Wikipedia talk:WikiProject Mathematics/Archive/2020/Feb

Universal hyperbolic geometry

Expert input at Wikipedia:Redirects for discussion/Log/2020 February 1#Universal hyperbolic geometry would be welcome. Narky Blert (talk) 00:46, 2 February 2020 (UTC)

Quartic Polynomials in Sums of three cubes.

Resolved

In Sums of three cubes, the statement is made that "However, 1 and 2 are the only numbers with representations that can be parameterized by quartic polynomials in this way.[5]". I don't understand why Quartic (degree 4) is used here. I could see Cubic or Sextic, but not Quartic.Naraht (talk) 19:28, 3 February 2020 (UTC)

Based on the previous paragraph, I suspect what it's going for is that the terms that are being cubed in the parametrizations are all quartic or less. –Deacon Vorbis (carbon • videos) 19:55, 3 February 2020 (UTC)

Yep, and the cited Mordell paper proves the theorem:

The equation x³ y³ z³ = n has no solutions with x, y, z as quartic polynomials in a parameter t with rational coefficients unless n = 2a³, or n = a³, where a is a rational number

— MarkH₂₁^talk 20:35, 3 February 2020 (UTC)

Thanx. I'm not even sure I'd be able to follow the proof to that point (I can't see all of Mordell's paper), but thought I'd check and this seemed the right place.Naraht (talk) 21:34, 3 February 2020 (UTC)

No worries, it's some five pages (i.e. everything but the freely-available first page) of calculations and case-checking. Mordell was quite good at that sort of thing! — MarkH₂₁^talk 22:18, 3 February 2020 (UTC)

Clockwise and counterclockwise on the Riemann sphere

The Riemann sphere can be visualized as the complex number plane wrapped around a sphere (by some form of stereographic projection – details are given below).

In this image of the Riemann sphere, going counterclockwise around ${\textstyle -i}$ corresponds to going clockwise around it in the usual way of depicting the plane. Should this reversal of orientation be considered a problem? Michael Hardy (talk) 20:54, 31 January 2020 (UTC)

Right, the sphere is folded so that the inside is the usual plane. It would be better with i and -i switched. (Also the fonts are quite ugly.) --JBL (talk) 23:31, 31 January 2020 (UTC)

@JBL: If you swap i with −i it would no longer be a stereographic projection of Argand's plane onto a sphere. At least not in the most obvious configuration. The resulting sphere would be an image of a stereographic projection to a sphere tangens from 'below', then rotated by 180° around its (real 1) -- (real −1) diameter. I'm afraid it's much harder for average reader to understand the plane-to-sphere correspondence in this case than in the one depicted above. --CiaPan (talk) 23:52, 31 January 2020 (UTC)

@CiaPan: If you swap ${\textstyle 0}$ and ${\textstyle \infty }$ and leave ${\textstyle \pm 1,\,\pm i}$ where they are, then that fixes the reversal-of-orientation problem and if the Argand plane is parallel to the plane containing ${\textstyle \pm 1,\,\pm i}$ and the center of projection is the point labeled ${\textstyle \infty }$ on the sphere, then you still have an ordinary stereogrpahic projection. Michael Hardy (talk) 04:19, 5 February 2020 (UTC)

The biggest problem with the font is that hyphens appear where minus signs should be:

${\begin{aligned}{\text{minus sign: }}&{-i}\\[5pt]{\text{hyphen: }}&{\text{-}}i\end{aligned}}$

Michael Hardy (talk) 06:12, 1 February 2020 (UTC)

@Michael Hardy: Fixed. --CiaPan (talk) 16:04, 3 February 2020 (UTC)

Or instead of interchanging ${\textstyle \pm i}$ one could interchange ${\textstyle 0}$ and ${\textstyle \infty .}$ Michael Hardy (talk) 06:16, 1 February 2020 (UTC)

Idea for new community workspace

Hi. I would like to create some kind of collaborative workspace where coordinators or members of various WikiProjects would gather and provide updates and information on what is going on at each wikiproject, i.e. regarding their latest efforts, projects, and where interested editors can get involved. For those of you at this very active WikiProject, your input would be very helpful, so I wanted to get your input on whether you'd be interested in helping me to make this happen.

we are discussing this proposal right now at:

* Wikipedia:Village pump (proposals)#Idea for new community workspace

Please feel free to let me know what you think of this idea, and please let me know your preference, regarding the options above. if you do not see any need for this idea, that is totally fine. However, I think that the majority of editors lack awareness of where the truly active editing is taking place and at which WikiProjects, and I would like to do whatever I can to help make people more aware of where the activity is, what they can do to help, and also which areas of Wikipedia offer ideas and efforts that might help them in their own editing activities. Please feel free to let me know.

• Would you be interested in an idea of this nature?
• If so, which option below seems most feasible to you?
  • Create a new page/talk page at the existing WikiProject Council, where members of various WikiProject can gather to offer updates, information and ideas on the latest efforts at each of their own WikiProject, such as Wikipedia:WikiProject Council/Town Hall.
  • Create an entirely new WikiProject with an inclusive name such as
    • Wikipedia:WIkiProject Town Hall,
    • Wikipedia:WikiProject Bulletin Board,
    • Wikipedia:WikiProject Water Cooler
  • Create a new collaborative page or forum, but not as a new WIkiProject, i.e. with some name like
    • Wikipedia:Town Hall or
    • Wikipedia:Water Cooler
  • Create a new sub-page in my own userspace, such as User:Sm8900/Town Hall
  • Create a subpage at an umbrella-type WikiProject that already covers a broad topical area, such as Wikipedia:WikiProject History/Town Hall

thanks. --Sm8900 (talk) 19:03, 9 February 2020 (UTC)

Name change: non-standard -> nonstandard

We are discussing here whether to remove the hyphen in nonstandard analysis, in line with most of the current literature on the topic. Please weigh in. --Jordan Mitchell Barrett (talk) 04:54, 14 February 2020 (UTC)

Seems we've reached a consensus to change. If you see any uses of the word "non-standard" in reference to nonstandard analysis or the use of ultrapower methods, please change these to "nonstandard". --Jordan Mitchell Barrett (talk) 06:01, 15 February 2020 (UTC)

Need a bit of help performing the move - I've done the main page and fixed up that page's content, but still need to do this talk page, everything in this category, etc... — Preceding unsigned comment added by Jordan Mitchell Barrett (talk • contribs) 06:48, 15 February 2020 (UTC)

One of your project's articles has been selected for improvement!

Hello, Please note that Length, which is within this project's scope, has been selected as one of Today's articles for improvement. The article was scheduled to appear on Wikipedia's Community portal in the "Today's articles for improvement" section for one week, beginning today. Everyone is encouraged to collaborate to improve the article. Thanks, and happy editing! Delivered by — MusikBot talk 00:05, 17 February 2020 (UTC) on behalf of the TAFI team

Page proposal - homotopy classification of fiber bundles

There should be a page describing the homotopy classification of fiber bundles. This could include the classification of vector bundles, sphere bundles over spheres, and complex line bundles. This topic motivates a lot of other topics in mathematics, such as characteristic classes and stacks. What are people's thoughts? Wundzer (talk) 22:54, 15 February 2020 (UTC)

Isn’t that what a classifying space (or its variant) is for? Do you have a proposed name for the article you’re proposing? —- Taku (talk) 23:07, 15 February 2020 (UTC)

Whoops, this will work. Thanks for the heads up. This section can be deleted. Wundzer (talk) 18:33, 17 February 2020 (UTC)

Matrix representation of tensors

This article is so problematic (in my view) that deletion is warranted, hence the AfD. If someone with better knowledge of this subject can rescue the article, then I'll withdraw my AfD.

I only had a brief exposure to differential geometry, but I firmly believe that the notion that we cannot represent a metric tensor as a matrix when it is a bilinear form on each tangent space instead of a linear transformation thereof is completely wrong, especially absent actual reliable sources for that view. See Wikipedia:Articles for deletion/Matrix representation of tensors for my full argument on that front. Pinging @D.Lazard, Joel B. Lewis, Slawekb, and RDBury: among others.--Jasper Deng (talk) 08:33, 19 February 2020 (UTC)

Draft:Derived Noncommutative Algebraic Geometry

A review of this draft is requested. Should it be accepted into article space? Robert McClenon (talk) 22:47, 10 February 2020 (UTC)

Unsure if it merits its own article at the moment, but merging it to Derived algebraic geometry (which is currently underdeveloped) is a viable option. — MarkH₂₁^talk 00:32, 11 February 2020 (UTC)

I agree the merger is a better option. My Google search tells that this is the derived version of noncommutative algebraic geometry and so merged with that article makes more sense. —- Taku (talk) 07:18, 11 February 2020 (UTC)

Hi everyone, I saw the DNCAG article was rejected because it was labelled as a spinoff of the article on derived algebraic geometry. Although these articles has similar sounding titles, they are distinct subjects. Here's a useful analogy: algebraic geometry is to noncommutative geometry as derived algebraic geometry is to derived noncommutative algebraic geometry. The basic objects considered in these fields are separate. In DNCAG the objects are triangulated categories while in DAG they are derived rings, such as simplicial rings or differential graded algebras. Here's a couple relevant links https://en.wikipedia.org/wiki/Noncommutative_geometry#Noncommutative_affine_and_projective_schemes https://en.wikipedia.org/wiki/Algebraic_geometry Is it fine if I resubmit this article and not have it declined because of the discussed reasons above? Is there anything you'd like me to add to the DAG article to try and differentiate the two subjects even further? Wundzer (talk • contribs) 19:17, 11 February 2020 (UTC)

Also, here are some plans for the article which further differentiates it from the DAG article: It will include discussions of fourier mukai transforms, deformations of FM transforms, deformations of abelian categories, derived categories of singularities and matrix factorizations. Moreover, check out my comments on the talk page of the DAG page. I've listed out some information for how the article could be expanded, without having a full on merger

Wundzer, what do you feel about the merger with Noncommutative algebraic geometry? If I remember right, thinking that a category (or higher one) is a type of noncommuattive space is central to NAG. So, the merger with the article makes more sense. (On the other hand, the merger with the DAG article is very bad idea). If a length becomes an issue, we can always spin-off the DNCAG portion later. -- Taku (talk) 00:57, 13 February 2020 (UTC)

TakuyaMurata, that's not a bad idea, but let's wait a week or so. I'll go ahead and add more to the DNCAG article and then we can make a decision then. I agree they are similar subjects, Rosenberg has a non-commutative geometry based on abelian categories. Moreover, -- User:Wundzer (talk)

Certainly. —- Taku (talk) 23:23, 13 February 2020 (UTC)

I have risen a potential issue with the article title (i.e., not completely sure if DNAG is the common name) at Draft_talk:Derived_noncommutative_algebraic_geometry#Main reference needed. -- Taku (talk) 00:31, 21 February 2020 (UTC)

Hey, does anyone know how to embed tikz diagrams into wikipedia? I want to draw out the diagram for TR4 in https://arxiv.org/pdf/math/0302304.pdf, but using the objects in the construction part of the article.Wundzer (talk) 20:06, 20 February 2020 (UTC)

@Wundzer: You can upload the diagram as an image, since there is no tikz-cd support in WP right now. Instructions are here, just ignore the xy-pic step. — MarkH₂₁^talk 20:46, 20 February 2020 (UTC)

Boris Tsirelson

Some very bad news regarding Boris Tsirelson is at Talk:Boris Tsirelson#Death. An IP has already added the information to the article, citing the talk page as a reference. This needs sensitive handling that is out of my reach. The IP has posted on my talk. I'm hoping that people here will be able to locate a reliable source. Johnuniq (talk) 08:23, 23 February 2020 (UTC)

This is very sad. Hopefully there will be a statement from the department or university. Obviously it should not be added to the article based on the talkpage comment. (I should add that I have spent some time looking for a RS but have not found one yet.) --JBL (talk) 21:51, 23 February 2020 (UTC)

I also looked for a little while but did not find anything, so I wrote to some colleagues who I think are closer to Tsirelson in the citation graph. Maybe at least I'll hear if an official announcement is in the works. XOR'easter (talk) 22:43, 23 February 2020 (UTC)

Thanks but the IP has found a ref and added it to the article. Please have a look and see what else should be done. Johnuniq (talk) 08:49, 25 February 2020 (UTC)

I was hoping it was a hoax, though I didn't think it was very likely. --Trovatore (talk) 20:17, 25 February 2020 (UTC)

Yau's nationality

Stomatapoll has made a bunch of edits to many different articles concerning the nationality of Shing-Tung Yau. Of the two I looked at slightly closely, one did not involve any sources, while the other involved a source in Chinese; I tend to think the latter is not actually about Yau. I think this would benefit from more eyes and some discussion. --JBL (talk) 19:54, 26 February 2020 (UTC)

I didn’t look at the user’s edits, but the timeline of his nationality is fairly clear with the passages from his recent autobiography:

Stephen Hawking invited me to discuss [the proof] with him at Cambridge University in late August 1978. I gladly accepted.... Travel was difficult, however, because the British Consulate had recently taken my Hong Kong resident card, maintaining that I could not keep it now that I had a U.S. green card. In the process, I had become stateless. I was no longer a citizen of any country.... until I became a U.S. citizen in 1990.

— Yau, Shing-Tung; Nadis, Steve (2019). The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry. Yale University Press. p. 125.

The only confusing thing is that he says in the quote that he became stateless despite not renouncing his Chinese citizenship. In fact, the New Yorker attributes the following quote to him:

I am proud to say that when I was awarded the Fields Medal in mathematics, I held no passport of any country and should certainly be considered Chinese.

— New Yorker article

.

As the footnote in Shing-Tung Yau added by another editor correctly states, he lost his HK residency card and didn't have a passport (probably what he meant by stateless in the autobiography quote) but was still legally a Chinese citizen and considered himself as such with regards to Fields Medal attribution. — MarkH₂₁^talk 20:36, 26 February 2020 (UTC)

@MarkH21: Thank you for looking into it! --JBL (talk) 13:29, 27 February 2020 (UTC)