# Wikipedia talk:WikiProject Mathematics

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## RfC: Reliability of the nLab

Some articles on Wikipedia, such as Higher category theory, Enriched category, ∞-groupoid, and Quasi-category, use the nLab as a source. However, according to past discussions on the nForum, such as [1] [2] [3] and [4] it is fairly clear that the nLab allows original research within the wiki. Because of that, the nLab is self-published content WP:RSSELF and shouldn't be used as a reliable source on Wikipedia. 96.63.208.27 (talk) 17:07, 18 April 2022 (UTC)

• This may technically be an ill-formed RfC, since RfC's are supposed to open with a neutral statement rather than advocate a particular conclusion. But setting that aside, the nLab is mostly written by subject-matter experts, so in principle it could be used in some circumstances per WP:SPS. However, because it is a wiki, figuring out who contributed what is time-consuming, and it is probably best to use it as a collection of pointers into the more formal literature. (I am adapting my remarks from my So, you've decided to write about physics and/or mathematics on Wikipedia general advice page, which I will update if the discussion here so indicates.) XOR'easter (talk) 17:27, 18 April 2022 (UTC)
• Well as a stickler for procedure I have removed the inappropriate RfC tag. IP, if there's some place you think the nLab is being used in a way that is problematic, you are welcome to tag it, to start a discussion on the article talk-page, or to boldly remove it (with the recognition that you might be reverted). --JBL (talk) 17:33, 18 April 2022 (UTC)
The mentioned articles don't use the nLab as an inline reference, as far as I noticed, but at the bottom as a general reference or external link. XOR'easter (talk) 17:47, 18 April 2022 (UTC)
I noticed that as well. ∞-groupoid does use it as an inline reference. (The sentence it's attached to seems oddly placed to me, fwiw.) --JBL (talk) 17:53, 18 April 2022 (UTC)
As an external link I think nLab is fine: generally of much higher quality than MathWorld, which we use regularly as an external link, for instance. I am not convinced it qualifies as a reliable source, though. —David Eppstein (talk) 17:55, 18 April 2022 (UTC)
In fact it is used as an inline reference in other places: see [5]. Perhaps 250 uses in total. --JBL (talk) 18:01, 18 April 2022 (UTC)
Thanks for checking! XOR'easter (talk) 18:27, 18 April 2022 (UTC)
As an inline reference, I think it is roughly comparable to using lecture notes that a researcher has posted on their website. That is: it's definitely better than nothing, and on some topics it may happen to be quite useful, but it should not be regarded as ideal and whenever possible should be replaced by better refs. Gumshoe2 (talk) 18:16, 18 April 2022 (UTC)
nLab is usually a mess, to be honest. Maybe refactoring some of the references to Lurie/Riehl's work might be appropriate. -- Fourier-Deligne Transgirl (talk) 07:37, 1 May 2022 (UTC)

## Calculus on Euclidean space

Beland has recently moved the draft Calculus on Euclidean space into mainspace. I think that in its current state, it really can't hold its own as a published article. So I was wondering what to do with this. While the draft was clearly started with the ambition to cover more advanced topics, the current content could probably be adapted very nicely into a section for Multivariable calculus, which is surprisingly thin. On the other hand, I don't fully understand how all of our higher calculus articles fit together, so perhaps that would not be the most natural place for the material. Felix QW (talk) 21:15, 30 April 2022 (UTC)

My first instinct would be to expand the Multivariable calculus article, which briefly touches upon differential forms, rather than creating a new article. Calculus on Euclidean space should not have been moved into mainspace: multiple sections are tagged as needing expansion, one section is nothing more than a "main article" link to somewhere else, a sentence just trails off without finishing, and a subsection is completely empty.
I don't think there is a plan for how our higher-calculus articles fit together, or how any articles fit together, really. XOR'easter (talk) 22:29, 30 April 2022 (UTC)
So, I am the one who started the article (and, in a way, the fault of not expanding it sufficiently goes to me, I guess). The issue is related to the question of what advanced calculus refers to: it can often mean multivariable calculus but can also mean an elementary part of real analysis, though it currently redirects to mathematical analysis. The article title "Calculus on Euclidean space" was meant to avoid this ambiguity of the term "advanced calculus".
In my opinion, the scopes of "advanced calculus" and "multivariable calculus" tend to differ; in the US at least, multivariable calculus seems to refer to a calculus course that follows one-variable one but does not cover more advanced topics like differential forms. If the main audience of "multivariable calculus" article is undergraduates taking such calculus courses, then treating that article with the advanced calculus topics is not a good idea (whence a separate article is warranted). -- Taku (talk) 09:00, 1 May 2022 (UTC)
Thanks, I understand a bit better now. In England and in Germany, the usual progression form maths or physics students is Sixth-Form calculus (1 variable) -> Real analysis in 1 variable -> Analysis in several variables, so the specific audience for multivariable calculus did not occur to me. I do think you have a point, since presumably engineering majors would make up a large part of the readership of the multivariable calculus page.
PS Don't worry, Taku - you didn't move it to mainspace, so you can hardly be faulted :) Felix QW (talk) 10:03, 1 May 2022 (UTC)
There are issues with how the articles fit together, e.g., Tensors covers a lot of material that belongs in Tensor fields.
The modern view of calculus is centered on differentiable manifolds, but understanding and using, e.g., the definition of charts, requires a basic understanding of multivariable calculus.
The baic results of multivariable calculus don't really depend on a Euclidean metric, but at the moment I can't think of a better title than "Calculus on Euclidean space". --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:28, 1 May 2022 (UTC)
I agree with others that it should not be in mainspace. Aside from the content problems pointed out by Felix QW, the intended scope of the article should be clarified. I think it is usually accepted (and is a principle which I believe anyway) that it is not good to write wiki articles based on parameters set by university coursework, which seems to be suggested above. Gumshoe2 (talk) 19:09, 1 May 2022 (UTC)
I have just approached the mover of the draft into mainspace whether he would agree with re-draftifying the page for now. I gathered from the very restrictive language at WP:DRAFTIFY that this would be necessary. Felix QW (talk) 17:18, 2 May 2022 (UTC)
Not sure this matters to the ultimate destination of this content, but checking the history, it looks like this content was actually branched off of: https://en.wikipedia.org/w/index.php?title=Differential_geometry_of_surfaces&oldid=971313451#Function_theory_in_two_variables
I would prefer this article not be sent back to draft space. It sat there in a zombie state for years with no one working on it, getting deleted and undeleted. With due respect to good intentions, TakuyaMurata created a lot of draft articles and then left them in this zombie state, and the point of bringing the promising ones into mainspace is to get the attention and contributions of other editors.
Given that knowledgeable editors people are looking at the content now, I think it's time to decide whether to delete, merge, or rewrite it. Delete is the easy case; it could be sent to Wikipedia:Articles for deletion now. If a rewrite under this title were desired, it can either be tagged as problematic and worked on here, just like plenty of other mainspace articles that are incomplete and poorly written. Or, if there's a lot of problematic content that definitely has no place in the rewrite, that content can simply be stripped, possibly making the article a stub in the spirit of Wikipedia:Blow it up and start over.
It sounds like the preferred option is merge to Multivariable calculus. If that can be done in a few days, it should just be done. If it's going to take a long time, Calculus on Euclidean space can simply be tagged for cleanup and merge and left until someone can deal with it, possibly after trimming any content that's clearly not going to be retained. Or, the content could get a rough cleanup and be merged now, and the new content on Multivariable calculus tagged for cleanup until someone can get around to it. If none of the content here is really helpful verbatim, but the ideas expressed could guide the expansion of Multivariable calculus, I would recommend making Calculus on Euclidean space a redirect there, and adding a note on Talk:Multivariable calculus with an outline of the proposed expansion. Or if that's too much work, just add a note there referring to the edit history of Calculus on Euclidean space and maybe someone will look at it some day, or maybe Multivariable calculus will grow organically without referring to this content, but at least content editors find ugly won't be publicly visible. If content needs to be rebalanced among math articles generally, cleaning up and merging Calculus on Euclidean space does not necessarily need to wait for that, and in fact doing that may clarify how the rebalancing would work. -- Beland (talk) 17:59, 2 May 2022 (UTC)
First to respond to @Gumshoe2: no, I don't believe the principle that math articles should be organized in a mathematically natural way regardless of how materials are taught in school. In fact, we are not allowed to do that; articles in wikipedia are titled and cover what typical readers would expect (and the expectation is sharped by school works). If we were to build some treatise on math in a manner faithful to math, that has to be a different project (I have an idea of such a project but that's another story). Note that no refs cited in Calc on E have titles with "multivariable calculus", which argue against a merger. Like I said above, the question is whether advanced calculus is the same thing as multivariable calculus and, if the answer is no, the merger is probably a wrong move.
To @Beland:, to me, the simplest solution is to put back the article back to the draftspace. Yes, there would be a danger that it stays there while not being developed actively. But I do still have an intension to develop the article, although, at least for now, I am too busy with real-life stuff. -- Taku (talk) 07:37, 3 May 2022 (UTC)
Would somebody restore Draft talk:Calculus on Euclidean space for this discussion ? --SilverMatsu (talk) 16:05, 3 May 2022 (UTC)
Talk:Calculus on Euclidean space exists and is available for this discussion to be continued there. Felix QW (talk) 16:12, 3 May 2022 (UTC)
The page doesn't seem to reflect the deleted 18 revisions.--SilverMatsu (talk) 17:15, 3 May 2022 (UTC)
Ah, I understand now. Sorry, I missed your point. Felix QW (talk) 18:06, 3 May 2022 (UTC)
Don't worry about it, or rather, Thank you for telling me that we need to merge the history after this page is restored. I missed that talk page.--SilverMatsu (talk) 00:44, 4 May 2022 (UTC)
Graeme Bartlett has helpfully moved the draft talk page contents (with history) to Talk:Calculus on Euclidean space. -- Beland (talk) 09:39, 4 May 2022 (UTC)
If you don't have time to work on this article, it's probably best to leave it to others. I just trimmed so it looks more like an article that could grow and less like an incomplete thought. It sounds like the question of whether or not this should be merged into multivariable calculus is unsettled, so I added merge discussion tags pointing here. I can implement a rough merge if consensus favors that solution, though a math enthusiast might do a better job. -- Beland (talk) 09:51, 4 May 2022 (UTC)
@Beland: In Wikipedia, no article belongs to anyone so it makes little sense to say "leave it to others". On Thu, I have a meeting but on Fri, I will probably have more time and so will try to expand the article so to address some of concerns. Also, to me, the consensus is that the article is not ready to be put in mainspace and so putting it back to the draftspace would be a natural obvious solution (is it just me?) -- Taku (talk) 10:34, 4 May 2022 (UTC)
@Gumshoe2: An addendum to my comment above. A good example of school courses affecting the way articles are organized is the fact we have two separate Stokes theorem and generalized Stokes theorem. Mathematically, this doesn't make much sense since there is only one Stokes' formula. But presenting the general version of Stokes theorem as Stokes theorem would be contrary to the readers who expect to see a version they saw in school. -- Taku (talk) 11:06, 4 May 2022 (UTC)
Also Green's theorem. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:13, 4 May 2022 (UTC)

## Pétur Blöndal

He is listed in Category:Icelandic mathematicians, but I was wondering whether he satisifes WP:PROF.--SilverMatsu (talk) 15:55, 2 May 2022 (UTC)

He may not pass WP:NPROF, but as a member of the Icelandic Parliament should be notable by WP:NPOLITICIAN. Felix QW (talk) 17:10, 2 May 2022 (UTC)
Thank you for your comment. I agree that this article meets WP: NPOLITICIAN, but I wondering whether it is possible to add Category: Icelandic mathematicians to this article.--SilverMatsu (talk) 16:52, 3 May 2022 (UTC)
@SilverMatsu Having a doctorate in mathematics does not make one a mathematician. Voting to not add to your proposed category unless you can document that he has produced substantial mathematical research output. PatrickR2 (talk) 08:28, 5 May 2022 (UTC)
Thank you for your comment. Removed Category:Icelandic mathematicians from article.--SilverMatsu (talk) 15:21, 5 May 2022 (UTC)
Getting a PhD requires writing a PhD thesis, which requires producing substantial mathematical research output. Separately, I doubt you will find consensus for the idea that "producing substantial mathematical research output" is a necessary criterion to be classified as a mathematician. --JBL (talk) 17:10, 5 May 2022 (UTC)
True about the need to write a PhD thesis, although I have personally witnessed a few cases where the corresponding research was not "substantial" (without mentioning any names, e.g., a case where the advisor moved to another school, the student was passed to another professor not really familiar with the area, and the student ended up putting in his thesis results that were not even original research but things that the first professor had mentioned and explained in one of his classes. The advising committee said it was pretty weak, but let him pass anyway, knowing he was going to go to a teaching school.) [Note I am not claiming this is the case here for Blondal, just mentioning in support of the point that a PhD does not a mathematician make.]. More of a case in point, looking at Math Genealogy project for example, you can see lots of new PhD's being granted every year. Quite a few of these don't stay in academics, move to industry, become programmers, work in finance, etc, either right after the PhD or after just a few years, realizing academics is not for them. I don't think anyone can say these people are mathematicians (not to diminish anything to what they might have done for their thesis). PatrickR2 (talk) 04:44, 6 May 2022 (UTC)
@JayBeeEll and PatrickR2: Thank you for your(s) comments. Both agree to comments. I'd like WP: PROF will give an explicit explanation for this case, but as already pointed out, there seems to be no consensus, so I think it is better to decide each case individually.--SilverMatsu (talk) 03:25, 7 May 2022 (UTC)
I think the relevant policy here is WP:Categorization of people, which states:
"For example, a film actor who holds a law degree should be categorized as a film actor, but not as a lawyer unless their legal career was notable in its own right or relevant to their acting career. Many people had assorted jobs before taking the one that made them notable; those other jobs should not be categorized."
So the question is whether our mathematician-turned-politician was notable as a mathematician. And this notability may come from WP:NPROF, but in our case the subject is almost certainly not notable by WP:NPROF standards. So on that basis I would remove him from the category. Felix QW (talk) 15:19, 7 May 2022 (UTC)
WP:COP is just what I was looking for. Thank you so much !--SilverMatsu (talk) 01:09, 8 May 2022 (UTC)

## Hole

The article Hole (topology) seems to revolve around an idiosyncratic definition which is better subsumed in the homology (mathematics) and homotopy groups articles, the term hole is often used in a colloquial sense to give an idea of what these notions mean but presenting it as a formal notion as in done in the article seems to be counterproductive to me (and it is not supported by the given reference). I think the article should be deleted or made a redirect (probably to the article on homotopy groups or homotopical connectivity ; it may also make sense as a disambiguation page). jraimbau (talk) 07:40, 3 May 2022 (UTC)

Just to clarify: Did you check the offline reference (If not, I could do so at some point this week in our library)? Felix QW (talk) 07:57, 3 May 2022 (UTC)
Never mind, I managed to check it and you are right. It doesn't support the formal definition. Felix QW (talk) 08:15, 3 May 2022 (UTC)
I blanked and redirected. I'll notify the page creator, if they disagree i'll make an afd. jraimbau (talk) 12:02, 8 May 2022 (UTC)
I feel like the original redirect target was better. —JBL (talk) 20:32, 8 May 2022 (UTC)
The reference[1] defines "a hole in dimension ${\displaystyle \ell }$  is something that prevents some suitably placed ${\displaystyle S^{\ell }}$  from shrinking to a point". While the definition is not written in mathematical notation, it is clear and accurate. The way to write it in mathematical notation is indicated at the bottom of the same page (specified in the opposite sense): it is "a continuous map ${\displaystyle f:S^{\ell }\to X}$  that cannot be extended to a continuous map ${\displaystyle {\bar {f}}:B^{\ell }\to X}$ ", or equivalently "a continuous map ${\displaystyle f:S^{\ell }\to X}$  that is not nullhomotopic". It is not colloquial - it is completely formal. The advantage of this definition over the one using homotopy groups is that it requires less previous knowledge - it does not require any background in group theory. In contrast, while the page on homotopy groups mentions that they are somehow related to holes, it is not clear from this page what a hole is.
If you still think that the concept of a "hole" does not deserve a page on its own, then I think it is better to merge it into homotopical connectivity. --Erel Segal (talk) 04:48, 9 May 2022 (UTC)

References

1. ^ Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed.). Berlin-Heidelberg: Springer-Verlag. ISBN 978-3-540-00362-5. Written in cooperation with Anders Björner and Günter M. Ziegler , Section 4.3
Since there was no objection, I changed the redirect to homotopical connectivity. --Erel Segal (talk) 11:24, 15 May 2022 (UTC)
I do strongly object to the mention of "hole" as a formal object in mathematics, be it on its own page or on the page about homotopical connectivity.
Here is the relevant excerpt from Matoušek's book :

Informally, a topological space X is k-connected if it has no “holes” up to dimension k. A hole in dimension k is something that prevents some suitably placed Sk from continuously shrinking to a point (...) Of course, things can be more complicated: A torus certainly has a hole in dimension 1 in this sense, but what about dimension 2? Fortunately, we need not contemplate such ﬁne points here, since the formal deﬁnition is simple

and a proper definition of a k-connected space follows. It is clear from this excerpt that there is no formal definition of "hole", as opposed to one of k-connectivity, in this reference and that it actually provides a rationale against such a formal definition: "things can be more complicated", meaning that there is no reason that a "hole" in a topological space should be a missing ball rather than something else; the word is employed here as an intuitive explanation bulding on the (deceptively) simple 2-dimensional case (what is the "number of holes" in a 3--manifold?).
I do support the suggestion of putting the original redirect, to Hole#In_mathematics, back (i chose "homotopy groups" as a target because i was not aware of this original redirect). jraimbau (talk) 16:03, 15 May 2022 (UTC)
I agree wholeheartedly with Jean Raimbault and Felix QW -- the presentation of this as a formal definition of "hole" is deeply misleading at best, close to source falsification (even if not intentionally so). JBL (talk) 17:16, 15 May 2022 (UTC)
I have gone ahead and restored the earlier redirect. --JBL (talk) 17:17, 15 May 2022 (UTC)
Question: the "main article" link is to Homotopy group, but the text at Hole#In_mathematics is about homology. (The latter usage is what I have always heard!) Should there be multiple main article links, and/or should the text under Hole in mathematics be adjusted? Russ Woodroofe (talk) 17:38, 15 May 2022 (UTC)
I added some stuff about homotopy in the hole article (i think the Matoušek quote given by Erel Segal actually fits perfectly there). jraimbau (talk) 18:13, 15 May 2022 (UTC)

## Vertical alignment of \overrightarrow

The latex command \overrightarrow is used many times in Euclidean space, affine space, and other articles of geometry. It is awfully aligned when used with two letters, as in ${\displaystyle {\overrightarrow {PQ}}}$  (to compare with ${\displaystyle {\overrightarrow {P}},}$  which is correct). This misalignment is less visible in displayed formulas. However, if the vector in enclosed with brackets, the brackets are much too long below the line, as in

${\displaystyle \left\|{\overrightarrow {PQ}}\right\|.}$

Also, in some cases, the upper part of the arrow is not displayed, as in
${\displaystyle {\overrightarrow {PQ}}.}$

Does anybody know some work-around, and/or asking for fixing the bug? D.Lazard (talk) 16:51, 4 May 2022 (UTC)

It may be too short … :
${\displaystyle {\vec {PQ}}.}$

${\displaystyle \left\|{\vec {PQ}}\right\|.}$

--SilverMatsu (talk) 15:11, 5 May 2022 (UTC)

The image below is what I see when I look at the posting by D.Lazard above. I suspect others looking at that, including D.Lazaard, see something different because of different settings. @D.Lazard: Is something "awfully aligned" about the arrows as they appear in this screenshot, or do you see something different when you look at the articles and at your own posting above? Michael Hardy (talk) 17:44, 5 May 2022 (UTC)

The screenshot is correctly formatted, except maybe that the vertical lines are too long toward bottom. On my screen, in the inline formula ${\displaystyle {\overrightarrow {PQ}}}$ , the bottom of P is aligned with the middle of text characters such as "n". For the displayed formula with brackets the bottom of PQ and the period are aligned with the middle of the brackets, when the formula should be centered with respect to the brackets. In both displayed formulas the upper part of the arrowhead is lacking. I ignore which sort of setting can produce this sort of display errors. D.Lazard (talk) 20:01, 5 May 2022 (UTC)
Apparently, this is a bug in "MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools)", as, when I change my math preferences to "PNG images", I get the same rendering as you. D.Lazard (talk) 20:11, 5 May 2022 (UTC)
I think the svg fallback is likely to look more or less the same as Michael Hardy's screenshot, so my guess is that Wikimedia thinks your browser can properly render mathml and is not using the fallback, but your browser's rendering of mathml is bad (as is most browsers' renderings of mathml). —David Eppstein (talk) 21:40, 5 May 2022 (UTC)

@D.Lazard: Why don't you post a screenshot, as I did, so that we can tell what you're trying to say? In your comment saying "the upper part of the arrow is not displayed, as in", I see something displaying the entire arrow normally. You require us to take on faith that you see something of which you offer this verbal description but no image matching the discription, while at the same time you appear to intend to show us an image. It's not working at all. Michael Hardy (talk) 18:09, 11 May 2022 (UTC)

I see the same problem as D.Lazard. Here is my screenshot: . Note that the connection between arrow and extension line is also misaligned. It looks bad. --{{u|Mark viking}} {Talk} 19:22, 11 May 2022 (UTC)

This is a problem with the SVG rendering, you can tell this by looking at the code in the developer console. It seems like somewhere in the process, the vertical-align style attribute is incorrect. I've added a Phabricator bug T308188. --Salix alba (talk): 21:19, 11 May 2022 (UTC)

## Labeling "press recognition" and "a proof" based on Quanta & press releases

See Talk:Jinyoung Park (mathematician)#"Widespread recognition" for a content dispute about a recent arXiv preprint that has been discussed in a Quanta article (link) and two department/institute press releases (link 1, link 2).

The dispute is on whether:

1. The Quanta article and press releases can be summarized in WP:WIKIVOICE as Park having received recognition for her preprint
2. The preprint contents can be described as a 6-page proof or a 6-page proposed proof

Any input is much appreciated. Thanks! — 05:50, 9 May 2022 (UTC)

Agree with MarkH21's comments at the link, particularly that the IAS and Stanford press releases are not good sources. The Quanta article is solid verification that the paper is of interest. But it is probably too early to say unambiguously that the result is proved, although (just making educated guess as non-expert in combinatorics) it seems very likely. Gumshoe2 (talk) 06:39, 9 May 2022 (UTC)
Thank you for the input here! Resolved. — Preceding unsigned comment added by Caleb Stanford (talkcontribs)

## Chinese Postman Problem and other arc routing Variants

I am reading a lot about the Chinese Postman problem, which is NP hard for mixed graphs that contain undirected edges and directed arcs. These arcs and edges can be weighted, and solving the mixed Chinese Postman is something I've been working on a lot recently its possible to fit everything about the Chinese Postman Problem in to the article Route Inspection. I would like to suggest a series or template on operations research and arc routing problems. I would like to make the documentation of the Chinese postman problem more comprehensive. ScientistBuilder (talk) 23:24, 9 May 2022 (UTC)

## Need to rephrase Commutative property

I think this article needs to rephrase, for example, the section in Commutative property#Example made the reader, probably, confused to read what it means. It's not also be made confused to read, but it also didn't well written. I'm afraid that this GA will be delisted due to didn't meet one of the criteria of GA. Dedhert.Jr (talk) 13:15, 11 May 2022 (UTC)