Wikipedia talk:WikiProject Mathematics/Archive/2020/Aug

Simpson correspondence

An editor suggests to rename the article Simpson correspondence to, e.g., "Simpson-Corlette correspondence", arguing that the current name does not properly reflect the contributions of Corlette on that topic. I am a bit unsure how to proceed: from what I can tell, this name is not used in the literature, despite the fact that Corlette's contributions are (as is also clear from the literature) very clearly noteworthy to that topic. What are the relevant guidelines for naming mathematical topics after their contributors etc.? Jakob.scholbach (talk) 09:13, 29 July 2020 (UTC)

This probably falls under WP:COMMONNAME, which advises to use the most common name for a topic. "Simpson correspondence' gets 401 hits on GScholar and "Simpson-Corlette correspondence" gets only two links, to the same thesis. WP:RIGHTGREATWRONGS is also relevant. --{{u|Mark viking}} {Talk} 09:41, 29 July 2020 (UTC)

Actually, in my opinion, the page should be renamed to Non-Abelian Hodge theorem or Non-Abelian Hodge correspondence, which is the generally accepted term in the mathematical community for this correspondence (Simpson correspondence is also frequently used of course). Based on Google scholar results if you include the variations (non-abelian, non abelian, theorem/theory) you get more results than Simpson correspondence (and even with just "non abelian hodge theory" produces 500 results). This is both a more evocative name for the correspondence, (slightly) more universally recognized, and avoids the issue of discussing who deserves more credit in the title (to be clear, both Simpson and Corlette made significant contributions to the final result, although the key arguments were really completed by Simpson, but such a summary of the contributions could be added to the article). I had planned on expanding this article myself in the near future, and will probably request a move to Non-Abelian Hodge theorem regardless of whether it gets renamed in the meantime. Tazerenix (talk) 10:26, 29 July 2020 (UTC)

OK, thanks -- this strikes me as a good solution, so I have moved the article to Nonabelian Hodge correspondence. Jakob.scholbach (talk) 08:58, 30 July 2020 (UTC)

After the move I have filled the page out with a long introduction to the theorem and a history of who proved what. This should completely resolve the problem. Tazerenix (talk) 11:24, 4 August 2020 (UTC)

Differential geometry of surfaces

Can someone have a look on this article and its talk page, where an edit war is starting about whether the section Differential geometry of surfaces#Function theory in two variables must be removed as out of scope, or must be kept. Thanks in advance. D.Lazard (talk) 20:35, 3 August 2020 (UTC)

@D.Lazard: I took a look and gave my thoughts. Let me know if the dispute develops further. — MarkH₂₁^talk 21:20, 3 August 2020 (UTC)

I also gave my thoughts. Tazerenix (talk) 00:27, 4 August 2020 (UTC)

Thanks for the help. The edit war continue. I have reach 3 reverts (even if it is unclear which edit should be counted as the first revert). So, your help is still needed. D.Lazard (talk) 13:11, 5 August 2020 (UTC)

Approximately vandal

Just a heads-up to all: about a year ago, there was a fairly disruptive vandal that had a habit of inserting statements like 3×3 approximately equals 9 (among other equally inane things). The original ANI thread is here, which led to a rangeblock due to rotating IPs. That range is currently blocked again, but I don't know if that's related or not. In any case, Special:Contributions/81.151.174.89 appears to be the same person back at it. They only got 4 edits in before being blocked by Materialscientist, but it's a short block, and if they're able to rotate IPs again, it might be worth keeping your eyes open for more of similar nonsense. –Deacon Vorbis (carbon • videos) 15:29, 5 August 2020 (UTC)

That is such a bizarre form of vandalism to be so persistent with! — MarkH₂₁^talk 19:36, 5 August 2020 (UTC)

Everybody needs a hobby, I guess.... XOR'easter (talk) 00:02, 6 August 2020 (UTC)

Links to "Fast Fourier Transform" that ought to link instead to fast Fourier transform

There are lots of links to Fast Fourier Transform that ought to link instead to fast Fourier transform. I've recently fixed a bunch of them. Can others help?

A subtler thing occurs when someone writes "For this purpose we use the Fast Fourier transform." where they ought to write instead "For this purpose we use the fast Fourier transform." This is subtler because when you click on "What links here", these are not distinguished from other links to the article's proper title, since the initial letter is not case-sensitive in links. (The psychologically contagious nature of capital letters is apparent from long experience with Wikipedia editing. Has anything been published about it?) Michael Hardy (talk) 00:07, 6 August 2020 (UTC)

Discussion about wikipedia "Wikipedia:Village pump (proposals)"

You are invited to join the discussion at Wikipedia:Village_pump (proposals)#Deprecate parenthetical citations, which is about a wikipedia that is within the scope of this WikiProject. – Finnusertop (talk ⋅ contribs) 06:21, 6 August 2020 (UTC)

Expert attention

This is a notice about Category: articles needing expert attention, which might be of interest to your WikiProject. It might take a while before the category is populated. There might be as few as one page in the category, or zero if someone has removed the expert request tag from the page. 2600:100E:B11E:43A3:DCBA:4FC5:7056:EF53 (talk) 14:42, 10 August 2020 (UTC)

Centroid

In the article titled Centroid, we find this:

The centroid of a non-self-intersecting closed polygon defined by n vertices (x₀,y₀), (x₁,y₁), ..., (x_n−1,y_n−1) is the point (C_x, C_y), where

$C_{\mathrm {x} }={\frac {1}{6A}}\sum _{i=0}^{n-1}(x_{i}+x_{i+1})(x_{i}\ y_{i+1}-x_{i+1}\ y_{i}),$ and

$C_{\mathrm {y} }={\frac {1}{6A}}\sum _{i=0}^{n-1}(y_{i}+y_{i+1})(x_{i}\ y_{i+1}-x_{i+1}\ y_{i}),$

and where A is the polygon's signed area, as described by the shoelace formula:

$A={\frac {1}{2}}\sum _{i=0}^{n-1}(x_{i}\ y_{i+1}-x_{i+1}\ y_{i}).$

In these formulae, the vertices are assumed to be numbered in order of their occurrence along the polygon's perimeter; furthermore, the vertex ( x_n, y_n ) is assumed to be the same as ( x₀, y₀ ), meaning $i+1$ on the last case must loop around to $i=0$. (If the points are numbered in clockwise order, the area A, computed as above, will be negative; however, the centroid coordinates will be correct even in this case.)

References

• Bourke, Paul (July 1997). "Calculating the area and centroid of a polygon".

Did I clumsily miss something, or should the second formula be as follows?

$C_{\mathrm {y} }={\frac {1}{6A}}\sum _{i=0}^{n-1}(y_{i}+y_{i+1})(y_{i}\ x_{i+1}-y_{i+1}\ x_{i})$

Michael Hardy (talk) 22:23, 5 August 2020 (UTC)

Think the second product factor in $C_{y}$ just has to match what is in $A$. Deriving the formulas probably yield what you suggested, but with a negative $A$, and cancelling the negatives give the original formulas, and save us from defining $A_{x},A_{y}$. I'm just guessing, though. Walwal20 ^{talk ▾ contribs} 22:59, 5 August 2020 (UTC)

(ec) @Michael Hardy: To calculate the centroid we decompose the figure into oriented triangles between points $O$, $P_{i}$ and $P_{i+1}$. The centroid of the $i$-th triangle is ${\frac {O+P_{i}+P_{i+1}}{3}}$, hence the term $0+x_{i}+x_{i+1}$ for $C_{x}$ and similar for $C_{y}$. The weight of the triangle's centroid in the sum is the triangle's area (signed!) which is a half of the cross-product of the $i$-th and $(i+1)$-st vectors - hence the same second paren both for x-es and y-s. The common factors 1/3 and 1/2 are moved outside the sum and make the 1/6 there.

If you swap the terms in the second parenthese, you'll effectively change the paren's sign and get a negated value for $C_{y}$ as a result. --CiaPan (talk) 23:07, 5 August 2020 (UTC), edited 07:11, 6 August 2020 (UTC) and 10:59, 6 August 2020 (UTC)

@Michael Hardy: You might just test it yourself: take a triangle with vertices (0,0), (0,1) and (1,0) and calculate its centroid. There will be just one non-zero term in each of there sums, and the hardest part of calculation will be a division (1/6):(1/2).
:) CiaPan (talk) 12:49, 6 August 2020 (UTC)

@CiaPan: and @Walwal: : Thank you for your attention to this. Michael Hardy (talk) 21:10, 10 August 2020 (UTC)

Abstract cell complex

• Abstract cell complex (edit | talk | history | protect | delete | links | watch | logs | views)

I just saw this article, the vast majority of which was written (with some broken English) by a single user who appears to be the author of a book/application that the article is serving as a bit of a coatrack for. As far as I can tell, the basic topic is probably at least borderline notable enough for a separate article (the Klette article cited has a description and some further references), but the digression into the research of Kovalevsky is probably too much. But I'd certainly welcome a second opinion on this one. Thanks, –Deacon Vorbis (carbon • videos) 14:09, 11 August 2020 (UTC)

Technical issues with Chrome rendering formulas

If anyone has experienced blurry math formulas in Chrome recently, you may be interested in a thread I've just started: Wikipedia:Village pump (technical)#Change to Chrome rendering of PNGs causing blurry formulas. –Deacon Vorbis (carbon • videos) 17:36, 12 August 2020 (UTC)

Expert attention on Differential Geometry of Surfaces

I would appreciate some experts on differential geometry to weigh in over here. Mathsci (talk · contribs) and I have both been editing the wiki page in the last few days. I find many of his edits to be written confusingly; according to my understanding of the material, his comments on the talk page do not address my complaints. Conversely he seems to think I am making too many major edits to his material. I have no interest in an argument and would like to defer to community consensus one way or another, but for the moment it's just me and him. Gumshoe2 (talk) 22:28, 10 August 2020 (UTC)

A lot of this article was edited by me in 2008. In the past I have edited a lot of mathematical content on wikipedia, starting in 2006. The concern with the current article has been to patch missing sections at the beginning of the article. That involved adding definitions from standard textbooks. Later, lecture notes of Nigel Hitchin suggested that it might be a good idea to have some material on covariant derivatives. I started by editing using Hitchin's notes and then Boothby's book on differential geometry. While editing, I had included Brioschi's proof of Gauss' Theorema Egregium (from Dirk Struik's book). Gumshoe2 then moved the material I edited on Brioschi's proof to another section. He also completely rewrote the section on covariant derivatives. From my point of view it is currently not properly sourced. That could probably be remedied using Thorpe's book on Elementary topics in differential geometry. The standard sources for this material are Helgason's book on Differential Geometry and do Carmo's book on Riemannian geometry. I like that material, but it is probably at the level of graduate students.

However, the aim in this article has always for it to be accessible to a wide readership. So covariant derivatives are probably out of the scope of the article, unless carefully presented (finding the sources).

I have twice given courses on the Atiyah-Singer index theorem in the UK: part of that required the theory of Riemannian covariant derivatives. It's on public record that I have had a stroke, which has had some consequences. Mathsci (talk) 23:35, 10 August 2020 (UTC)

I you have health problems that have no consequence on your work as Wikipedian, this is not worth to mentioning them. It they have consequences, it is to you to decide whether they allow you to conveniently edit Wikipedia, and if they not, to decide to stop editing Wikipedia. So, in any cases, it is not worth to mention here your health problems. D.Lazard (talk) 09:29, 11 August 2020 (UTC)

By the way, Mathsci has opened a WP:ANI discussion, entitled "D.Lazard and Differential geometry of surfaces", in which it is discussed whether WP:BOOMERANG must apply. D.Lazard (talk) 09:29, 11 August 2020 (UTC)

The usual five pillar always apply: articles require WP:RS when creating content. I am currently reading John A. Thorpe's book, "Elementary topics on differential geometry." I looked at your editing history. The article system of polynomial equations was created by you in 2010. That content described your own research. Mathsci (talk) 11:48, 11 August 2020 (UTC)

In my mind, each of the sentences in the previous post by Mathsci contains pretty much no relevant information to the discussion at hand. @Mathsci: if there is an issue here, it would be helpful to precisely (and concisely) state what is going on and refrain from adding unrelated bits of information. Jakob.scholbach (talk) 07:14, 12 August 2020 (UTC)

No problem. For smooth surfaces $S$, the standard formalism requires (tangent) vector fields $X$ viewed as derivations of $C^{\infty }(S)$. The notion of affine connections is introduced through the covariant derivative $\nabla _{X}$ which yields a vector field $\nabla _{X}Y$ from two vector fields $X$ and $Y$. The Riemannian connection of Levi-Civita is easy to construct directly using a projection operator, assuming an isometric embedding in Euclidean space. Its properties of compatibility with the metric and symmetry follow from the construction or can be proved directly as part of the fundamental theorem of Riemannian geometry. The curvature operator is defined as $R(X,Y)=[\nabla _{X},\nabla _{Y}]-\nabla _{[X,Y]}$. The assignment $(X,Y,Z,W)\mapsto (R(X,Y)Z,W)$ is $C^{\infty }(S)$-linear in all of its four variables. Elementary algebra shows that, if $v_{1}$ and $v_{2}$ are linear independent tangent vectors at a point in $S$, the quantity $(R(v_{1},v_{2})v_{2},v_{1}))/((v_{1},v_{1})(v_{2},v_{2})-(v_{1},v_{2})^{2})$ is independent of the choice of basis. It is the Gaussian curvature at that point. As a corollary, any local isometry of surfaces preserves Gaussian curvature.

This is standard material that generalizes to any even dimension; there are lots of sources (including Thorpe's book). The material can be presented in a coordinate-free way (as here), with Christoffel symbols (classical) or both (perhaps the best option). Mathsci (talk) 09:06, 12 August 2020 (UTC)

I fail to see how any of this (in the post right above) relates to an alleged misbehavior of D.Lazard. Jakob.scholbach (talk) 09:21, 12 August 2020 (UTC)

The question for the noticeboard was not about D.Lazard. It was about the section in the article on covariant derivatives. My post above yours specifically addressed that topic. The area of the article has always been studied by undergraduates. The aim of the article was to present the material for a general readership. The first diff of Gumshoe2 was about a technical detail with covariant derivatives, which can be resolved (using my previous post, specialized to the material of Hitchin, Thorpe et al). Where there might be a disagreement is with inline citations: for a general readership it seems they really have to be supplied. Mathsci (talk) 10:49, 12 August 2020 (UTC)

This is a notice that I started Draft:Calculus on Euclidean space. As I see, there are two issues: (1) how to cover calculus topics in some systematic and centralized manners as opposed to having separate articles and (2) how much background materials should be in differential geometry of surfaces. I am with Mathsci that the issue (1) is indeed an issue; thus, I have started that draft page by copying the section on functions in 2 variables. Mathsci has said above: "This is standard material that generalizes to any even dimension." I want to believe that draft page (eventually a mainspace article) can cover such standard materials. As for (2), I don't have much opinion other than one I made at the talkpage of the diff-geo article. -- Taku (talk) 00:11, 17 August 2020 (UTC)

I need to mention that there is Draft:Analysis of vector-valued curves, which has a section closely related and thus I am thinking of moving that section to Draft:Calculus on Euclidean space. -- Taku (talk) 00:52, 17 August 2020 (UTC)

Taku, thans for your replies. I agree with you about the topics you've raised. As far as calculus on Euclidean space is concerned, I think everything generalises to any dimension. Hörmander takes a little care about C^k issues. On the talk page of your calculus draft, I have mentioned that mixing elementary material on calculus with more advanced material, such as differential topology (smooth manifolds, differential forms, etc) seems unrealistic. Calculus is quite elementary. Understanding differential forms, orientablity, etc, is more advanced. Also for smooth surfaces, there's no need to invoke the general theory of manifolds, submanifolds, Stokes's theorem, etc. Mathsci (talk) 13:44, 17 August 2020 (UTC)

The disagreement over two-dimensional calculus was an independent problem some people had with Mathsci at the Differential geometry of surfaces page, not related to this one. I've made a comment on the talk page to your draft Gumshoe2 (talk) 09:29, 17 August 2020 (UTC)

Yes, but I do believe Mathsci has a valid point that some background stuff seems missing or not well-organized in a single place in Wikipedia, that is needed to read differential geometry of surfaces. He often refers to materials in existing literature, and, since Wikipedia is supposed to be *a summary of established math*, we do indeed need to have some presentation of those materials. The question is "how" not "if" (the draft like this one I started should be one approach). I will be responding to points specific to the draft in the talkpage of the draft. -- Taku (talk) 03:57, 18 August 2020 (UTC)

Has Kunen died?

An IP editor has been editing Kenneth Kunen as though he has died. Is that true? I don't find any news story about it on a brief search. --Trovatore (talk) 18:53, 15 August 2020 (UTC)

I don't know but it's obviously not acceptable to put it into the article without a source, so I've reverted the IP. (I've also left a message on the IP's talk page asking if they have a source.) --JBL (talk) 19:11, 15 August 2020 (UTC)

I concur; I was about to revert it myself but you got there first. Thanks for taking care of it and for leaving a note at the IP's talk page. XOR'easter (talk) 19:43, 15 August 2020 (UTC)

Answer appears to be yes, sadly. Article now has a source for it. —David Eppstein (talk) 17:13, 18 August 2020 (UTC)

Expected mean squares

I have created an article titled Expected mean squares. I think the plural may be justified by the fact that nobody (as far as I know?) ever has occasion to think about just one expected mean square, in view of their use in forming F-tests. Michael Hardy (talk) 00:05, 20 August 2020 (UTC)

Administrators' noticeboard section on differential geometry

There is currently a discussion at Wikipedia:Administrators' noticeboard regarding an issue with Mathsci (talk · contribs), Gumshoe2 (talk · contribs), D.Lazard (talk · contribs) and the articles on Symmetry of second derivatives, Differential geometry of surfaces. At the moment I'd like this to focus more on a possible process to follow rather than the actual dispute. --Salix alba (talk): 16:03, 22 August 2020 (UTC)

Page deletion - Mirror symmetry conjecture

Hi,

I migrated the material on Mirror symmetry conjecture to Mirror symmetry (mathematics). Will someone remove the first article since the second's title is more in line with wikipedia standards? Here's the analogy: Mirror symmetry is to Mirror symmetry (mathematics as Gauge theory is to Gauge theory (mathematics). Wundzer (talk) 16:35, 18 August 2020 (UTC)

Unfortunately, by simply moving the content over, you have destroyed the edit history. The preferred way to make such a change is described at Wikipedia:Moving a page. You can do it yourself. :) Mgnbar (talk) 16:46, 18 August 2020 (UTC)

Actually, now that you've created Mirror symmetry (mathematics), you won't be able to move Mirror symmetry conjecture. You'll have to create a request at Wikipedia:Move requests. Mgnbar (talk) 16:51, 18 August 2020 (UTC)

What does it mean that the second title is "more in line with wikipedia standards"? Generally article titles on Wikipedia use parenthetical disambiguation when more natural disambiguation is not available. I have marked the new article for speedy deletion; after it is removed, we can start over with appropriate process, including perhaps a discussion of whether retitling is appropriate at all. --JBL (talk) 16:54, 18 August 2020 (UTC)

(edit conflict):It appear that you have copied the article instead of doing a move (see WP:MOVE). Moreover the title you suggest is definitively not in line with WP standards, in particular with WP:LEAST, as, for most mathematicians, "mirror symmetry" is synonymous with reflection symmetry. So, I'll redirect the new article, and its talk page to Reflection symmetry. If you want to change an article title, please follow the procedure described at WP:Move request. D.Lazard (talk) 16:58, 18 August 2020 (UTC)

I think that's largely incorrect. As far as professional mathematicians are concerned, mirror symmetry typically refers to the results from string theorists in the 90's and the related programs which came out of it. Here's a list of resources by professional mathematicians alive today who use Mirror symmetry to refer to this area: http://www.claymath.org/library/monographs/cmim01c.pdf , https://ncatlab.org/nlab/show/mirror+symmetry , https://mathoverflow.net/questions/tagged/mirror-symmetry , https://arxiv.org/search/advanced?advanced=&terms-0-operator=AND&terms-0-term=mirror+symmetry&terms-0-field=all&classification-mathematics=y&classification-physics=y&classification-physics_archives=math-ph&classification-include_cross_list=include&date-filter_by=all_dates&date-year=&date-from_date=&date-to_date=&date-date_type=submitted_date&abstracts=show&size=50&order=-announced_date_first Wundzer (talk) 17:17, 18 August 2020 (UTC)

How can I recover the edits I made on Mirror symmetry (mathematics)??? I'm very frustrated these changes were deleted: I want to put them on the Mirror symmetry conjecture page... Wundzer (talk) 17:11, 18 August 2020 (UTC)

Is this page about the same topic as Homological_mirror_symmetry??? --JBL (talk) 17:12, 18 August 2020 (UTC)

No! Homological mirror symmetry is a separate formulation of mirror symmetry. These are not interchangeable and mean different things. Wundzer (talk) 17:14, 18 August 2020 (UTC)

There's some discussion on the talk page about the topic and the expository approach. (It's not 100% clear to me that it warrants its own page, but I'm not an expert on the topic.) It'd be nice to have some more commenters. Gumshoe2 (talk) 17:26, 18 August 2020 (UTC)

Let me explain the reasoning: Mirror symmetry generally refers to the more analytic and combinatorial part of the subject. It studies things like Quantum cohomology, Gromov-witten invariants, and Picard-Fuchs differential equations. On the other hand, homological mirror symmetry is more focused on studying a (partly) conjectural equivalence of categories, the derived category of coherent sheaves and the Fukaya category. This area uses tools like A-infinity categories, Hochschild homology, and derived geometry. I think separating out the subjects is warranted, but the Homological mirror symmetry page is in serious need of a clean-up: it reads like a pop-science article but contains sparse content. This could be re-written to include some of the formulations and discuss some of the proofs, like HMS on the elliptic curve, Seidel's proof for K3 surfaces using Vanishing cycles, and Sheridan's article on HMS for hypersurfaces. Wundzer (talk) 17:52, 18 August 2020 (UTC)

Just be careful to make sure your content is as accessible as possible. I believe the ideal wiki article is quite different from an ideal review article. Gumshoe2 (talk) 18:12, 18 August 2020 (UTC)

I agree with making the material accessible and that's the main reason why I care about writing these articles. I think writing in the survey/review format is good for a baseline model because it is easy to expand upon and link to relevant material. Moreover, it organizes the material in a top-down fashion which (I think) can help make it a great wiki article. I do try my best to make content accessible, but will make sure to keep a keener eye for linking relevant material. Wundzer (talk) 20:03, 18 August 2020 (UTC)

Fixing page redirect

It seems like there is an edit war afoot with the Mirror symmetry (mathematics) link. I outlined above reasons why this should either be kept where it was, or directed to the Mirror symmetry conjecture page. But, here's an itemized list of these reasons

1. I think the general mathematics community should dictate the use of the terminology "mirror symmetry".
2. There are a few ways to measure this dictation: by looking at different resources mathematicians use and see how they use "mirror symmetry" and what subject it refers to.
3. Before continuing on to the list, note that the redirect is going to a small, basic idea, part of a single lecture or two on group theory, instead of a large wide-open field with many interesting problems that several prominent mathematicians have studied and are continuing to work on to this day.
4. A quick search on the arxiv shows that most papers being published refer to mirror symmetry in the sense of string theory
5. There are several books related to the study of mirror symmetry, including this Clay math monograph. You can look at [1] for the keyword "mirror symmetry" and find countless other books only discussing it in the sense of string theory.
6. Mathoverflow uses the mirror-symmetry tag to refer to questions related to the mathematical physics topic.

Moral of the story, I think having this redirect toward Reflection symmetry is myopic at best, and petty at worst. Wundzer (talk) 20:01, 19 August 2020 (UTC)

Without weighing in on the merits here, it is at least clear that the actions D.Lazard has put in motion are in poor form. For example, it's plainly indefensible to have requested this move as an "uncontested technical request" after it was clear that Wundzer would object. --JBL (talk) 22:15, 19 August 2020 (UTC)

Also pinging @Anthony Appleyard:, who actually carried out the move. (The current status is that Mirror symmetry and Mirror symmetry (disambiguation) are both disambiguation pages, which is obviously ridiculous.) --JBL (talk) 22:18, 19 August 2020 (UTC)

Hi, thanks for your response. I thought the original disambiguation page was put into oblivion and basically rewrote it into the Mirror symmetry page. This is because many of the redirects at the top of wiki pages used the Mirror symmetry redirect. Wundzer (talk) 22:27, 19 August 2020 (UTC)

I've reverted Mirror symmetry (mathematics) back to redirecting to the dab page Mirror symmetry, this would allow any user to find the page they are looking for, being either the Mirror symmetry conjecture or the far more common usage of it being used as a synonym of Reflection symmetry. I think the principle of least astonishment WP:R#ASTONISH holds here. A user expecting to find the common usage would be highly astonished to arrive at a string theory article. --Salix alba (talk): 22:23, 19 August 2020 (UTC)

I'm not convinced this is a common usage of the term "mirror symmetry". Do you have any common references for where this is used? It is the first time I've run across this terminology. If it is the case that I'm ignorant about this usage, then I think this is the correct course of action, otherwise I think it's unwarranted Wundzer (talk) 22:27, 19 August 2020 (UTC)

When I throw the words "mirror symmetry" into my favorite search engine (in private browsing mode), I get approximately equal numbers of hits for the elementary geometric meaning and for the string theory-related meaning on the first few pages of results. When I use my second-favorite search engine, I get about 4-to-1 hits for the string theory meaning versus the elementary meaning. When I use my third-favorite search engine, I get about 3-to-1 hits for the elementary meaning versus the string theory meaning. To me, this suggests there's no primary topic. I would propose restoring the situation as it was before D.Lazard's latest actions: Mirror symmetry a disambiguation page, with Mirror symmetry (mathematics) pointing towards it, and no such page as Mirror symmetry (disambiguation). --JBL (talk) 22:49, 19 August 2020 (UTC)

JBL, unilateral/bold page moves which are contested after the fact (in some reasonable time proximity) may be reversed using the technical queue. (Think of it as the revert in BRD.) They then can be submitted to the full move request process. See WP:RMUM. --Izno (talk) 22:46, 19 August 2020 (UTC)

Thanks, Izno. Because many things are going on simultaneously, it may be best in this case to reach consensus before patching everything back up again. --JBL (talk) 22:49, 19 August 2020 (UTC)

Some alternative redirect names

• Mirror symmetry (mathematics) -> Mirror symmetry conjecture
• Mirror symmetry (algebraic geometry) -> Mirror symmetry conjecture
• Mirror symmetry (group theory) -> Reflection symmetry

Here's my running opinion: since search engine results give some ambiguity, I think Mirror symmetry (mathematics) should direct to the disambiguation page. This disambiguation page should have a subsection for uses in mathematics and a subsection for other uses. Then, create redirection pages Mirror symmetry (algebraic geometry) -> Mirror symmetry conjecture and Mirror symmetry (group theory) -> Reflection symmetry. Wundzer (talk) 00:04, 20 August 2020 (UTC)

Deciding whether there is a primary topic

I agree that I was bold by considering that the equality of an object with its mirror image was the primary meaning of "mirror symmetry", and adapting Wikipedia accordingly. Nevertheless, if there is a consensus on this primary meaning, my edits and the move are fully in accordance with MOS:DAB and must be restored. Otherwise, it is the previous state that must be restored.

The only argument that is given above against a primary topic is the number of hits given by research engines. IMO, this argument is biased for the following reasons. Until circa 1990, "mirror symmetry" was a synonymous of "reflection symmetry", that was often preferred by non-mathematicians as more intuitive. This can be seen by limiting the Scholar Google search to the period before 1990. Since this date, there is a tremendous research activity around the extension of this topic to theoretical physics and algebraic geometry. This explains why the new meaning of the term is predominant when a preference is given to recent articles. So, the number of hits given by research engines is not very significant for deciding a primary topic.

Another criterion for deciding a primary topic is historical establishment. This is in favour of the etymological meaning, as it is established for centuries, and the new meaning is derived from it.

IMO, the main criterion here is WP:LEAST: One may espect that most readers (that is all readers except theoretical physicists and algebraic-geometers) are looking for reflection symmetry, and will be confused to have to click twice and to choose between links that are esoteric for them, before finding the desired article.

By the way, as all the targets of these links are mathematical articles, Mirror symmetry (mathematics) and Mirror symmetry must have the same target, whichever it is.

Please, discuss here whether the older meaning is a primary topic, and wait for a consensus before further changes. D.Lazard (talk) 10:03, 20 August 2020 (UTC)

"Mirror symmetry" is the same as "Mirror symmetry (mathematics)" — there's a joke in there, somewhere, but I can't quite find it. Oh well. It's probably not a very good joke. --Trovatore (talk) 17:21, 20 August 2020 (UTC)

For myself, and I think for essentially all mathematicians I personally know, the phrase "mirror symmetry" has taken on a definitive meaning which refers to the string theory topic and to the corresponding mathematical conjectures and results. I just mean that as an observation, the limitations of which speak for themselves... Gumshoe2 (talk) 17:53, 20 August 2020 (UTC)

I think that is correct. Looking at all references to "Mirror symmetry" on Mathematical Reviews ("anywhere" on mathscinet), there are 2429 listings, most of which relate to the 1990 sting theory discoveries of Aspinwall, Candelas, Greene, Vafa, Witten, Yau, et al. The same is probably true for Paul Ginsparg's "arXiv". The SMF-AMS book on Mirror Symmetry by Claire Voisin is a reasonable reference. Mathsci (talk) 21:41, 20 August 2020 (UTC)

When should there be a decision about whether consensus is reached? Wundzer (talk) 22:41, 24 August 2020 (UTC)

Comment: Within the mathematical community Mirror symmetry always refers to the the algebraic geometry notion. I don't think there are any mathematicians who would use the word mirror symmetry to refer to basic reflection symmetry ideas (partly because the name has been well and truly co-opted by algebraic geometry, and partly because no one studies that kind of thing anymore). I disagree with Mirror symmetry going directly to the reflection symmetry page, but I also think it's probably better to have a DAG page instead of going straight to the mirror symmetry conjecture. If I had to pick I'd say make it the MSC page, as this more accurately reflects what mainstream mathematics views the term to mean.Tazerenix (talk) 23:23, 24 August 2020 (UTC)

This sort of no true Scotsman snobbiness, defining the mathematical community as only being the people that study the topics that the in-group of research mathematicians have deemed to be important research, and disavowing the mathematics done even as academic research by anyone else, is exactly the sort of thing Branko Grünbaum decried over 40 years ago in his lectures on lost mathematics. Meanwhile, in the broader mathematical community, including people who prove theorems in academic research but not as members of pure mathematics departments, people who teach mathematics to schoolchildren, people who write textbooks for those teachers, or people who read or write Wikipedia articles on mathematical topics, "mirror symmetry" remains more likely to be understood as a synonym for reflection symmetry than as a specialized topic in advanced theoretical physics. One can find many current research articles, if not in what you would think of as real mathematics, that use "mirror symmetry" in its colloquial sense: see, e.g. approximately 640 papers since 2016 in Google scholar that use the exact phrase "mirror symmetry" in connection with bilateral symmetry, in fields including cognitive psychology, computer vision, ophthalmology, mathematical chemistry, etc. When you say "no one studies that kind of thing anymore", perhaps you mean it as a shorthand for "no one of any importance", because those other fields are not important? —David Eppstein (talk) 00:05, 25 August 2020 (UTC)

In the same time frame, there appear to be at least several thousand results on google scholar for "mirror symmetry" "conjecture", and even more if you include adjectives such as "geometry." Perhaps Branko Grünbaum would find this an affront, but I'm not particularly concerned with what a single individual from outside the pure maths community thinks thought about modern differential geometry, which appears to be what he is decrying in the introduction to that article. Perhaps he wasn't aware that the universe is described by such useless concepts, or disagreed that that is an important thing to study.

I was merely reporting on the status of the term within the pure mathematics research community. If your objection is that I used the term "mathematical community" instead then fair enough. I have no intention of debating who is or isn't a mathematician or what is or isn't important mathematics. It is probably correct that most people, if they were to want to know more about reflection symmetry, would be a bit surprised if they googled mirror symmetry and the page went directly to an algebraic geometry conjecture in pure mathematics, but WP:BUTIDONTKNOWABOUTIT seems to suggest to me this is just the kind of situation for a disambiguation page?Tazerenix (talk) 19:58, 25 August 2020 (UTC)

Yes, the theoretical physics community is very prolific. And claiming not to want to debate who is a mathematician, while in the same breath labeling Grünbaum (of all people!) as a non-mathematician, comes across as simultaneously disingenuous, ignorant, and upping the ante on your unappealing snobbery. —David Eppstein (talk) 20:14, 25 August 2020 (UTC)

I wasn't being snobbish, I was giving the perspective of someone from that area of pure maths (a not irrelevant point of view I would think, given this is literally a discussion about that topic). I didn't call this man not a mathematician (something which you seem to be projecting onto me, perhaps because of your overlapping areas of interest), I said he wasn't a modern differential geometer, which is obviously true given that his interests appear to lie more in computational geometry and convex geometry (his geometric interests in any case), both subjects of considerable interest both before and after his time even within the pure maths community may I add (see for example Hilberts 18th problem). I have no interest in having a debate about who is or isn't a mathematician with you, and I don't think its relevant to this conversation. Clearly people who aren't algebraic geometers have just as much right to google mirror symmetry and come to wikipedia to learn more about the thing they have in mind as algebraic geometers do, and there are certainly going to be much more of the former people, but since there seems to be contention as to the role of the page and its naming, it seems best to me to have a DAG page. I'd prefer not to have baseless accusations be made at my character for putting my input in on the naming of a wikipedia page.Tazerenix (talk) 21:35, 25 August 2020 (UTC)

To be precise, you said that Grünbaum was "outside the pure maths community". Which is both false and ignorant. And your ignorance reflects on how seriously I should take your apparent preference that the mathematical physics meaning of "mirror symmetry" should be the WP:PRIMARYTOPIC. It is reasonable for it to be the topic of disambiguation. It is not reasonable to declare that a narrow group of specialists can monopolize a phrase with a notable colloquial meaning. —David Eppstein (talk) 21:43, 25 August 2020 (UTC)

Of course, specialists will try, but we shouldn't let them get away with it. :-) XOR'easter (talk) 21:47, 25 August 2020 (UTC)

I meant not within the modern differential geometry community, but alas, your mind is made up. I also said it should be a DAG page four times (my remark that I "choose" the MSC page was meant to be if I had to choose one or the other with no DAG option, and of course my comment is not a decision, just a comment representing my own input, which can happily be disagreed with or ignored. Indeed you are probably right that if we had to choose it should go the other way, but as a snobbish pure mathematician who hoards all knowledge and common phrases, changing my mind or engaging in discussion is out of the question)Tazerenix (talk) 21:54, 25 August 2020 (UTC)

Personally I think this would be a good case for a disambiguation page. The elementary concept is vastly more important than the string theorem/algebraic geometry concepts, but the article on the broader concept is not titled "mirror symmetry" and there are other, more common names for that concept. So we are balancing a specialized notion very strongly associated with the name against a much broader notion more weakly associated with the name; I find it hard to see a case for a primary meaning, especially given the search engine results I mentioned. Therefore I propose:

• The current redirect Mirror symmetry should be deleted
• The current disambiguation page Mirror symmetry (disambiguation) (which has a nontrivial edit history) should be moved to Mirror symmetry (where it used to be)
• The pages on the string theory/algebraic geometry concepts should all have hatnotes pointing to the disambiguation page

(Obviously this requires an administrator to actually carry it out.) --JBL (talk) 21:30, 25 August 2020 (UTC)

• We should always put the reader first. A few readers will be professional mathematicians, but most of us thought a Calabi–Yau manifold was a car part. A mixed audience may make different assumptions as to what "mirror symmetry" means. In such case, the best way to avoid presenting anyone with unexpected topic is to put the disambiguation page at the base name. Certes (talk) 21:59, 25 August 2020 (UTC)

Filters in topology

• Filters in topology (edit | talk | history | protect | delete | links | watch | logs | views)

This article was just created by Mgkrupa. We already have an article at Filter (mathematics), which (aside from basic definitions) is mostly focused on their use in topology. I'm a little skeptical that this should be spun out into a separate article, especially so because what's there now falls very squarely on the wrong side of WP:NOTTEXTBOOK. I'm trying to limit my activity here these days, but I'd certainly welcome others' opinions on this. Thanks, –Deacon Vorbis (carbon • videos) 00:30, 20 August 2020 (UTC)

On a side note, it makes extensive use of special Unicode characters, like (U+212C ℬ SCRIPT CAPITAL B) for example, which I'm under the impression should generally be avoided due to rendering support. –Deacon Vorbis (carbon • videos) 00:41, 20 August 2020 (UTC)

My general impression of Mgkrupa's contributions is that they tend to be very WP:TECHNICAL. For subjects that really are technical, this may be ok, but it tends to spill over onto other subjects where the technicality is an unnecessary obstacle (for instance, I had to revert several times Mgkrupa trying to rework the definitions in convex hull to focus on topological vector spaces rather than Euclidean spaces). —David Eppstein (talk) 00:53, 20 August 2020 (UTC)

I have had a view that the focus of the use in topology in Filter (mathematics) is a *problem*. A "filter" is after all a general concept. A filter (in particular an ultrafilter) is also used in abstract algebra in the form of ultraproduct and also is a useful concept in the theory of Boolean algebras (if I recall, please correct me if you know this stuff). It seems natural to have a separate article on the use of a filter in topology in an independent article (in that case, it is essentially equivalent to net but should probably be separated from that). -- Taku (talk) 01:11, 20 August 2020 (UTC)

This would require an expert (not me) but, for example, we might want to mention a result of G.M.Bergman - Ehud Hrushovski, Linear ultrafilters or some other similar results. In any case, the point is that a filter is a general concept. -- Taku (talk) 01:28, 20 August 2020 (UTC)

Another related matter: ultrafilter is a separate article from "filter (mathematics)"; which is not necessarily bad but if we can separate the topology stuff from "filter (mathematics)", then there will be more real estate to merge the ultrafilter article to the filter article. —- Taku (talk) 02:32, 22 August 2020 (UTC)

I don't really think ultrafilters should be merged into filters. There's plenty to say about ultrafilters as a topic on their own. Also the problems studied with regard to ultrafilters tend to have a bit of a different character from those that come up using filters in general. --Trovatore (talk) 22:43, 25 August 2020 (UTC)

Yes, "ultrafilters" certainly makes sense as an independent topic; that does not mean it needs a separate article. For example, "embedding" discusses both embeddings of a manifold and a category; even though there is *plenty to say* about embedding of a manifold (e.g., Whitney embedding theorem). I suppose the problem is that currently filter (mathematics) is somehow underdeveloped than ultrafilter; the latter mentions a filter (in particular an ultrafilter) on a Boolean algebra while the former has nothing on the use in a Boolean algebra. It would be helpful to the readers including non-specialists (like myself) if there is a single article to read on filters as well as ultrafilters; a spin-off of ultrafilter is needed only after that single article becomes too long. It's possible that filter (mathematics) ends up discussing mostly ultrafilters; I don't think that would be a problem. -- Taku (talk) 00:04, 26 August 2020 (UTC)

No, I really don't agree. I feel very strongly that ultrafilters should retain a dedicated article. Ultrafilters come up largely in the context of ultraproducts. They're mostly a technique for getting elementary embeddings. A typical ultrafilter is generally not definable. That's not true at all for general filters, which can easily be definable, and are studied in lots of other contexts. --Trovatore (talk) 00:37, 26 August 2020 (UTC)

I agree with Trovatore. JRSpriggs (talk) 04:12, 26 August 2020 (UTC)