assessment for mathematicians should happen on a different scale to the assessment for mathematics pages? Of those mathematicians listed, how many of them could we really say are of an equal priority for presentation on the wikipedia as, say, Calculus or Manifold or Algebra? Not many: probably Euler, Euclid, Newton, Leibniz, and maybe a few others. I think compared to some of the top priority mathematical pages on the project, most of the mathematicians in top should really be ranked high, and some even mid.

I don't have much skin in the game really, but maybe a good heuristic is if the mathematician appears in the lead of a top priority mathematical article, we should consider them a top priority mathematician article? Tazerenix (talk) 02:57, 22 January 2023 (UTC)

I am demoting Knuth, Hadamard, and Atiyah to 'high' priority. –jacobolus (t) 05:00, 22 January 2023 (UTC)

I definitely think we have too many mathematicians at top priority. I would prefer to demote the vast majority to high. Maybe Gauss, Euclid, Euler, Brahmagupta, al-Khwarizmi as top and the rest to high. A few others, perhaps (Cauchy? Hilbert? Weierstrass?), but not many. - CRGreathouse (t | c) 07:02, 22 January 2023 (UTC)

There are thousands of articles about mathematicians on Wikipedia. It seems entirely fine to me if a few dozen of them are "top" priority. –jacobolus (t) 08:47, 22 January 2023 (UTC)

What about those who should be considered top priority in some other field but not in Mathematics, e.g., Donald Knuth? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:40, 22 January 2023 (UTC)

In practice, the "importance" ratings are not important. Hardly anyone is more likely to write about Fourier or less likely to write about Hadamard because their importance ratings have changed. —Kusma (talk) 13:38, 22 January 2023 (UTC)

My understanding is that they have accomplished a bit more at some other Wikiprojects, where there was a concerted effort to bring articles among the top couple levels of the importance scale up to “B” level or the like. There are many extremely influential mathematicians and many fundamental mathematical topics which currently have mediocre articles. Someone can click through to e.g. Top-importance C-class or High-importance Start-class articles to get some ideas for articles that are especially in need of care and attention. –jacobolus (t) 18:44, 22 January 2023 (UTC)

Invitation

Hello all, I would like to invite you to attend in Articles for deletion/Similarity-based-TOPSIS and submit your opinion. I know that this article is in the field of operations research but there is no project related to operations research. Thank you in advance. Scholartop (talk) 06:28, 23 January 2023 (UTC)

Harish Chandra Rajpoot links

The IP accounts Special:Contributions/103.21.125.84 and Special:Contributions/103.21.127.79 keep adding links to academia.edu and arXiv articles by Harish Chandra Rajpoot to the external links sections, e.g. to Trapezohedron, Great-circle distance, Solid angle, Descartes' theorem, Circle packing. My speculation is that these IPs are being used by Mr. Rajpoot himself (apparently a graduate student at IIT Bombay) to promote his papers here. I removed several of these links because, while relevant, the content raises some other red flags: Rajpoot's papers don't cite any prior sources and name known results after himself. I left a comment on his talk page suggesting he may want to try publishing his work in a peer-reviewed journal; in response he put back a new link, this time to the paper "HCR’S THEORY OF POLYGON 'Solid Angle Subtended By Any Polygonal Plane at Any Point in the Space'" "published" in the journal International Journal of Mathematics and Physical Sciences Research by "Research Publish Journals", which does not seem to be peer reviewed. Does someone else want to try to talk to this IP user and try to get them to engage in conversation? –jacobolus (t) 16:52, 26 January 2023 (UTC)

Including maths rating

I would gladly include {{maths rating}} in some other articles that almost contain mathematical topics. However, is it still allowed to include this template in articles that contain fewer mathematical subjects? I was considering that it could be possible to add it in Quasicrystal since it has fewer mathematical subjects, but most of this describes chemistry. I am not sure whether it would be appropriate for this project. Dedhert.Jr (talk) 12:45, 25 January 2023 (UTC)

I went ahead and added it to Quasicrystal. In general there doesn't seem to be any problem with putting partially mathematical topics into the math wikiproject. –jacobolus (t) 16:59, 26 January 2023 (UTC)

I see. Thank you. Dedhert.Jr (talk) 02:25, 27 January 2023 (UTC)

Discussion at Wikipedia:Village pump (idea lab) § Standardizing Mathematical Notation

 You are invited to join the discussion at Wikipedia:Village pump (idea lab) § Standardizing Mathematical Notation. CactiStaccingCrane 13:40, 29 January 2023 (UTC)