Wikipedia talk:WikiProject Mathematics/Archive/2022/Jan

Mathematically Correct

Mathematically Correct (edit | talk | history | protect | delete | links | watch | logs | views)

I've noticed that this article, about a website involved in the math wars, contains major factual errors. In particular, the article falsely claimed (until now) that the website went down c. 2013. It is scant on references, especially reliable ones. It hasn't changed much since 2009, and still lacks a content assessment rating. –LaundryPizza03 (dc̄) 03:41, 1 January 2022 (UTC)

Help needed

Talk:Original proof of Gödel's completeness theorem has a discussion that could use some eyes on it. David notMD (talk) 02:43, 31 December 2021 (UTC)

I would be happy to help, but I am not entirely sure that it is appropriate to have a separate page on Gödel's original proof of the Completeness Theorem.

To establish notability, we would need independent secondary sources treating specifically Gödel's proof of that theorem (rather than the theorem itself). I am only aware of the treatment by Jeremy Avigad in his essay (doi:10.1017/CBO9780511750762.004) and some discussions on the influence of Skolem's earlier work on Gödel. If this is deemed enough, one could try and rework our article based on Avigad's treatment. Felix QW (talk) 13:14, 4 January 2022 (UTC)

Some more research has uncovered the chapter by van Attan and Kennedy in The History of Logic (https://doi.org/10.1016/S1874-5857(09)70014-7), and there is also non-trivial coverage in the Introductory Note to Gödel's dissertation, contained in the Collected Works Vol. I. So that seems to be sufficient to pass WP:GNG? Felix QW (talk) 15:17, 4 January 2022 (UTC)

Transcendental equation

Is this a meaningful concept, treated by reliable sources? I am skeptical. The fact that only one sentence is sourced is not encouraging. --JBL (talk) 01:20, 29 December 2021 (UTC)

• Aside from being dubiously sourced, the contents are also factually dubious. Of the three transcendental equations in the lead with allegedly no closed-form solution, the first and third do have closed-form solutions involving the Lambert-W function , which is not really that obscure. Reyk _YO! 01:27, 29 December 2021 (UTC)
  • It could have meant something meaningful and correct, but just not stated entirely precisely. What's "closed form" depends on what function symbols you allow. If rephrased as "cannot be obtained from the rational numbers via elementary functions", I expect that's true. --Trovatore (talk) 20:32, 29 December 2021 (UTC)
• Even the two first sentences are factually dubious ("A transcendental equation is an equation containing a transcendental function of the variable(s) being solved for. Such equations often do not have closed-form solutions"): it is unclear whether ${\textstyle \exp({\frac {\log x}{2}})=5}$ is transcendental, as it simplifies easily to an algebraic function; the phrase "closed form solution" is meaningless without listing the accepted basic functions.
  It seems that there are no general theory nor significant results on such non-algebraic equations. So I suggest to nominate this article at AfD. D.Lazard (talk) 10:18, 29 December 2021 (UTC)
• I believe to remember that "transcendental equation" is used for an equation (over numeric domains) that is not (equivalent to) an algebraic equation. The large number of translation links indicates that the concept is widely known. The link de:Transzendente Gleichung gives 2-3 fairly reliable sources (in German); also the depicted Herschel book looks reliable, and interesting at first glance. So, I'd be in favor of fixing the flaws of this article and keeping it as a stub. In the long run, it could accumulate methods to solve particular kinds of nonalgebraic equations, which are useful to obtain "closed-form"/"analytic" solutions in special cases. - Jochen Burghardt (talk) 11:41, 29 December 2021 (UTC)
  • I agree that I think the "right" definition of "transcendental equation" is "non-algebraic equation". And maybe you're right that an article could be written about that concept. I don't think it would include any of the material currently in the article, though; do you? --JBL (talk) 15:44, 29 December 2021 (UTC)

    Not exactly: a differential equation is a non-algebraic equation that nobody calls transcental. In fact one could define a transcendental equation as the equation for the zeros of a non-algebraic function. This point of view suggests redirecting to Zero of a function, and adding a sentence to the target article for defining "transcendental equation". Redirecting to Root-finding algorithms is another option. D.Lazard (talk) 16:13, 29 December 2021 (UTC)

    I'll try to fix the article during the next days. I suggest that after that, we can discuss whether to leave it standalone or to merge/redirect it somewhere. - Jochen Burghardt (talk) 18:19, 31 December 2021 (UTC)

    I would not be in favor of either of the redirects suggested by D.Lazard above. We shouldn't redirect a term to an article just because the article suggests ways of handling the search term. The equation is not a zero of a function, and it's not a root-finding algorithm. A redirect to a glossary article might be a possibility, though. --Trovatore (talk) 01:22, 4 January 2022 (UTC)

    Algebraic equation seems like another possible redirect target. --JBL (talk) 03:14, 4 January 2022 (UTC)

    I think it's a code smell when there are multiple, equally plausible targets for a redirect. At least we should look for the most "canonical" target. I think in this case it would probably be a glossary. --Trovatore (talk) 18:51, 4 January 2022 (UTC)

 Done Anyway, I'm through with editing. I've avoided "closed form" and emphasized the ad-hoc character of this "field of research application". It may be possible to expand the article further, based on the works by Varyukhin and Boyd (who devotes p.233-308 to "Analytical methods", including "explicit solutions", see the public), but I haven't access to any of them (except for Boyd's TOC and Varyukhin's Russian original).

I admit I'm not happy with the mess of transformation examples along Bronstein et al. in section Transcendental_equation#Transformation_into_an_algebraic_equation. They could possibly be grouped into "top-down" and "bottom-up" approaches, operating at the expression tree top (root) and bottom (leaves representing the unknown), respectively; however, we can't conceal that it is (necessarily) a catalogue of almost unrelated tricks. - Jochen Burghardt (talk) 20:25, 4 January 2022 (UTC)

Discussion on variant of infinity symbol

Please see Talk:Infinity symbol#Euler's variant and participate in the discussion if you have an opinion. —David Eppstein (talk) 20:57, 4 January 2022 (UTC)

Edit war started

Some help would be helpful for the edit-war that is starting at Inner product space. Pinging Mgkrupa. D.Lazard (talk) 15:01, 22 December 2021 (UTC)

@D.Lazard: it takes two to tango. If there are 4 reverts within a 24 hour period, that might lead to a report at WP:EWN, but not here. The edits to the article inner product space seem like cosmetic and harmless format changes (<math>, </math>, latex format vs. more primitive mathematical coding). Possibly it might be surprising that the complex conjugate of a Hilbert space is not mentioned in the article. [For a (complex) inner product space, its dual space is naturally a Hilbert space (with a canonical conjugate structure in the complex case).] Isn't it more usual to use the coding

$\int _{a}^{b}f(t){\overline {g(t)}}\,dt$

with dt instead of dt, which seems clunky? Mathsci (talk) 16:05, 22 December 2021 (UTC)

On the last point, apparently this is a known difference of conventions. The traditional usage in the States (and maybe Britain, not sure) is to use italic d, but in France and maybe some other places they prefer to put it in roman text, sometimes bold. I think the idea is to save italics for variables. Sometimes they go as far as to render e in roman, on the grounds that it's a constant rather than a variable. --Trovatore (talk) 18:00, 22 December 2021 (UTC)

@Trovatore: I thought that was more of a mathematicians-v.-physicists divide rather than a geographical difference. Michael Hardy (talk) 20:09, 22 December 2021 (UTC)

Could be. My memory of the discussions is hazy. --Trovatore (talk) 20:37, 22 December 2021 (UTC)

I don't think so. In my maths degree I have seen both $\mathrm {d} x$ and $dx$. (usually those that are very fussy about their presentation tending to use the former, many others using the latter) --George AKA Caliburn · (Talk · Contribs · CentralAuth · Log) 19:29, 24 December 2021 (UTC)

Looking at my hard copy of Laurent Schwartz's 1966 classic "Théorie des distributions", $dx_{1}$, etc, is the standard style adopted. The Notes for proofs in the article are unintelligible seas of red and blue, of little use for readers of wikipedia: Inner_product_space#Notes The French article Espace préhilbertien is fine. Mathsci (talk) 18:48, 22 December 2021 (UTC)

Hi, I'm the other editor and this 09:38, 22 Dec version of the article is what I would like to commit. After this 20:48, 21 Dec edit was partially reverted (resulting in this 21:18, 21 Dec edit that D.Lazard said was "clearer"), I changed my now-reverted 20:48, 21 Dec edit to be more similar to that of D.Lazard's 21:18, 21 Dec edit (resulting in what I consider to be an improvement) and I also made some changes that I hoped would remedy some of his concerns. Long story short, the result of my changes was this 09:38, 22 Dec edit (which I'd like to commit) that was fully reverted (resulting in the latest version of the article). Is D.Lazard right that my desired version of the article is flawed enough that it should not replace the current version of the article? Thanks. Mgkrupa 01:11, 23 December 2021 (UTC)

The eighth reference seems like a wiki, can it be used as a wikipedia reference like PlanetMath ?--SilverMatsu (talk) 13:29, 26 December 2021 (UTC)

BrilliantMath is a low-quality source. It was added (along with a bunch of other mediocre-to-poor sources) in this edit by Miaumee -- I think any of the sources added in that edit could/should be removed. --JBL (talk) 14:35, 26 December 2021 (UTC)

Thank you for your reply. A search of BrilliantMath on wikipedia found that it was used in the section of references in over 20 articles. Would you(we) like to create a new section for this? But today it takes longer than usual to load a wikipedia article.--SilverMatsu (talk) 15:39, 26 December 2021 (UTC)

Reference removal is complete in the Inner product space.--SilverMatsu (talk) 16:06, 26 December 2021 (UTC)

• User:D.Lazard seems to be edit-warring yet again. But his edits to inner product space show WP:CIR (both for language and mathematics). As background to my WP editing, in creating content on Hilbert algebras, I created the article commutation theorem, prompted by a real life friend User:R.e.b.. That is part of Bourbaki territory (Jacques Dixmier, Jean Dieudonné and Roger Godement), part of the Gelfand–Naimark–Segal construction and spectral theory. That mathematical theory and the relevant reliable sources are still valid.

Wikipedia:Babel

en-2This user can contribute with an intermediate level of English.

Search user languages

D.Lazard's mathematical specialty is outside this area. The WP:CIR problems are shown by the edit to Wikipedia talk:WikiProject Mathematics#Articles on "differential calculus" and "integral calculus", involving the phrase "The strong relation between these two subjects makes artificial to distinguish them". That can be excused on talk pages, like here, but unfortunately not for poor quality edits to main space content. In inner product space, D.Lazard has "corrected" field of real numbers to their preferred field of the real numbers without any justification. OTOH, D.Lazard's language userbox indicates an intermediate proficiency in English (en-2); D.Lazard is free to change that if he wishes. It's not hard to explain why the French phrase "le corps des nombres réels" is translated into English as "the field of real numbers". Simply use WP:RS and WP:V. Bourbaki's General Topology has a section IV.4 entitled "The field of real numbers". In the original French version, Topologie Générale, section IV.4 is entitled, "Le corps des nombres réels". The same applies to Dieudonné's Foundations of Modern Analysis/Fondements de l'Analyse Moderne. D.Lazard's edits shows that WP:CIR. Mathsci (talk) 10:29, 4 January 2022 (UTC)

This is not a place for discussing my behavior. Instead of discussing the competence of other editors, Mathsci should improve their own competence, and, in particular, learn where such a discussion may occur. Also, they should learn that the French "des" is a contraction of "de les". So, the proper translation of "le corps des nombres réels" is "the field of the real numbers", and, conversely, the proper French translation of "field of real numbers" is "corps de nombres réels". However, Wikipedia is not the place for discussing the accuracy of English translations of French books. D.Lazard (talk) 12:14, 4 January 2022 (UTC)

We are discussing your edits, that's all. User:D.Lazard is now stalking my edits.[1][2][3][4] In one of the edits, D.Lazard gives a short unsourced description as a would-be expert:{{Sort of von Neumann algebra}}. Can D.Lazard explain what Sort of von Neumann algebra means? A standard example has been given of the algebra of Hilbert--Schmid operators on a Hilbert space. It is not a von Neumann algebra. So WP:CIR, your edits are hopelessly inaccurate: they look like WP:NOTHERE. It's clear that you have not identified User:R.e.b.. Mathsci (talk) 12:22, 4 January 2022 (UTC)

It would be difficult to overstate how inappropriate and useless the linking to WP:CIR and WP:NOTHERE is in the present context -- find some less inflammatory way to make your point. --JBL (talk) 13:08, 4 January 2022 (UTC)

@Mathsci: First, as you wisely pointed out above, it takes two to tango. If you disagreed with D. Lazard's revert of your change to inner product space, you should have started a discussion on the talk page there instead of reverting his revert. Second, you clearly are discussing both D. Lazard's edits and conduct. This project page isn't really appropriate for either dispute, especially since the content dispute has not yet been discussed on the relevant talk page. Danstronger (talk) 03:24, 5 January 2022 (UTC)

Ultrapolynomial

This brand-new article is little more than a dictionary definition, with weak sourcing. Two minutes on MathSciNet convinced me that this probably is a thing, but it could use attention from a passing good samaritan. --JBL (talk) 22:46, 2 January 2022 (UTC)

When I searched for ultrapolynomial in the Anywhere field of MathSciNet, all the papers I found were by Stevan Pilipović and his students (there were 7 in total, of which 5 were by Pilipović himself). So my guess is that the definition is not common enough to justify a Wikipedia article. Ebony Jackson (talk) 01:31, 3 January 2022 (UTC)

Mmm you're right I didn't look carefully at the authors -- even the 1994 one (where the appearance is in the form "ultrapolynomial growth") is someone who heavily coauthors with Pilipović. --JBL (talk) 01:49, 3 January 2022 (UTC)

Even if it's a term used (at least so far) only by a restricted community that includes the person who coined it, it does look like there's enough peer-reviewed work to justify coverage. There are at least dozens of hits on Google Scholar. That said, it shouldn't stay a dictionary definition. Someone who understands the subject needs to explain why it's important. --Trovatore (talk) 17:47, 3 January 2022 (UTC)

It looks as if nearly all the hits on Google Scholar also are from Stevan Pilipović and his students, so can one really justify inclusion based on this? There may be other reasons to keep an article about this, perhaps with a different name - some of what I read suggests that it relates to work of Arne Beurling and others in the 1960s on generalizations of classical differential operators. I'm not an expert on this, so I'm not sure. Ebony Jackson (talk) 21:39, 3 January 2022 (UTC)

It's a judgment call of course. My sense right now is, yes, with that much peer-reviewed published work, it's likely worth keeping, even if the uses come from authors with connections to one another. --Trovatore (talk) 21:48, 3 January 2022 (UTC)

(I am the article's creator) The term's use (currently) being confined to a small subcommunity of authors is in my opinion not a valid argument for excluding this article. When a mathematical subdomain is specialized enough, then there are often only a small handful of select mathematicians working in it who, in addition, typically have some sort of connection to one another. This might be concerning if some key figures within this community are of ill repute; however, in the case of ultrapolynomials, as far as I can tell, real, reputable mathematicians put this tool to use in real, reputable, peer-reviewed work. --Fytcha (talk) 13:30, 4 January 2022 (UTC)

I have copied the article into http://Power_series#Power_series_in_several_variables https://en.wikipedia.org/wiki/Power_series#Power_series_in_several_variables (It obviously needs improvement). For such a specialized topic it probably makes sense to write a subsection of a broader topic instead of a new article. Vitamindeth (talk) 19:02, 4 January 2022 (UTC)

Honestly, I don't think it's appropriate in that location. It's not really interesting to most people reading about polynomials power series. It's interesting to people reading about the area of study of Pilipović and his group, whatever that is exactly (I suspect I could get at least a general idea of that if I wanted to spend the time, but I haven't so far).

So in my opinion it's probably fine as a standalone article, but it needs to be better contextualized. We're not supposed to have articles that just define something and do nothing else. One possibility might to write an article on that area of study and then redirect ultrapolynomial there. --Trovatore (talk) 19:42, 4 January 2022 (UTC)

I agree. I think that section explains the characteristics of the domain of convergence. (e.g.log-convex).--SilverMatsu (talk) 03:20, 7 January 2022 (UTC)

I am not part of this field of study but it seems there is no reason to think this is a notable concept by itself. There have been some two million peer-reviewed published math papers published in the last twenty years, and the argument for keeping this page seems to represent the lowest possible nontrivial standard for selecting concepts from among them. From a little searching through mathscinet and google scholar, it looks like a better case could be made for the (related?) concept of ultradistribution. Gumshoe2 (talk) 02:48, 5 January 2022 (UTC)

I agree with the last comment, as far as i can tell (from the article and looking around on Zentralblatt) this is a purely technical definition that makes no sense out of context. So if there should be an article it would be better if it was about that context (i guess the study of some class of PDEs). And if i'm wrong and these ultrapolynomials are really the crux of the matter then it should be explained why in the article. jraimbau (talk) 11:50, 5 January 2022 (UTC)

Yes, this seems very believable to me. --JBL (talk) 11:52, 5 January 2022 (UTC)

"Nonlinear algebra"

The article named Nonlinear algebra seems essentially content-free in its current version, vague to the point of uselessness in some parts and just pointing to specific topics reflecting the interests of its editors in others. By default "nonlinear algebra" should refer to all parts of algebra that are not purely linear algebra (e.g. commutative algebra, group theory, ...) and as far as i know there is no unified field of research that represents them all. So unless the term is used in a precise technical sense in some field i'm not familiar with (computational algebra?) the article would be more appropriate as a disambiguation page. jraimbau (talk) 12:04, 5 January 2022 (UTC)

The article is very incomplete, but doesn't seem wrong as far as it goes. My understanding of nonlinear algebra is as an applied mathematics field that goes beyond linear algebra to consider polynomials. Examples are the survey Nonlinear Algebra and Applications, the book Invitation to Nonlinear Algebra and the course Introduction to Non-Linear Algebra. That said, I think you make a good point, in that the topic means different things to different people. Taking the approach of a broad concept article or a DAB may be a good option. --{{u|Mark viking}} {Talk} 04:11, 7 January 2022 (UTC)

Unlike linear algebra, which is also considered a pure maths field, nonlinear algebra seems to me to be used distinctly for computational aspects.

I am not sure how exactly, but I suspect it is closely linked to computational algebraic geometry. Felix QW (talk) 05:56, 7 January 2022 (UTC)

OK, with the Michalek--Sturmfels book as support in particular i think it would make sense to attempt a re-writing of the the article with a lede like

Nonlinear algebra is a name recently used to design a collection of techniques from areas of algebra outside of linear algebra (in particular computational algebraic geometry, tensor algebra, representation theory,...) to problems in applied mathematics.

and then a more detailed list of techniques and applications. This seems much clearer than the current version. It would also make sense to put stuff like computational group theory (which seems outside the scope of Michalek--Sturmfels at least) in a "see also" section. jraimbau (talk) 09:09, 7 January 2022 (UTC)

Pentangle puzzles

Math geeks born between 1940 and 1970 may remember Pentangle puzzles, a company in Over Wallop, Hampshire, UK, which made and sold burr puzzles and other puzzles. I'd like to create a Wikipedia article about it, but have trouble finding evidence of notablity. Any help at Draft:Pentangle puzzles would be most welcome. Maproom (talk) 21:55, 9 January 2022 (UTC)

Combining dimensions

There is currently an unsourced stub at Combining dimensions which mentions combining dimensions to be the visualisation of a manifold in a lower-dimensional space. A merger into Projection (mathematics) was discussed in 2013, but no suitable merger target was identified. With the advances in data mining over the last 10 years, Dimensionality reduction is now clearly the primary topic for the search term, so I would like to create a redirect there. My question: Is it worth to disambiguate Combining dimensions as a topology concept? Or do we have a better merge target now? I am not convinced with the meaning given in the article that this is a well-defined concept at all. Felix QW (talk) 09:01, 11 January 2022 (UTC)

I have never heard this term. It does not describe either projection or dimensionality reduction well. Quick Google searches don't give any evidence for it. My gut reaction is that it's original research and should be deleted. However, if many readers are searching for it, then we should redirect it to Dimensionality reduction or whatever we think it means. Mgnbar (talk) 12:36, 11 January 2022 (UTC)

My vote would be delete, but if we end up disambiguating or redirecting, one potential target would be Embedding#Topology_and_geometry or something like that, based on the content that's there now. Danstronger (talk) 13:46, 11 January 2022 (UTC)

Thanks for the initial responses! Before we have to duplicate a longer discussion, I have taken it to AfD (See Wikipedia:Articles for deletion/Combining dimensions). Felix QW (talk) 14:22, 11 January 2022 (UTC)

Edit warring for Fundamental theorem of Riemannian geometry

Would appreciate any extra eyes at the page Fundamental theorem of Riemannian geometry, see its talk page for context Gumshoe2 (talk) 16:54, 16 January 2022 (UTC)

odd format in EB 1911

Hi. I'm proofing the math, chemistry &c articles of the 1911 EB on Wikisource, and there's something odd here (the line just above "[VALIDATOR, VERIFY ODD FORMAT]"). I am replicating apparent typos, but will fix up the formatting where it's obviously trivial. Is that an acceptable way to format the line, or am I missing something? (Please ping.) — kwami (talk) 04:33, 17 January 2022 (UTC)

Inverse functions and differentiation

I have recently discovered the article Inverse functions and differentiation. It is presently unsourced, despite having been in existence since 2002. It is rated as Start Class and Mid-Priority. It appears to me to be amateurish. What little content is truly valuable is probably already found in one of the substantial articles on inverse functions, the derivative, or the inverse function theorem. Before I start action to delete the article or merge its contents, I would appreciate some feedback on what others think about the article. Dolphin (t) 04:16, 7 January 2022 (UTC)

Two comments- 1) as written it seems more like "cheat sheet"/formula list or tutorial rather than encyclopedic; 2) it would be pretty easy to add sources. I guess I think it should be merged into other articles. Actually, all of its contents probably already appear elsewhere here. Gumshoe2 (talk) 07:45, 7 January 2022 (UTC)

We do have pages for the power rule, the product rule and so on. In fact, the article Inverse functions and differentiation is linked in the sidebar template Calculus, which is transcluded on many calculus pages. I agree that the current state is poor, though, and that the page should probably be renamed in line with the other articles on differentiation rules (the article on differentiation rules just calls it the inverse function rule). Felix QW (talk) 14:39, 11 January 2022 (UTC)

I suggest redirecting to the Inverse function theorem.--SilverMatsu (talk) 03:13, 13 January 2022 (UTC)

I agree that mathematically speaking, the interesting question is the differentiability of the inverse rather than the calculation of the derivative. However, Inverse function theorem is clearly aimed at those working on real analysis upwards, while I think there is value in having the inverse function rule covered in the set of calculus articles pitched a level lower. Felix QW (talk) 11:17, 13 January 2022 (UTC)

I have now moved the page to Inverse function rule and rephrased the lead to match. I also changed the corresponding wikilink in template:Calculus. Felix QW (talk) 10:03, 18 January 2022 (UTC)

Hawkes process

I have created an article titled Hawkes process, which could use further work. Michael Hardy (talk) 19:26, 19 January 2022 (UTC)

About modern triangle geometry

Given that wikipedia doesn't have an article the modern geometry, I wonder if it can create an article the Modern triangle geometry.--SilverMatsu (talk) 04:13, 13 January 2022 (UTC)

Probably should be merged into History of geometry. Danstronger (talk) 14:10, 13 January 2022 (UTC)

Possibly I'm just bad at reading but I cannot at all understand from that article what "modern triangle geometry" is about. The cited definition from 1887 is impenetrable to me. Also, it seems there are only three pages of google results for "modern triangle geometry". Color me confused. Gumshoe2 (talk) 18:49, 13 January 2022 (UTC)

In its current form, the article is too long for merging. Instead, a "History" section should be split off from the lead. However, like Gumshoe2, I feel unable to express the introductory description, which should make up the lead after splitting, i.e. I didn't understand what the article is about (except: an arbitrary(?) collection of triangle-geometry results obtained after 1850). I suspect the 1887 "definition" cannot be translated into formal mathematical language; but maybe the lead author just picked it unluckily. Finally, I guess the geometric results presented in the article body do deserve a Wikipedia article, but "Modern triangle geometry" may not be the best title to collect them under. - Jochen Burghardt (talk) 13:48, 14 January 2022 (UTC)

Splitting the triangle geometry that is currently redirecting to a triangle can be useful for something. --SilverMatsu (talk) 02:43, 21 January 2022 (UTC)

Article for David Cox

We are looking to clean up the article on David Cox to make sure the description of his work is accurate and cited properly. Your help would be most welcome. Joofjoof (talk) 04:46, 21 January 2022 (UTC)

Non-Hausdorff redirect nominated for deletion

Non-Hausdorff currently redirects to Non-Hausdorff manifold, which is misleading to say the least. I have nominated the redirect for deletion. Please take a look at Wikipedia:Redirects for discussion if you want to add your opinion. PatrickR2 (talk) 04:42, 20 January 2022 (UTC)

Would appreciate the opinion of others in Wikipedia:Redirects_for_discussion/Log/2022_January_20#Non-Hausdorff to build consensus, as some outsider has a different opinion. PatrickR2 (talk) 04:26, 22 January 2022 (UTC)

Mathematical errors in Fields medal commentary

I would appreciate any thoughts on this new comment on the Fields medal page. It seems to me that several mathematical achievements of Fields medalists have been misstated in various ways. It seems that the expert commentaries at ICM have been summarized by non-experts in a published non-technical book, which were then copied uncritically to the Fields medal website and then copied over to wikipedia. So the expert commentaries have become a little corrupted. But my own expertise is limited, maybe this is all my error, so I would appreciate any knowledgeable persons having a look. Gumshoe2 (talk) 07:57, 25 January 2022 (UTC)

There are no problems with the Proceedings of the ICMs. The International Mathematical Union, however, is a different organisation; it manages the online ICMs and makes its own postings. Vaughan Jones did not edit wikipedia, except here. [5] None of his students could have helped with this BLP, since it doesn't mention subfactors. That topic was first treated on WP by User:R.e.b. ... Although it's no quite clear what Gumshoe2's aim is, he has to follow WP:consensus. Polishing Fields medal (remember it doesn't tarnish), requires reading the WP:RS (the Proceedings) and summarising them carefully, possibly without direct quotes. For cosmologists (also theoretical physicists), there is a similar problem with Nobel prizes, e.g. Kip Thorne. I don't know how that works. Mathsci (talk) 20:37, 25 January 2022 (UTC)

Maybe you still do not understand the situation. Kip Thorne, to take your example, was awarded the Nobel prize "for decisive contributions to the LIGO detector and the observation of gravitational waves", and that is an officially given reason. (This is present in the opening paragraph of his wiki page and has good references, so I'm not sure how you missed it.) I have no idea what you think is the relevance of your comments on Vaughan Jones and r.e.b., so I am unable to respond to them. I recommend that you take some more time to focus your thoughts. It would be very helpful for discussions. Gumshoe2 (talk) 01:00, 26 January 2022 (UTC)

??? In RL, I was involved in organising section speakers for an ICM and was later an invited speaker — a different perspective & possibly a COI for the article. Mathsci (talk) 13:15, 26 January 2022 (UTC)

I do not understand the relevance of this remark, sorry. Gumshoe2 (talk) 14:10, 26 January 2022 (UTC)

Short Description Guidelines

I've noticed that remarkably few mathematics articles outside of very large scope articles (and bio pages) seem to have a short description in line with what's described in WP:SHORTDES. In particular, the short description

• Should provide a very brief description of the field covered by the article
• Disambiguate search results
• Avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject
• Should not attempt to define the subject of the article nor summarize the lead.

It's challenging to write about math without overusing jargon, so that one I get. However, the majority of pages I click on do not seem to align with the goals of describing the field covered by the article or to help disambiguate search results, and most of them attempt to define the subject and/or summarize the lead. I've edited many articles now to fix the short description, but there seems to be such a large proportion of articles that need adjusting (almost every article I click), that I'm seriously doubting myself. It feels like I'm being gaslit by the entire mathematics corner of Wikipedia. Is there something I'm missing, like a page somewhere that has different guidelines for the short description specifically for math articles?

I wanted to bring this up because either I am wrong about what the short description should look like (in which case I will happily revert my edits), or this is a very widespread issue throughout the mathematics articles which needs more attention. Donko XI (talk) 07:46, 21 January 2022 (UTC)

@Donko XI: The short descriptions I've seen you add to articles on my watchlist today are, pretty much uniformly, bad. The only information a reader can glean from them is that "it's mathematics". One of the main uses of short descriptions is to disambiguate search results, so (as well as being short) they need to provide enough detail about the topic they describe to distinguish it from other topics that have similar enough names to come up in the same searches. One of the worst examples of your bad short descriptions was on Lattice (order), which you changed from the informative and short-enough "Partial order having least upper bounds and greatest lower bounds" to the uninformative "Algebraic structure in order theory". Beyond failing WP:SDNOTDEF's guideline to avoid repeating article title words in short descriptions, saying that it's an "algebraic structure" fails to distinguish it from, and in fact makes it more likely to be confused with, Lattice (group), which is more clearly an algebraic structure rather than an ordering. Another bad example was logarithmic spiral which you changed to "mathematical curve", which would completely fail to clarify what kind of spiral it is among many other possible spirals in a search result. My advice would be: if you don't understand a mathematical topic well enough to formulate a short description which is sufficiently informative, you should recognize your ignorance and let someone else deal with writing its short description, rather than making things worse by reducing the short description to the level of your non-understanding. Or if you must work on short descriptions, put some effort into thinking what kinds of searches the title might come up in, and what information about the topic needs to be put into the short description to disambiguate those searches. It doesn't need to be a precise definition (those are often too long), but cutting down a definition to its essentials is often a better choice than trying to summarize the broader context, because that broader context is too often the same as other similarly-titled articles that it might need disambiguation from. —David Eppstein (talk) 08:08, 21 January 2022 (UTC)

@David Eppstein: Your character attack is unwarranted. These are good faith edits and, as an algebraist, I feel comfortable enough with these topics to describe them. I read WP:SHORTDES very carefully and looked through numerous examples of short descriptions on high profile articles before making any edits to make sure I had a good idea of what I was doing. I have immense respect for Wikipedia and take these edits seriously. In particular, the short description should not attempt to define the subject of the article. Both revisions restored a short description which defined the subject of the article rather than indicate the field the article covered. When it comes to providing disambiguation for search results, there are many articles one could be looking for with the term "lattice", some of which are not mathematical at all. For someone searching for Lattice (music), or Lattice (pastry), it is much more useful to them to see immediately that this is a mathematics article rather than be confronted with jargon like "partial order". I do agree that the short description I provided was not optimal for distinguishing it from Lattice (group) (and I'm more than open to improvements), but, taken on the whole, I do think it is an improvement and more adequately satisfies the guidelines on WP:SHORTDES. It's clear to me that your revisions (and overall Wikipedia history) are in good faith so I would much prefer this discussion to proceed civilly. Donko XI (talk) 08:38, 21 January 2022 (UTC)

@David Eppstein: Before you continue to revert my edits en masse, hear me out. The short descriptions I wrote on pages like Universal algebra and Abstract Algebra are very much in line with the standard of their peers. Abstract algebra is a branch of mathematics (like Algebraic geometry or Homological algebra, which I did not edit) in the same way Babe Ruth is an "American baseball player" instead of "American baseball player known for <whatever he's actually famous for>". The short description "American baseball player" clearly doesn't serve to define the subject of the article in the same way that "Generalization of vector spaces from fields to rings" does in your revision of my edit for Module (mathematics) does. The format "<Nationality><Profession>" is the standard for biographical articles and "Algebraic structure in Ring Theory" seems to fit in with this paradigm quite well. Again, I'm more than open to improvements, but it seems clear to me that there is an issue with the short descriptions currently used on many of these mathematics articles, and shutting down my attempt to bring them into line with the standards on WP:SHORTDES isn't productive. Donko XI (talk) 09:07, 21 January 2022 (UTC)

In the abstract, the points made by both users here seem very reasonable to me. Donko XI, do you have some particular examples in mind of obviously problematic descriptions? I would find it helpful to see. Gumshoe2 (talk) 09:29, 21 January 2022 (UTC)

I support David's reverts for the articles that are in my watchlist. Donko XI changed other short desc. in my watchlist. Some are improvements, such as, for Group (mathematics) changing "Algebraic structure with a single binary operation" into "Algebraic structure" (the long version does not distinguish groups from monoids, semigroups, etc., and this adds nothing to the short version). But, in most cases, the previous version was better, and I have restored it. In some other cases, such as function (mathematics), I have reverted Donko XI's version and edited the previous version. D.Lazard (talk) 10:15, 21 January 2022 (UTC)

@Gumshoe2: Here are a few. Most of these involve some combination of attempting to define the subject, using jargon, and being too long (more than 40 characters).

• Archimedean property - "Absence of infinitesimals in a mathematical system"
• Uniform polyhedron - "Polyhedron which has regular polygons as faces and is vertex-transitive"
• Archimedean solid - "Convex uniform polyhedra first enumerated by Archimedes with all vertices the same"
• Archimedean spiral - "Spiral named after the 3rd-century BC Greek mathematician Archimedes"
• Logarithmic spiral - "Self-similar growth spiral whose curvature pattern appears frequently in nature"
• Group (mathematics) - "Algebraic structure with one binary operation" (This one isn't that bad, but the info about having one operation doesn't seem appropriate here)
• Logarithm - "Inverse of the exponential function, which maps products to sums"

If you look at my edit history, you can see I'm not cherry picking here. This is a continuous block of short descriptions I edited. I visited these pages back to back. Here are a few more:

• Homeomorphism - "Isomorphism of topological spaces in mathematics"
• Topological property - "Object of study in the category of topological spaces"
• Function (mathematics) - "Mapping that associates a single output value to each input"

For comparison, here are some short descriptions from a few high profile articles to get an idea of the level and type of detail that's expected

• Blueberry - "Section of plants"
• Florida - "U.S. state"
• Mathematics - "Field of study"
• Number Theory - "Branch of mathematics"
• Pink Floyd - "English rock band"
• The Lion King - "1994 animated film"
• Babe Ruth - "American baseball player"

With this in mind, the description "Mathematical operation" for Logarithm, "Branch of mathematics" for Abstract algebra, or "Mathematical relationship in topology" for Homeomorphism seem perfectly in line and appropriate (even if they're not perfect). Donko XI (talk) 10:37, 21 January 2022 (UTC)

I agree with Gumshoe2 that this is hard to discuss in the abstract, and what best serves WP:SHORTDESC#Purposes is very case-specific. I'll just comment on a few:

• Abstract algebra, from "Mathematical study of algebraic structures" to "Branch of mathematics": This change looks good to me. In line with, say, Geometry. A problem is that "algebraic structures" is itself jargon. For readers who aren't sure if Abstract algebra is the article they're looking for, seeing "algebraic structures" won't help.
• Group (mathematics): In this context, "algebraic structure" actually adds value. I agree with Donko XI and D.Lazard that the shortened version is better than the longer version.
• Homeomorphism, "Isomorphism of topological spaces in mathematics" or "Isomorphism in topology (mathematics)" or "Mathematical relationship in topology": This one is tougher. "Isomorphism" is a word roughly at the same level as "homeomorphism". "Topological equivalence" might be a little more understandable, while still trying to stay descriptive technically. (Note that Topological equivalence is a redirect (WP:PRIMARYREDIRECT) to homeomorphism.) For "relationship", I guess I wouldn't use that word to describe it normally. And then of course there's always the option of "Concept in _____", which can feel like a cop-out, but is commonly used – there's nothing wrong with it, and there isn't always a more satisfactory option.

Adumbrativus (talk) 12:21, 21 January 2022 (UTC)

To me, this comparison just says that if a topic is something that one might not encounter until going to graduate school for mathematics, then a "short description" of it will be on the longer side. I can't say I find that very surprising. XOR'easter (talk) 01:57, 22 January 2022 (UTC)

I do not care enough about short descriptions to have a substantive position about this, but I would like to point out a semantic issue: "should not attempt to define the subject of the article" sounds prescriptive, but surely it should be read as "need not attempt to define the subject of the article" -- otherwise it would be objectionable if the short description on triangle were to successfully define what a triangle is in under 40 characters, and that's (obviously?) absurd. --JBL (talk) 12:13, 21 January 2022 (UTC)

This talk page is not the place for discussing specific short descriptions. For each short descriptions for which there is no consensus, the discussion must go the talk page of the article (this is stated in WP:SHORTDESC). IMO, WP:SHORTDESC is sufficient as a style guideline for short descriptions. However, I can add some specific recommendations:

• It must be clear from the title and the short description together that an article is about mathematics. As "mathematics" has 11 characters, this has the consequence that it is often very difficult to have a short dscription of less than 40 characters.
• As soon as it is clear that an article is about mathematics, there is no problem with using technical terms known by most readers who are possibly interested in the article. For example, one can suppose that a reader that has never heard of isomorphism and topology, will not be interested by Homeomorphism (he will propbaly understand nothing in the article). So "Isomorphism in topology (mathematics)" is sufficiently informative for readers interested by the article; for other readers also, since it makes clear that the article is not for them. On the other hand, "Mathematical relationship in topology" and "topological equivalence" must be avoided because "relationship" and "equivalence" have many different meanings that cannot be disambiguated in a short description, and are therefore confusing.
• Many article have a title such as "Someone theorem" or "Fundamental theorem of ..." . It is common that a reader knows the theorem without knowing its name. This must be clarified by the short description.

D.Lazard (talk) 15:37, 21 January 2022 (UTC)

I agree with most of what you bring up here and keep these points in mind in the future. However, I disagree on the Homeomorphism example specifically and it speaks to something broader about these short descriptions.

I do think "isomorphism" is too much. It's very possible that a student taking a first topology course wouldn't be familiar with the term "isomorphism" but would find the page helpful nonetheless. For someone looking to distinguish Homeomorphism from Homomorphism, knowing that the former is topological is the key piece of information, and for somebody searching for Homeopathy or Homeostasis, merely knowing it's a math article is what matters. On the other hand, I can't picture a scenario where someone will identify the article as the correct one because it discusses a type of isomorphism, but not because it's a topological relationship (even if relationship isn't the best word to use here).

This isn't intended to be a discussion about Homeomorphism specifically. WP:SHORTDES suggests avoiding jargon for a reason. Even if we, at the moment of editing, can't think of a scenario where someone unfamiliar with a piece of technical jargon would be interested in the article, that doesn't mean this audience doesn't exist. I would think first course topology students comprise a large body of readers who would find Homeomorphism useful, and turning them away is the wrong move. I've personally spent a lot of time browsing through Wikipedia articles that weren't in my technical specialty and have been reading articles beyond my technical depth since I was a kid (and this has been very valuable for me). I don't think it's right to assume the audience of these articles is a narrow group of people with a technical education on the subject. For example, an adult without an advanced mathematics background attempting to teach themselves to fulfill a lifelong dream might find the article valuable, as would a curious non-math student (or even a child) who's seen the picture of the donut-mug homeomorphism and wants to learn more.

I'm not suggesting that the short descriptions should all be fully understandable by children; that's obviously taking it too far. It should, however, be understandable at a level sufficiently below that of the article itself. There is likely an audience for a given article (or an audience attempting to navigate to a different article) that we won't anticipate while writing a short description, and the short description should be helpful to them too.

The wording on WP:SHORTDES is "avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject". I think it's safe to say that "Isomorphism" is jargon. While this guideline is particularly difficult to do justice for mathematics topics, I don't think we should ignore this. It just makes the job of coming up with a good description harder. Donko XI (talk) 21:26, 21 January 2022 (UTC)

I think the "should not attempt to define the subject of the article" is being misread. Short descriptions should not be full and complete definitions of their subjects, mostly because that would not be short enough. However, it is usually a better choice to include in the short description what makes this topic different from topics with related names rather than what makes it the same, because only what makes it different will be helpful in distinguishing it in search results. Among spirals, for instance, it is not helpful to call them "mathematical curves" (as Donko XI did) because that's true of all of them; we need some brief information about which specific spiral each one is. Summarizing a key point from the definition (not providing it in full) is often a good way to come up with distinguishing information in this way. —David Eppstein (talk) 16:48, 21 January 2022 (UTC)

Agree with that. It looks like they should be the sort of thing one sees in disambiguation pages or a list to distinguish entries frome each other. NadVolum (talk) 17:41, 21 January 2022 (UTC)

I agree with you that "mathematical curve" wasn't the best. Of each of the short descriptions I wrote, I like this one the least for exactly the point you make. When I wrote this in for Archimedean spiral and Logarithmic spiral, I was more interested at the time in disambiguating search results beginning with "Archimedean" and "Logarithmic". The previous descriptions (especially Archimedean spiral) had significant issues and were in need of adjustment, but I had difficulty coming up with something of approximately 40 characters which also indicated what type of spiral it was.

Given the descriptions for pages like Babe Ruth, Pink Floyd, and Blueberry, which make no attempt to distinguish them within a broad class analogous to "spirals" in the present discussion, I don't think I was totally off the mark, but I do agree that it should have been better. If the SD is a "concise explanation of the scope of the page" as in the first paragraph of WP:SHORTDES, it doesn't seem like distinguishing particular spirals from each other is necessarily the appropriate function of the SD. However, I do think that there is a discussion to be had, but it seems sufficiently context dependent and likely belongs over on the relevant pages. Donko XI (talk) 22:03, 21 January 2022 (UTC)

It is false that Babe Ruth makes no attempt to distinguish within a broad class. The broad-class description here would be "Biography" or maybe "human"; instead, Babe Ruth's short description makes clear that he was American and a baseball player, enough to disambiguate him from other people named George Ruth or Ruth George who might plausible come up in some searches. Please remember also that many search results come from content within the article, and not just the title words. The reason to avoid title words in the shortdesc (when reasonable) is not so much because they're the likely search terms, and more because they're automatically visible anyway in the search results, so it's better to use the limited space of a shortdesc to provide new information instead of repeating what's already there. The same reasoning also suggests avoiding the word "mathematical" in many short descriptions of mathematical topics: if other words from the article title are already recognizably mathematical, it provides no extra information. Additionally, in "concise explanation of the scope of the page", scope ≠ context. Scope is what this particular article is about; context is what broader topic it might be part of. We need to explain what this particular article is about, not set it into context. —David Eppstein (talk) 22:14, 21 January 2022 (UTC)

My general sense is that David tries to put too much into short descriptions. The main point of short descriptions is to give mobile users some very broad context, so that (to use M Hardy's favorite example) someone who's looking up psychological notions doesn't need to click on schismatic temperament. If they do that, their main job is done; more is not required.

Giving more detail is OK, possibly even useful, if:

1. It doesn't go over the "soft limit" of 40 characters
2. It doesn't confuse users who were searching for something in a completely different field

But the extra detail not being part of the core mission of short descriptions, it shouldn't be added if it violates either of those. Of course this is just my opinion. --Trovatore (talk) 01:59, 22 January 2022 (UTC)

I agree with the "soft limit" and "not confuse" parts, but disagree with "extra detail not being part of the core mission". An experiment for you to try:

1. Go into the mobile app (I think it's the same on Android and IOS)
2. Enter the word spiral into the search box

All you will see is titles and short descriptions and tiny illegible images. The first hit is for the main spiral article, with a short description that is too long (the target length is 40 characters but this one is 86). But If what you were really looking for is a specific kind of spiral (maybe the Euler spiral), but you can't remember which mathematician it was named for, you will never find it because (currently) it has no short description and you will be lost in the many other results.

For examples like this, it is essential, and part of the core mission, to have short descriptions that provide enough extra detail to find what you are looking for.

—David Eppstein (talk) 02:15, 22 January 2022 (UTC)

PS I shortened the spiral short description and added one for Euler spiral, so you won't get exactly the same results now. —David Eppstein (talk) 02:20, 22 January 2022 (UTC)

Summarizing the positions, from "most context" to "most detail":

• User:Donko XI (henceforth Dk) argues that Short Descriptions (SD) should say what field the article is part of, avoiding technical terms.
• User:Trovatore (Tr) underlines the importance of helping users who are looking for something in a "completely different field" and argues against excess detail.
• User:D.Lazard (DL) argues that the SD should include the word "mathematics"; additional detail may include technical terms.
• User:David Eppstein (DE) argues that SDs should distinguish articles from similar articles in the same field, possibly using technical terms, and prefers avoiding the word "mathematics" if other words from the title are "recognizably mathematical".

The problem is that many things are "recognizably mathematical" only to people with some mathematical background. Math loves giving specific mathematical meanings to generic terms like "field", "lattice", "structure", "kernel", and "group", as well as inventing special words not recognized at all by non-mathematicians, like "monoid", "diffeomorphism", and "tensor". For the general terms, the SD must differentiate the mathematical meaning from the non-mathematical one without using even more technical terms. For the special terms, it must point out that it's a mathematical term. It doesn't necessarily need to use the word "mathematics"; I think "algebra" and "geometry" are recognized as mathematical by the general user, though "topology" and "model theory" are surely not; "mathematical logic" must be differentiated from logic in rhetoric and philosophy.

It's certainly nice to distinguish from similar things with similar names (logarithmic spirals from Archimedian spirals), but it's even more important to clarify that they're plane figures in mathematics rather than astronomical features, software development methods, etc.

So I agree with Dk, Tr, and DL that the SD should explicitly mention that the topic is mathematical. I agree in principle with DL that additional detail can include technical terms, but the character budget is pretty tight. User:Gumshoe2 (G2) has not expressed an opinion.

By the way, many of the longer SDs still fail to actually differentiate the topic from similar topics. The SD for factorial "product of consecutive integers" does differentiate it from double factorial and the general Bhargava factorial, but not from falling and rising factorials. I don't see how to both make it clear that these are mathematical functions (and not experimental designs or data encodings) and to differentiate among the various mathematical definitions, all in 40 characters or not much more. --Macrakis (talk) 19:18, 22 January 2022 (UTC)

I wouldn't bother with making the simpler ones more complicated to distinguish from much less well known ones. And perhaps it might be enough to say variant of or something like that for special ones. It's to help someone find what they want but they'll sometimes have to look at a second article if the first isn't exactly what they wanted.. NadVolum (talk) 19:24, 22 January 2022 (UTC)

I agree. I was pointing out that even when the SD tries to clearly differentiate from other topics instead of providing context, it's well-nigh impossible in 40 characters.

SDs should stay simple. My SD for factorial, which DE reverted, was "Mathematical function on integers". --Macrakis (talk) 19:42, 22 January 2022 (UTC)

I though 'product of consecutive integers' was a good one and more descriptive. Or even just numbers instead of integers. Saying mathematical is only worthwhile for words like group or set where one genuinely has to distinguish it from oter common uses. And function is a word that people looking up factorial might not understand. NadVolum (talk) 19:51, 22 January 2022 (UTC)

I'd be happy to change it to 'product of consecutive numbers'. That's more recognizable to non-experts, and it's not supposed to be mathematically precise. In this example, "numbers" is already good enough to make it recognizable as mathematics; "mathematical" is just unnecessary and useless redundancy, and (because the other two main meanings of factorial are also somewhat mathematical) fails to distinguish it from them. Similarly, for all of the various spirals, "curve" is a familiar word that is enough to make it recognizable as geometry, leaving plenty of characters within the 40-character limit to say something more specific about which kind of curve it is. —David Eppstein (talk) 19:58, 22 January 2022 (UTC)

I'm not sure which readers are well-served by the definition "product of consecutive numbers/integers". Imagine an ag major who is told that a certain study used a "factorial design". Is that a design that has something to do with a product of numbers? Maybe?

BTW, I have updated the SD of factorial experiment, which was far too long and descriptive (195 characters!) to "Kind of experiment in statistics"; similarly, factorial should, I argue, be something like "Mathematical function", with additional optional information (like "on numbers/integers"). Interestingly, the Factorial experiment article's lead actually begins with "in statistics" and the Factorial article's lead begins with "in mathematics" -- if the article needs that level of context-settings, surely the SD does, too. --Macrakis (talk) 20:31, 22 January 2022 (UTC)

Your hypothetical ag student needs a descriptive short description on factorial design. Making the factorial short description much more vague by saying it's a "mathematical function" rather than a "product of consecutive numbers" is not going to make things any more clear for them or for anyone else. Terseness and avoiding jargon are virtues here but vagueness for its own sake is not. Also, yes, 195 characters is way too long. I don't think "kind of" or "in" add any information, so if you're going to use that short description you might as well go with the shorter "statistical experiment". Maybe "statistical experiment over all combinations of values" would still work? But it's still a little too long and I don't see a good way of packing the same information in more tightly while remaining understandable. —David Eppstein (talk) 21:38, 22 January 2022 (UTC)

I agree that factorial design needed a better description, and I provided it (with an editing glitch along the way).

I would claim that "mathematical function" is about the right level of description. If I could fit in "used in combinatorics", I would, but "product of consecutive numbers" is simply a definition, and doesn't tell the naive reader what it is related to. Though "combinatorics" is a pretty fancy (and long) word, too.

"Mathematical function" is not vague. It says what kind of thing it is, which is the main goal, and is the sort of thing you might find on a disambiguation page. (cf. Γ).

I agree about "kind of". --Macrakis (talk) 23:45, 22 January 2022 (UTC)

The Gamma function is definitely a function as its primary meaning. For factorial, I'm not so sure. 5! is a factorial, but it is a number, not a function. The sequence 1, 1, 2, 6, 24, ... is a sequence of numbers, not a function, but it is the sequence of factorials. It is not wrong to think of "factorial" as defining a function rather than referring to the individual numbers that are its values or the sequence of those numbers, but I think it involves a more advanced mathematical perspective, which maybe for short descriptions we should not be doing. Also, you could just as well say that a factorial code is a function (from data values to their codes), so calling it a function fails to disambiguate. —David Eppstein (talk) 23:58, 22 January 2022 (UTC)

For Factorial, I suggest to replace "product of consecutive numbers" with "product of first consecutive numbers". This remains sufficiently short, and, by distinguishing it from falling and rising factorials, may be less confusing for people who have learnt and forgotten the definitions. D.Lazard (talk) 21:46, 22 January 2022 (UTC)

Could be "product of numbers from 1 to n"? I don't think "first" sounds very idiomatic in this context. "Initial" is better but unnecessarily technical. —David Eppstein (talk) 21:48, 22 January 2022 (UTC)

Very good for me. D.Lazard (talk) 22:21, 22 January 2022 (UTC)

Short descriptions (SD) seem marginally useful to help a mobile user pick a correct entry from a search list, but in the grand scheme of things, I think it should not matter too much if the SD is kept at a very general level for that particular purpose. If the mobile user picks the wrong entry, no big deal, they just go back and try another one, as we all do. On the other hand, something that this discussion has not adressed so far, the SD is also used more and more in "annotated link" entries in See Also sections of articles. For that particular purpose, since we are already reading a mathematics article that sets up the broad context, it seems to me that a more focused description as user:David Eppstein advocates would be much more useful. PatrickR2 (talk) 01:33, 23 January 2022 (UTC)

That would be a very minor consideration indeed when drafting a short description. The number of instances where {{Annotated link}} is used in See also sections is extremely small, and its use is never mandatory. Within mathematics it's often impossible to make careful and sometimes subtle distinctions between articles within the WP:SDSHORT soft limit of 40 characters. In this field, it's often better to continue using a wikilink with manual text (of unlimited length) in the traditional way. MichaelMaggs (talk) 15:37, 23 January 2022 (UTC)

This is a useful thread, and some good points are being made. From my perspective (significant experience with short descriptions, but not a mathematician), Donko XI is right to note that the majority of mathematics articles have SDs that are badly non-compliant with WP:SHORTDESC. Many may have been copied over from old Wikidata descriptions which are intended for a different purpose and which don't of course attempt to comply with Wikipedia's guidance at WP:SDFORMAT and WP:SDSHORT. Those ought to be replaced. The essential things to bear in mind for mathematics articles, I think, are:

• There should never be a need to go beyond the soft limit of 40 characters - WP:SDSHORT. If you feel compelled to, it's probably because you are attempting to define the subject or copying the first sentence of the lead, contrary to WP:SDNOTDEF, or trying to make some unnecessary distinction from another mathematics article.
• WP:SDNOTDEF asks editors to "avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject". That implies that the target audience is not mathematicians, or even scientists, but readers who know little mathematics apart from words in general common use. Now of course it's frequently impossible to provide "a very brief indication of the field covered by the article" without occasionally using words that are a little more technical, but that's OK if the title itself or something within the SD states or conveys that this is an article in the field of mathematics. Even then, though, avoid terms that would be known only to mathematicians, or terms that mathematicians use in a special, unexpected sense.
• Trying hard to distinguish between two specialist subjects within the overall field of mathematics really isn't something to focus on, especially at that's often impossible within around 40 characters while at the same time avoiding jargon. It doesn't matter if multiple mathematics articles end up with the same SD, any more than it matters in biology that there are tens of thousands of articles with "Flowering plant", or in geography that there are as many with "Town in <country>" – though naturally if there is enough space within the 40 character budget, more information can usefully be added.
• If an article is too abstruse to capture within around 40 characters, "Concept in mathematics" works perfectly well; or if "mathematics" is already stated or implied by the title, something slightly more definite such as "Concept within group theory" could be used. MichaelMaggs (talk) 17:10, 23 January 2022 (UTC)

Agree with MM above. Attempting to distinguish a topic from related ones sometimes requires hatnotes such as {{for}} or {{about}}. That is not the purpose of SDs. "Concept in mathematics", or "Concept in algegra" are fine, just like "University in Odisha, India" would be fine for every one of 300+ articles. In general, I agree with Donko's SDs, having made similar changes to shorten hundreds of SD in many topic areas (including some that I remember in mathematics), often imported from WD but not always. MB 18:53, 23 January 2022 (UTC)

"Concept in mathematics" is much more vague than "University in Odisha, India", more like "place in Asia". It is better than no description at all, and better than a 200-character description that attempts to define the subject in full mathematical detail, but not much better. 40 characters is plenty to both convey to a general audience that this is mathematics and provide more specificity within mathematics. What would you feel if you saw a "See also" section of a mathematics article that listed a bunch of topics related to the article, for each of them giving its title and short description, as for example Intersection (set theory) § See also does, but if all of the short descriptions were replaced by "Concept in mathematics"? Would you think that short descriptions like that were a useful piece of information for that context? —David Eppstein (talk) 20:22, 23 January 2022 (UTC)

"Concept in mathematics" isn't a recommendation by any means. I just commented that it would work perfectly well if an article is too abstruse to capture within around 40 characters. Normally there should be something that works much better, as you say. MichaelMaggs (talk) 21:39, 23 January 2022 (UTC)

There's a bit I disagree with "avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject". It is a good aim but I wouldn't push it too far. If jargon is obviously jargon gibberish as far as a reader is concerned then they know it probably is not what they want! Avoiding the jargon may mean too big a number of possibilities are not distinguished for someone who would understand the jargon. Of course jargon that sounds lke something the user is interested in but is in fact something completely different is bad. NadVolum (talk) 01:40, 25 January 2022 (UTC)

I think you just want too much from short descriptions. If you need to use jargon to provide value in a short description, consider just not having one (more precisely, using an empty short description), which is a perfectly fine option provided the title itself gives context. --Trovatore (talk) 01:07, 26 January 2022 (UTC)

Have a look at Homology for instance. The descriptions are fine even though many include jargon. I is pretty clear that "Homologous series, a series of organic compounds having different quantities of a repeated unit" has nothing to do with homological algebra for instance even though organic, compound and units have all sorts of different jargon meanings. NadVolum (talk) 13:29, 26 January 2022 (UTC)

My field of research directly involves homological algebra, but it would still take me a second to recognize that this article is not what I am looking for. On the disambiguation page you linked to, the situation is clear by the fact that its listed under the heading "Chemistry", but in the search results, it would take a moment to process (not long, but it wouldn't be immediate). I imagine a student learning introductory homological algebra or algebraic topology might click on that article after reading that description. Given that the disambiguation page has additional structure to complement the job of the SD, it might be more worthwhile to emphasize the role of SDs in the search results (not to discard their value in disambiguation pages, but put this at slightly lower priority).

It's worth noting that the text in the disambiguation page isn't even the short description. The article is currently missing one. That text is directly part of the disambiguation page. The fact that we can customize the disambiguation page is another reason why the use of SDs in search results should be prioritized. If the short description isn't optimal for a disambiguation page or in most other locations it might appear, the text which appears can be customized to suit that particular need.

Something that I think is being missed in this discussion is that these descriptions aren't intended to be carefully read. They're just given a glance before the article is either moved on from or clicked on. Nuance and precise content will not be very useful in this setting and are more likely to cloud the readers decision than something very simple and less detailed. That's not to say that the SDs shouldn't be well thought out, but that the effort should be in carefully choosing a wording that lends itself to immediate clarity rather than nuance or precision. On the disambiguation page, the heading "chemistry" is all that was needed for me to know that I'm not looking at a homological algebra article. The same would be true in the search results. Seeing the term "chemistry" show up at the very beginning would be far more useful than the chemistry definition which is used instead. Donko XI (talk) 01:30, 27 January 2022 (UTC)

The Homology example isn't relevant to this discussion. That is a WP:DAB page, and like almost all such pages the text there has nothing whatsoever to do with short descriptions. It has been manually added and is part of the DAB page itself. Because DAB pages need to discriminate in such a wide range of situations, the {{Annotated link}} template should not be used there, per the template documentation. MichaelMaggs (talk) 10:14, 27 January 2022 (UTC)

Requested move at Talk:Siméon Denis Poisson#Requested move 29 January 2022

There is a requested move discussion at Talk:Siméon Denis Poisson#Requested move 29 January 2022 that may be of interest to members of this WikiProject. Favonian (talk) 22:43, 29 January 2022 (UTC)

< math > produces wrong symbols

Direct sum

Earth symbol

\oplus and \otimes are used for direct sum and tensor product, but they generate the wrong symbols. They should be ⊕ (U+2295 CIRCLED PLUS) and ⊗ (U+2297 CIRCLED TIMES), but instead we get 🜨 (U+1F728 ALCHEMICAL SYMBOL FOR VERDIGRIS) -- the astronomical symbol for the Earth -- and U+1F774 LOT OF FORTUNE (in the pipeline for Unicode 15). Can they be fixed? The circle should not touch the operator -- in fact, a variation selector is provided to force a font to display properly (with a "white rim"), e.g. U+2295+FE00 produces ⊕︀. Please ping, — kwami (talk) 01:11, 28 January 2022 (UTC)

People are so weird. —JBL (talk) 01:19, 28 January 2022 (UTC)

Where by "people", maybe you mean the font designers or unicode standards-wonks who somehow decided that the LaTeX de facto standard for typesetting mathematics was not good enough and decided to introduce gratuitous differences? —David Eppstein (talk) 01:43, 28 January 2022 (UTC)

It's really specifically the idea that it's wrong to have the plus touch the circle that gets me, I think. I'm trying to imagine some linear algebra instructor somewhere carefully drawing her direct sum circles to not touch the inner plus sign, because the unicode people think it's wrong if they touch? It definitely feels weirder than the "the 'd' in dx is non-italic because ISO" thing. (As a person too young to know life before LaTeX, it did cause me to go look up a bit of history -- unsurprisingly, LaTeX is several years earlier than Unicode.) --JBL (talk) 03:38, 28 January 2022 (UTC)

The Unicode people do not think it's wrong if they touch. As pointed out above, in order for it to not touch, you need to add the variation selector (see also the PDF, plainly showing that the default/canonical (for lack of a better term) glyphs do indeed have the circle and operator touching). Not sure where kwami got the idea that they shouldn't touch from; I've never heard of that as an issue. eviolite (talk) 03:44, 28 January 2022 (UTC)

@Kwamikagami: I have to admit that I'd never heard that touching the circle was wrong; indeed I'd always drawn it that way myself when doing mathematics on paper. Where does the notion that it's wrong come from? Double sharp (talk) 10:19, 28 January 2022 (UTC)

From my understanding from Unicode, fonts vary in whether the + touches the circle or not due to poor font design, so if you want to force a font to display "correctly", Unicode supplies a fix. (Of course, the font has to support the fix, or it will just ignore the variation selector.)

Perhaps I'm wrong about this. If it's standard in Latex, then I guess it's irrelevant. There's also a second circled plus in Unicode, ⨁ (U+2A01 N-ARY CIRCLED PLUS OPERATOR).

JBL: "I'm trying to imagine some linear algebra instructor somewhere ..." Well of course. In handwriting, you're not going to bother being so careful. You won't necessarily distinguish 1, l and I in handwriting either, but that doesn't mean you should use one for the other in print. (Well, I remember an old mechanical typewriter that saved space by not having a one or zero key, and you were expected to letters instead. But that probably wouldn't have flown for most publishers even back then.)

eviolite: "in order for it to not touch, you need to add the variation selector." Actually, that's not the case. In some fonts they touch, in some they don't. On my browser, I see a "white rim" around the plus even without the variation selector. In the default math font that came with my OS, MathJax, they don't touch, nor do they in Liberation or FreeSans fonts (though they do in FreeSerif). Note that there is no variation selector to force them to touch: that is, there's a VS to "correct" the display, but not one to force the "incorrect" form. Unicode may be wrong about the touching form being wrong, but AFAICT that's the reason for the VS. I can ask someone who would know the history of it if you like. — kwami (talk) 10:53, 28 January 2022 (UTC)

Following up on eviolite's comment: Sorry, but I'm having trouble establishing the basic facts here (perhaps because of the fonts I'm using). In LaTeX the operator touches the circle, right? In Unicode the operator touches the circle by default, right? In every math book and lecture that I can remember, the operator touches the circle. What's the problem? Mgnbar (talk) 12:40, 28 January 2022 (UTC)

How do we write \bigoplus ($\bigoplus$) and \bigotimes ($\bigotimes$) in Unicode ?--SilverMatsu (talk) 01:41, 30 January 2022 (UTC)

Solution: We use the default behavior, in which they touch. Or is the issue the "big" operators as opposed to the "small" ones? Or am I still missing the problem? Mgnbar (talk) 04:02, 30 January 2022 (UTC)

Thank you for your reply. This PDF says that if we write \bigoplus in Unicode, it will be use U + 2A01, and if we write \oplus in Unicode, it will be use U + 2295. In this PDF and LaTeX, it (\bigoplus and \oplus) seems to me that the operator touches the circle. The display of my browser on wikipedia is that U + 2295 does not touch the circle and U + 2A01 the operator touches the circle.--SilverMatsu (talk) 05:25, 30 January 2022 (UTC)

Earth mass uses \oplus for the earth symbol.--SilverMatsu (talk) 08:48, 30 January 2022 (UTC)

Examples from direct sums and Earth mass

$\textstyle A=\bigoplus _{i\in I}A_{i}$ (Use bigoplus)

$\textstyle A=\oplus _{i\in I}A_{i}$ (Use oplus)

$M_{\oplus }=(5.9722\;\pm \;0.0006)\times 10^{24}\;\mathrm {kg}$ (Use oplus)

$M_{\bigoplus }=(5.9722\;\pm \;0.0006)\times 10^{24}\;\mathrm {kg}$ (Use bigoplus)

If bigoplus and oplus cannot be exchanged, I think it will be difficult to write articles.--SilverMatsu (talk) 09:21, 30 January 2022 (UTC)

In that PDF, I too see both U+2A01 and U+2295 touching the circle. In your four examples above, I see all of them touching the circle. The issue is that some browsers render U+2295 in a non-touching way? Is this a typeface (font) issue? Or does Wikipedia emit Unicode that explicitly tells them not to touch? Mgnbar (talk) 12:34, 30 January 2022 (UTC)

In that PDF and examples (mw:Extension:Math), so do I. About the "issue", I don't know the solution.--SilverMatsu (talk) 14:25, 30 January 2022 (UTC)

"Proofs involving..." articles

Lately I am tackling the backlog of unassessed mathematics articles. While doing that I encountered articles whose titles start with "Proofs involving..." and which have developed from deprecated /proof subpages.

As a way of maintaining proof archives for particular pages, they seem problematic since their development tends to diverge from the original article. As stand-alone articles, they often have an ill-defined scope. There are currently five such pages I am aware of:

Proofs involving covariant derivatives

Proofs involving the Laplace-Beltrami operator

Proofs involving ordinary least squares

Proofs involving the Moore-Penrose inverse

Proofs involving the addition of natural numbers Felix QW (talk) 19:58, 10 January 2022 (UTC)

I have just discovered WP:WikiProject Mathematics/Proofs, which confirms my suspicion that the proofs presented there are insufficiently notable to warrant their own articles.

My current plan would be to merge them somewhere where they can be of use, which may or may not be their previous superpage.

Proofs involving the Laplace–Beltrami operator can probably be merged into Laplace-Beltrami operator without too much difficulty.

I find Proofs involving the Moore-Penrose inverse to be excessively detailed for Moore-Penrose inverse, and I am not sure what others think.

I think material from Proofs involving the addition of natural numbers makes most sense in Peano axioms as a demonstration of how the definitions of addition and multiplication given there can be used to derive well-known basic properties of natural addition.

The first two sections of Proofs involving covariant derivatives could be merged into Contracted Bianchi identities and Einstein tensor respectively. The third section was never linked to another page in the first place and I am insufficiently familiar with the material to know what to do with it.

Proofs involving ordinary least squares is more difficult, since parts of the material have been merged from Linear least squares (mathematics) and split from simple linear regression in 2018.

Any thoughts would be very much appreciated! Felix QW (talk) 18:06, 18 January 2022 (UTC)

Thank you for bringing this to attention. I think the "not a textbook" principle is extremely important for maths wikipedia. Furthermore, many of these "proofs" are actually just computations, and so are especially suitable to textbooks. I think that in many cases it would be most appropriate to remove them altogether, but to provide precise references to where they appear in standard textbooks. Gumshoe2 (talk) 21:10, 18 January 2022 (UTC)

Maybe the remaining unmergeable proofs could be moved to some wikiversity page(s), so the effort that has gone into typesetting them would not be wasted? - Jochen Burghardt (talk) 06:49, 19 January 2022 (UTC)

The German Wikibooks actually has a Beweisarchiv, which is essentially an indiscriminate collection of proofs in German. I don't think that English Wikibooks has anything similar, though, and despite some searching through their catalogue I couldn't really find a place for any of our proofs in an existing Wikibook. The exception would be the addition of natural numbers, which would fit the remit of the Abstract Algebra Wikibook, but it already has a derivation of some of the identities listed here, and besides it does not include 0 in its natural numbers. Felix QW (talk) 08:21, 26 January 2022 (UTC)

I have now requested transwikiing Proofs involving the Moore-Penrose inverse to Wikibooks so that it can be used towards the Linear Algebra chapter of the (more advanced) wikibooks:Topics in Abstract Algebra. This should keep the content available in a place where it is more suitable. Felix QW (talk) 14:39, 31 January 2022 (UTC)

• Not so much a thought as a related problem: Draft:Bose integral is essentially an unsourced proof that the Bose-Einstein integral can be expressed as a product of the Gamma function and Zeta function. If this material is worth keeping, it perhaps should go somewhere in Polylogarithm, but it doesn't look like the general case and I don't know how interesting or useful this material is. — Charles Stewart (talk) 22:55, 18 January 2022 (UTC)