Wikipedia talk:WikiProject Mathematics/Archive/2024/Mar

Notability of John H. Wolfe
The article John H. Wolfe has gone through a PROD, but still has issues as it is based on one secondary textbook claim that his work on model-based clustering matters. It was created directly by a novice editor (Stat3472 33 edits). The article model-based clustering supports him as the inventor, but whether this is big enough for notability is unclear. Comments on that talk page please. Ldm1954 (talk) 09:57, 2 March 2024 (UTC)

≙
There is a discussion about the ≙ character that needs attention from mathematical editors at Redirects for discussion/Log/2024 March 2. Thryduulf (talk) 12:35, 2 March 2024 (UTC)

Mental calculation
Does anyone feel like cleaning up Mental calculation? It's roughly as disorganized as one would expect. XOR&#39;easter (talk) 18:35, 3 March 2024 (UTC)

any, every, some

 * For every number $$\varepsilon>0, \ldots$$


 * For some number $$\delta>0, \ldots $$

It is clear that in standard English usage, the words "every" and "some" as used above are respectively universal and existential quantifiers.

"Any" can be a universal quantifier, as in:

"Any fool can see that."

(But "Anyone can be elected chair of the committee" doesn't mean the same thing as "Everyone can be elected chair of the committee.) "Any" can also be an existential quantifier, as in:
 * There isn't anyone here who can answer that question.
 * There isn't anyone here who can answer that question.


 * Is there anyone here who can answer that question?


 * If anyone knows the answer, please step forward.

I thought that there are three contexts in which "any" is an existential quantifier:


 * negations,
 * questions, and
 * conditional clauses,

those being the three exhibited above.

But then in the article titled Causality conditions, I found this:


 * A manifold satisfying any of the weaker causality conditions defined above may fail to do so if the metric is given a small perturbation.

Here, "any" is used as an existential quantifier, and it is not clear to me that it is one of those three kinds. Thus my list appears to be incomplete.

A grammar question rather than a math question, but one to which mathematicians are in more desparate need to pay attention than is perhaps anyone else.

What should be added to this list? Michael Hardy (talk) 18:51, 21 February 2024 (UTC)


 * In the above quotation, "any" is a universal quantifier. D.Lazard (talk) 19:02, 21 February 2024 (UTC)
 * You can still see "any" here as a universal quantifier, in the sense that "for all of these weaker causality conditions, a manifold satisfying said condition can fail to do so if  ." I would argue that the existential quantifier here is actually hidden in "can", in the sense that "a manifold satisfying said condition can fail to do so if..." is shorthand for "there exists a manifold satisfying said condition that fails to do so if..." GalacticShoe (talk) 19:09, 21 February 2024 (UTC)


 * Because pushing a negation through a $$\forall$$ flips it to a $$\exists$$ and vice-versa, examples involving negation &mdash; including "not", "fails", "never", etc. &mdash; can be argued about endlessly. It seems to me that math textbook authors solve this problem by stating each definition and theorem as clearly as they can, relying on the proof to clarify the exact meaning of a theorem in a pinch, and tolerating looser talk in discussions between theorems. Mgnbar (talk) 19:30, 21 February 2024 (UTC)
 * The correct phrasing is "for any (every) said condition, there exists a manifold satisfying it that fails to do so if...". So the hidden existential quantifier does not refer to the same thing. D.Lazard (talk) 19:36, 21 February 2024 (UTC)
 * The meaning of the expression "a manifold satisfying any of the weaker causality conditions defined above" is a manifold which falls into one or more of the classes defined by the previous causality conditions; as previously stated in the article, if it falls into one of them, it also falls into the previous classes, as they are nested with stricter conditions listed later. But the manifolds of particular interest for that section are the strongly causal ones (the immediately preceding condition). My understanding based on the article's text is that "stably causal" means a strongly causal manifold which remains strongly causal under any possible perturbation of a chosen (arbitrarily small) magnitude. Or another way of saying this: if a manifold is "stably causal", then there exists some specific size of perturbation for which every smaller perturbation of the manifold preserves the strong causality property. From what I can tell the perturbations of other kinds of causality-condition-satisfying manifolds are not at issue (beyond the initial mention, for context, that for each of the earlier conditions there exists some manifold satisfying it which can be perturbed into not satisfying it by an arbitrarily small perturbation). –jacobolus (t) 19:41, 21 February 2024 (UTC)

Some months ago, the was consensus that "any" should be avoided (in order not to require the reader to be familiar with discussions like the above one), see MOS:MATH. - Jochen Burghardt (talk) 20:10, 21 February 2024 (UTC)


 * Rephrasing this particular passage is more complicated than the examples given there, as it expresses a somewhat tricky logical claim. I don't think this one is really ambiguous in context, but it could be rephrased as e.g. "For each of the weaker causality conditions defined above, there are some manifolds satisfying the condition which can be made to violate it by arbitrarily small perturbations." –jacobolus (t) 21:43, 21 February 2024 (UTC)


 * Jacobulus last suggestion is perfect. To answer Micheal Hardy's original question, there is yet another sense of any: in this case, it's "menu choice": "pick any one item from this menu". Menu choice is similar to exclusive-or, but is not truth-valued, it is object-valued. Menu choice shows up as a fragment of linear logic (for example, the quantum no-cloning theorem, which says "you can only have one of these") but also in vending machines "for a dollar you pick one item" and in mutex locks in computing (one user at a time.) Menu choice is a really cool tool in foundational logic. 67.198.37.16 (talk) 07:34, 4 March 2024 (UTC)

Brouwer–Hilbert controversy
Should this article be renamed to Grundlagenstreit? This is the name often given in the literature to this debate. I do not know much about it but it seemed odd when I was looking for it. See for example Brouwer's biography ReyHahn (talk) 10:01, 4 March 2024 (UTC)


 * For me, naming an obscure topic from 100 years ago using an unfamiliar non-English word (German?) is the same as deleting the article.
 * Maybe "Grundlagenstreit, the Brouwer–Hilbert controversy"? Johnjbarton (talk) 15:45, 4 March 2024 (UTC)
 * Maybe the term Grundlagenstreit should be included in the lede; it seems common enough in writings about the topic. XOR&#39;easter (talk) 16:18, 4 March 2024 (UTC)
 * Apparently Grundlagenstreit means "foundational debate", and was related to Hilbert's book Grundlagen der Geometrie. Seems fine to me to create a redirect and mention the name in the lead section (doesn't need to be bolded in my opinion). –jacobolus (t) 16:30, 4 March 2024 (UTC)
 * No, but theree should be a printworthy redirect from Grundlagenstreit to the article. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:28, 4 March 2024 (UTC)
 * Thank you all, I prefer to keep it bold but that can be discussed. As for the main topic I consider this ✅.--ReyHahn (talk) 21:06, 4 March 2024 (UTC)

Merge?
On pl wiki, User:Epsilon598 suggested AM–GM inequality, QM-AM-GM-HM inequalities and Generalized mean may need a merge. Thoughts? Piotr Konieczny aka Prokonsul Piotrus&#124; reply here 02:07, 26 February 2024 (UTC)


 * Actually, Pythagorean means should also be at least linked to the others. In Polish all of these inequalities are usually called simply "inequalities among means", which is also used in at least one of these articles. This name is not nearly as fitting in English as it is in Polish, but would be my first guess. Epsilon598 (talk) 02:45, 26 February 2024 (UTC)
 * I usually hear this called "Power Mean Inequality" in English (which is currently a redirect to Generalized_mean). Elestrophe (talk) 16:38, 7 March 2024 (UTC)

Notice of discussion
A discussion at Wikipedia talk:Good article nominations might be of interest to members of this project. &#126;~ AirshipJungleman29 (talk) 22:23, 7 March 2024 (UTC)

Inconsistent
In the interest of keeping this Project rational, it can be noted that as things stand, a function may be partial or total or multivalued or univalent. The terms "partial function" and "multivalued function" are self-contradictory, they are oxymorons. According to WP:Article names, consistency is one of the parameters of evaluation. Tolerating contradiction, as in the two article names, invites arbitrary deductions since any proposition may be deduced from a contradiction. A function is a type of relation so its variants are best described with properties of relations. A partial function is a univalent relation, and a multivalued function is a relation. Rgdboer (talk) 01:09, 10 March 2024 (UTC)


 * It's established mathematical terminology, and it's also pretty common in English generally (see, for example, Subsective modifier). - CRGreathouse (t | c) 01:17, 10 March 2024 (UTC)
 * Lots of things have names of the form [modifier] [something] to indicate that it is a generalization or variant form of something or something modified in a certain way rather than a special case of something. A Reuleaux triangle is not actually a triangle. A truncated icosahedron is not actually an an icosahedron, and a snub cube is not a cube. "Partial function" is no different. There is nothing inconsistent about this naming convention. See also WP:COMMONNAME and WP:NEO. —David Eppstein (talk) 01:29, 10 March 2024 (UTC)
 * Well put. I would add that a skew field may be a field but is not necessarily a field, which maybe is more directly analogous to the case at hand, since a partial function may be a function but is not necessarily a function. --Trovatore (talk) 03:28, 10 March 2024 (UTC)
 * I don't believe Wikipedia claims to be "rational", nor would we want it to be. Rationality has its limits; irrationality knowns no bounds. Johnjbarton (talk) 01:56, 10 March 2024 (UTC)
 * It's also often much harder to keep things rational. — MarkH21talk 03:51, 10 March 2024 (UTC)
 * You could argue that irrationality has its limits too :P GalacticShoe (talk) 04:09, 10 March 2024 (UTC)
 * The first goal of article names should be reflecting common usage among reliable sources, especially those from professional practitioners, with common alternative names listed/explained in the article text. This helps the widest range of readers to get up to speed with the terminology and conventions they will find in other sources. Other goals are subsidiary to that, and any "irrational" features of the most widely used and accepted nomenclature can be explained in text.
 * If you have a problem with widespread mathematical conventions, the place to fix it is in the mathematical literature, not in Wikipedia. (But making an explicit note when terminology is confusing, ambiguous, historically revisionist, politicized, a misattribution, etc. could be helpful.) –jacobolus (t) 04:27, 10 March 2024 (UTC)
 * Also, for considering the original example, the general meaning of "function" refers to univariate total function, but, in many texts, partial functions and multivariate functions are simply called functions. These generalized functions may be considered as functions in the first sense, by changing of domain. This is for this reason that I have added recently the subsections "Partial functions" and "Multivariate functions" to Function (mathematics), with explanations on these terminology shifts. D.Lazard (talk) 09:54, 10 March 2024 (UTC)

Requested move at Talk:N = 2 superconformal algebra
There is a requested move discussion at Talk:N = 2 superconformal algebra that may be of interest to members of this WikiProject. Killarnee (talk) 23:44, 14 March 2024 (UTC)

Torsion tensor
Could you join the dispute at Talk:Torsion tensor?

The summary of the discussion (in my view point) is written in the section Discussion between Tito Omburo and Idutsu.

---Idutsu (talk) 14:20, 14 March 2024 (UTC), editor of japanese Wikipedia.


 * I've spent a long time trying to make sense of the torsion tensor in terms of normal coordinate systems. I came to the conclusion a long time ago that the #Twisting of reference frames section of the torsion page was wrong. Not in interpretation, but literally mathematically incorrect. The relationships asserted between the torsion tensor and the development of a frame along a curve don't match: the expression people think of for the rotational development of a coordinate frame correspond only to the covariant derivative of the frame along the curve, not to the difference of covariant derivatives as appears in the torsion tensor.
 * I've never seen any source which actually went through the details of this interpretation and explained it, and I've seen many mathoverflow posts just like Bill Thurstons which wax lyrical about interpretations of torsion without ever explaining in mathematical detail how the formula of torsion relates directly to the development of a coordinate frame along a curve.
 * I don't have any skin in the game of your discussion but if it were me I would try to hold this to a very high standard of reference because it is a notoriously wishy-washy subject in differential geometry. The conclusions of Tu & Spivak that there is no actual detailed mathematical link between the name torsion and some of the more elementary interpretations of twisting of a frame around a curve seem to hold up to my scrutiny at least. Tazerenix (talk) 06:23, 15 March 2024 (UTC)
 * Is this the part you disagree with?
 * The foregoing considerations can be made more quantitative by considering a small parallelogram, originating at the point $$p\in M$$, with sides $$v,w\in T_pM$$. Then the tangent bivector to the parallelogram is $$v\wedge w\in\Lambda^2 T_pM$$.  The development of this parallelogram, using the connection, is no longer closed in general, and the displacement in going around the loop is translation by the vector $$\Theta(v,w)$$, where $$\Theta$$ is the torsion tensor, up to higher order terms in $$v,w$$.
 * Gumshoe2 (talk) 13:36, 15 March 2024 (UTC)
 * No, that's the standard interpretation of the torsion tensor geometrically. However I reject that it has much to do with the english word "torsion". The section of the page I was referring to has since been removed. My comments were just general that care should be taken with this subject to get high quality sources! Tazerenix (talk) 22:09, 15 March 2024 (UTC)

The article has been substantially revised since the bad version that User:Tazerenix is referring to. I wrote the above description in terms of the tangent bivector to replace the mathematically wrong section that had been there before. What I wrote is correct and supported by sources. There may however be different factors of two in place in the article, which I have not checked in detail. So this interpretation is satisfied up to a factor of two that is subject to checking conventions.

The connection with development, however, is well-known and easily understood. I have given a detailed example in the image in the lede. Basically the idea is to take a closed curve $$\gamma$$ in the manifold, and a parallel coframe $$\theta^i$$ along $$\gamma$$, and then solve the ODE $$dx^i=\gamma^*\theta$$ for coordinates $$x^i$$. When the torsion vanishes (and the curve is null homotopic), the developed curve is also closed (a consequence of the Ambrose-Singer theorem, or alternatively even Stokes' theorem is sufficient.)

When the torsion does not vanish, it means that there is a non-trivial translation component to the holonomy for the affine group, and so the developed curve need not be closed. I think the current image at the top of Torsion tensor nicely illustrates this, and as a bonus shows the connection to Frenet-Serret torsion. Tito Omburo (talk) 20:15, 15 March 2024 (UTC)

Tom Ilmanen
Good day! Is there some experienced editor interested in helping me create an article about Tom Ilmanen? He seems like notable enough (many papers cited by hundreds each), but it's hard to find sources about him (not about his work). :( I've made a beginning draft: Draft:Tom Ilmanen. Thanks! Gererhyme (talk) 10:27, 15 March 2024 (UTC)


 * I wouldn't say that "his best known mathematical works are in cooperation with Gerhard Huisken," since they only have two research papers together. It would be better to say something like: "Huisken and Ilmanen used inverse mean curvature flow to prove the Riemannian Penrose conjecture, which was resolved at the same time in greater generality by Hubert Bray using alternative methods." This article could be used as a reference.
 * I also wouldn't refer to "the Huisken-Ilmanen conjecture" unless grammatically in the particular context of talking about a particular conjecture by Huisken and Ilmanen. As far as I know, there has not been anything widely known as "the Huisken-Ilmanen conjecture." Even the article by Dong and Song resolving the conjecture says only "This confirms a conjecture of G. Huisken and T. Ilmanen." (It's not clear to me how significant the conjecture or its proof should be regarded as being.) Gumshoe2 (talk) 13:31, 15 March 2024 (UTC)


 * Wow!!! Thank you very much, Gumshoe2!!! Gererhyme (talk) 13:34, 15 March 2024 (UTC)
 * Happy to help. Not sure what can be done to help establish wiki-notability, although I believe it's fully orthodox to regard Huisken-Ilmanen's paper as seminal and the other three publications you've listed as highly notable as well. (Speaking of which, his book should be regarded as a research contribution and not as a textbook.) You might have to just hope to come across a sympathetic admin when submitting the draft. Gumshoe2 (talk) 13:49, 15 March 2024 (UTC)
 * It may be a small help to cite Yau's well-known list of open problems where the Riemannian Penrose inequality is the fifteenth problem. Gumshoe2 (talk) 14:05, 15 March 2024 (UTC)
 * Thank you so much!!! "Review waiting, please be patient. This may take 8 weeks or more." EIGHT WEEKS OR MORE....... ZZZzzzzzZzZZzZ "be patient" hahaha. :) Gererhyme (talk) 14:30, 15 March 2024 (UTC)
 * And now in mainspace, and passed through NPP. A nice short article.  My one constructive suggestion would be to use the Quanta article as a source to say something meaningful about Ilmanen, rather than just dump it into a "further reading" section.  --JBL (talk) 23:00, 15 March 2024 (UTC)
 * Nice suggestion, JBL!! Thank you! ^^ I'll follow it, but I need some rest before doing so (yesterday I edited Wikipedia for something like 12 straight hours!). In fact, it was from Quanta Magazine I first heard of Ilmanen! Gererhyme (talk) 11:18, 16 March 2024 (UTC)

"Idealwise separated" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Idealwise_separated&redirect=no Idealwise separated] &#32;to the article Completion of a ring#Krull topology has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. Kk.urban (talk) 06:22, 19 March 2024 (UTC)

Draft:Bianticupola
I have been looking for sources for my article on Bianticupolae. However, even after practically scouring the internet, the only mention I can find of them is on the Wikipedia article for cupolae. If anyone knows a good place to look, I would greatly appreciate that. Thank you! — Preceding unsigned comment added by Toxopid (talk • contribs) 17:32, 17 March 2024 (UTC)


 * @Toxopid please use the Add Topic button in Talk pages.
 * I fixed your problem: I deleted the word "Bianticupolae" from the article Cupola (geometry) so now the internet will not mention it.
 * Ok, sorry, that was mean. But the line was not sourced so we have no way to know if someone just made it up. The point of Wikipedia is to summarize knowledge: if you have no source then don't write an article. Move on to another topic. Every single wikipedia article has many ways to improve it, including I'm sure Cupola (geometry). Find some good sources and edit! Johnjbarton (talk) 21:43, 18 March 2024 (UTC)


 * has no sources, and the only mention I can find in the academic literature is from a 2023 arXiv preprint. Perhaps the section should just be deleted as original research. "Bianticupola" does not seem like a notable topic. –jacobolus (t) 22:24, 18 March 2024 (UTC)
 * I just deleted the section. If someone can find reliable sources, feel free to restore it. –jacobolus (t) 22:40, 18 March 2024 (UTC)
 * @Jacobolus I added the tag unreferenced, because there are lot of sections that do not have any sources to cite the facts. Is there any possiblity that they could be removed? Dedhert.Jr (talk) 11:24, 19 March 2024 (UTC)

Levi-Civita symbol
I just reverted a pile of COI edits at Levi-Civita symbol and made some other small fixes. It currently has 3 citation needed tags; in particular, there's a long stretch of $$n$$-dimensional calculations without any indication that going beyond 3 dimensions is a thing that warrants all that detail. (Like a lot of math pages, the increase in verifiability between one reference per section and one reference per sentence would not be that great in practice. But it needs a little work to get up to the former standard.) XOR&#39;easter (talk) 17:32, 17 March 2024 (UTC)


 * Looks fine to me in it's current form (but I only skimmed it). The 4-d version sometimes shows in general relativity contexts, and the n-dimensional version sometimes shows in riemannian geometry and differential geometry textbooks where the author wants to perform some detailed, explicit calculation showing the gory details of Poincare duality or maybe how to use the Hodge star to define some inner product on some space of forms or weak derivatives or something. Perhaps Jurgen Jost "Riemannian Geometry" textbook, he likes to do explicit calculations; but my memory is faulty. When I was in school, one homework problem was to take the n to infty limit of this tensor; turns out it is the same as some harmonic oscillator over grassman variables, a determinant of some feynmann path integral. I forget; it has some famous name attached to it - Berezin integral or something like that. The joke is that physicists know how to do only one integral. 67.198.37.16 (talk) 00:16, 22 March 2024 (UTC)

Confusing image at Quadratic formula
is garbled in Firefox. Looking at its history, the previous version was fine, but the change to "fix rendering issues in Chromium" seems to have broken it. XOR&#39;easter (talk) 15:33, 21 March 2024 (UTC)


 * For me, both versions seem to look fine (i.e. the same to each other), on both Firefox and Chromium. Felix QW (talk) 15:43, 21 March 2024 (UTC)
 * It's also ruined in my computer, for both Firefox and Chromium. Note that if I click through to the actual svg file it renders correctly, it's only garbled when I see it in the Wikipedia article or the Media Viewer. Tercer (talk) 15:50, 21 March 2024 (UTC)
 * Maybe we should just replace it with a PNG? XOR&#39;easter (talk) 16:01, 21 March 2024 (UTC)
 * That would be a depressing choice. Clearly SVG is the appropriate format for this image, and by now it is very old technology. We should be capable of getting it to render correctly. Tercer (talk) 18:28, 21 March 2024 (UTC)
 * There's relatively little advantage to SVGs here for most readers. Wikipedia/Mediawiki renders them as a PNG image anyway, both in a thumbnail and when clicked to view larger on screen, and very few readers click through to the source file. The Mediawiki SVG renderer doesn't do a great job with antialiasing so the lines often look better when downscaled from a highish resolution raster image.
 * SVGs including text (including mathematical formulas) have to be carefully encoded/exported to make the font render properly, and the safest is often to resort to converting all of the fonts to explicit outlines. Getting the layout to exactly match the author's intentions can take extra work in an SVG. Wikipedia doesn't support any of SVGs interaction features that could plausibly make it an attractive format for animation or interactivity.
 * The main benefits of using an SVG are (1) if there is explicit English text, it can be more easily translated, and (2) if someone wants to take the image and print it in a book or put it on a billboard or something they might get a marginally better result. In practice many of our SVG images have ugly color and font choices, poor layout, etc., all of which are more important to get right than the choice of raster vs. vector format. –jacobolus (t) 18:50, 21 March 2024 (UTC)
 * As an explicit example, here are two images which nominally show the same subject (used in logarithm), but where the PNG image is significantly better than the SVG based on other graphical choices:
 * Logarithm_plots.svg Logarithm_plots.png
 * –jacobolus (t) 18:57, 21 March 2024 (UTC)
 * So what you are saying is that MediaWiki should stop ruining perfectly good SVGs and just deliver them as-is to the browsers, which do a good job of rendering them. Unlike MediaWiki.
 * One can make bad choices of font and colour in either format; the difference is that in a SVG it is trivial to fix them, whereas in a raster format it is not.
 * The fundamental point is that an SVG encodes information as what it is: paths as paths and text as text. This makes it much easier to do anything with it. (I have in fact used those capabilities. A PNG erases all the underlying data and gives us just a representation of the information.
 * The low resolution can be mitigated by using larger file sizes, as you say, but this is just another instance of an inferior solution. Tercer (talk) 21:04, 21 March 2024 (UTC)
 * Mediawiki has not changed in this regard in like 15+ years, so I'm not holding my breath.
 * My point is just that there's nothing magical about one file format or another, and the choice of format is not the most important feature of an image. All else equal, the vector image would have some advantages, but often there's a trade-off and the choice isn't quite as clear cut. For instance, if a raster image saves any appreciable amount of effort, it can be an advantage to spend the time saved on making more images instead of fiddling with the file format of a few. File:Regular tetrahedron inscribed in a sphere.svg is a good example of an image with a lot of problems, some of which are unrelated to the format such as illegibly small labels which are partly blocked by lines and a poor choice of bright pink color for radii, and others of which might be improved by using a raster image, e.g. shading the sphere (you can get somewhat acceptable sphere shading using SVG gradients, but it's not obvious, kind of tricky, and often done poorly). –jacobolus (t) 21:37, 21 March 2024 (UTC)
 * Well have you opened a ticket in Phabricator? They won't change anything if people don't ask for it.
 * As for my figure, since it's an SVG you can easily change everything you dislike about it. If it were a PNG you wouldn't be able to. Tercer (talk) 21:52, 21 March 2024 (UTC)
 * What makes images easy to edit or not is only tangentially related to the output format. Most images are created using some other software application (or applications), and the best way to help someone edit them is to include a link, textual description, file, etc. of the original input format. For example this might be tikz source, POV-ray source, raw PostScript code, a Blender file, a layered Photoshop document, an SVG with Inkscape-specific editor metadata, or a link to a Desmos or Geogebra plot. What tools other editors can work with or find familiar is going to vary depending on their experience and available software. –jacobolus (t) 22:27, 21 March 2024 (UTC)
 * Anyway, sorry, I'm not trying to give offense. My point is not to call out this particular image, which I'm sure is much more helpful than not having an image, but only to point out that the file format is way down the list of important features, and argue that people shouldn't be "depressed" to see high-quality images of any format created for the project. –jacobolus (t) 02:29, 22 March 2024 (UTC)
 * It is depressing to let the technical flaws of MediaWiki dictate our choice of file format. I searched a bit on Phabricator, and I'm afraid you are right: they are never going to fix their SVG rendering T40010 and nor are they going to allow browsers to render SVGs instead T5593. Tercer (talk) 08:56, 22 March 2024 (UTC)
 * It also seems they are stuck on an old version of librsvg, so even smaller improvements (than native rendering or a better library) are blocked: T265549 —David Eppstein (talk) 16:13, 22 March 2024 (UTC)
 * And that's since 2020. It's frankly ridiculous. WMF can't do even the bare minimum to keep the website running. I'm going to stop donating. They are clearly not using my money for what matters. Tercer (talk) 16:24, 22 March 2024 (UTC)
 * Taking arbitrary user-generated files and serving them up is a huge new "attack surface" which most sites serving SVGs are not affected by, and I'm not sure there's a super obvious existing set of tools for mitigating it. So it's definitely not a trivial thing to tackle. But it would be nice if someone would devote some resources to this, since the potential of SVGs is also pretty big.
 * I'd love to work with people on making interactive math diagrams for Wikipedia, if it were possible. I think the best bet is to just host anything animated or dynamic off-site and include a static version in articles. –jacobolus (t) 17:43, 22 March 2024 (UTC)
 * Telling readers to go look at some off-site resource is an equally large attack surface, to be fair. At least if it were served up on Wikipedia it might be expected to have passed some sanity checks. —David Eppstein (talk) 22:58, 22 March 2024 (UTC)
 * Regular tetrahedron inscribed in a sphere.svg also has an issue unrelated to its format: the use of quantum mechanics notation for its labels makes it unsuitable for topics beyond quantum mechanics. —David Eppstein (talk) 22:12, 21 March 2024 (UTC)
 * The topic is quantum mechanics, the filename is a misnomer. Tercer (talk) 22:43, 21 March 2024 (UTC)
 * All the files in the history look equally useless to me. Far too many equations on the graph. Johnjbarton (talk) 16:11, 21 March 2024 (UTC)
 * For me, on Safari, there are two problems: Firstly, on all versions, commas are vertically misplaced (At the level of denominators instead as at the level of fraction bars). On most versions, the horizontal bars (fraction bars and vincula of square roots) are horizontally misplaced with respect to the remainder of the formula. This misalignment disappears when clicking on the image or on thumbnails of the history. So, the problem seems to come from the method of writing and inserting formulas.
 * I agree with Johnjbarton that there are too much formulas in the image. Moreover, the directrix, the focus and the vertex of the parabola, and their coordinates are clerly out fo the scope of ths article.
 * So, I recommend to remove this image. D.Lazard (talk) 16:37, 21 March 2024 (UTC)
 * OK, I have removed it from Quadratic formula and also from Quadratic equation. An improved version (reliable rendering, leaving out the focus and directrix, etc.) would be nice. XOR&#39;easter (talk) 17:28, 21 March 2024 (UTC)
 * I tried purging the image (Commons:Help:Purge) but that didn't help, so it's not a caching issue. I think the file itself is not good. —David Eppstein (talk) 17:50, 21 March 2024 (UTC)
 * I think it's related to this regression in SVG rendering: https://phabricator.wikimedia.org/T97233 –jacobolus (t) 19:25, 22 March 2024 (UTC)
 * Argh this only gets more infuriating. The bug was reported upstream, who fixed it in 3 days. That was 4 years ago. WMF couldn't care less, apparently upgrading a library is too much work. They said they will only upgrade it together with the whole Debian distribution. The thing is, they can't be arsed to do that either. The Debian stable with the fix was released 3 years ago. Nothing. There was even another Debian stable release after that, last year. Nope. They are still on Buster, that was released in 2019. Fun fact, that will be end-of-lifed in 3 months, so we will have one the largest websites in the world running on unsupported software.
 * What on Earth are these clowns doing with out donation money? Tercer (talk) 21:12, 22 March 2024 (UTC)
 * @XOR'easter I've been working on this article recently, and intend to replace this image with several related images made in Desmos (I'm not sure if readers will notice, but anyone clicking through will then find a link to an interactive version), and also move the relevant section up toward the top and expand it. It will probably just be PNG images from a screengrab, since it takes at least twice the effort to get an SVG to render the same, and the benefit is relatively marginal. –jacobolus (t) 17:48, 21 March 2024 (UTC)
 * I'd welcome any other questions/requests/comments/recommended sources/collaboration on this article. It should be a high priority for us, as it gets a lot of page views (60k/month), more than related articles like quadratic equation, quadratic function, completing the square, or parabola, and seems likely to be routinely consulted by middle/high school students. –jacobolus (t) 17:49, 21 March 2024 (UTC)

I've put up a proposal  on VPWMF to solve this issue. Tercer (talk) 16:06, 23 March 2024 (UTC)

I replaced the top image of this article, which wasn't very clear, and also added an image to the derivation by completing the square section, both shown here:



After looking at again it though, I think including the formula in the middle of the first image is too much text, and it would probably be better to cut out the explicit quadratic formula part, even though that's the article. I'll try to figure out how to clearly (but not too busily) show the analytic-geometry meaning of the discriminant and other parts of the quadratic formula in another image or two; it's hard to make such images simple and legible while still trying to demonstrate more than one thing in a figure. –jacobolus (t) 19:01, 23 March 2024 (UTC)


 * The middle of the first image does look a little text-heavy. (Maybe remove the $$ y = 0 \Rightarrow x = $$ part and just show the evaluation of the formula?) But thanks very much for working on this. XOR&#39;easter (talk) 20:26, 23 March 2024 (UTC)

Requested move at Talk:Flatness (mathematics)
There is a requested move discussion at Talk:Flatness (mathematics) that may be of interest to members of this WikiProject. Favonian (talk) 10:17, 24 March 2024 (UTC)

Is Wolfram Mathworld reliable?
Related to the previous discussion, is Wolfram Mathworld reliable? I took the reviewing Talk:Arithmetic/GA2, and I claim that Wolfram Mathworld is not reliable sources, but the nominator claimed the otherwise. Now I'm very confused. Dedhert.Jr (talk) 07:12, 2 March 2024 (UTC)


 * I believe it's been discussed here before, although I can't find it now. In my opinion a mathworld source is better than no source, but not much beyond that. (I think that was also the general consensus from previous discussion.) Gumshoe2 (talk) 17:01, 2 March 2024 (UTC)
 * It seems to never have been discussed at WP:RSN, but it has been discussed here many times, including the following:
 * 2006/04 (several threads on that page are relevant)
 * 2011/01
 * 2011/06
 * 2011/12 (also mentioned in two other threads on that page)
 * 2014/01
 * 2016/01
 * 2019/04
 * 2019/10 (two consecutive sections mention it)
 * 2021/03
 * I would say that these threads indicate a consensus among math editors that MathWorld is a usable but mediocre source, reliable for basic factual questions, but questionable as an indicator of notability and questionable when it comes to issues of terminology. --JBL (talk) 18:57, 2 March 2024 (UTC)
 * Mathworld usually doesn't make outright false mathematical claims, but has a tendency to repeat (or invent?) dubious historical/naming claims. –jacobolus (t) 19:40, 2 March 2024 (UTC)
 * It is now open for discussion. Dedhert.Jr (talk) 13:50, 28 March 2024 (UTC)
 * I agree with the above two comments. It is not so unreliable that it must be immediately removed and replaced by a [citation needed] tag, as some sources are, but it is so frequently error-riddled that it is almost always better to use a different source. For a Good Article review, in particular, I think that better sources should be used. For Arithmetic, I replaced one MathWorld source by a much better one (a chapter in The Princeton Companion to Mathematics) and removed the other one as it was redundant and used only to source some alternative terminology, the sort of thing MathWorld is worst at. There still remains a MathWorld external link, of dubious value according to WP:ELNO #1. —David Eppstein (talk) 19:37, 2 March 2024 (UTC)
 * It seems Eric Wolfgang Weisstein created and maintains MathWorld, which is licensed by Wolfram Research. It is not self-published and from Weisstein's credentials, I don't see a good reason for categorizing this as an unreliable source. Are there any obvious points from WP:RS that suggest otherwise? Phlsph7 (talk) 13:39, 6 March 2024 (UTC)
 * It's not the worst ever source (Weisstein doesn't write outright nonsense and usually cites some other sources), but I'd put it on par with some professor's blog, course notes, math overflow answers, or similar: content written by someone with expertise in the general topic, but not vetted or carefully fact-checked. It's much less reliable as a source than e.g the articles by O'Connor and Robertson at MacTutor, and even those are often not a perfect reflection of the current scholarly consensus. Where possible it's best to compare multiple recent sources by subject-specific expects. –jacobolus (t) 15:19, 6 March 2024 (UTC)
 * Weisstein's degrees were all in astronomy. And I'm not even aware of anybody trained in mathematics who could be a reliable source for so much mathematical material. Gumshoe2 (talk) 17:44, 6 March 2024 (UTC)
 * I don't particularly care about Weisstein's credentials, but I have too often found mistakes and neologisms in MathWorld to give my full trust in it. There are of course also many mistakes in Wikipedia itself, but we don't allow Wikipedia to be used as a reference. —David Eppstein (talk) 18:29, 6 March 2024 (UTC)
 * @David Eppstein I'm curious now. Can you give me an example of some mistakes in MathWorld? Also, what about external links? Can MathWorld be used for external links as well? Dedhert.Jr (talk) 04:02, 7 March 2024 (UTC)
 * Mathworld can be used as either a source or in the 'exernal links' section, but also doesn't have to be. If a particular Mathworld page doesn't add anything that isn't in an article or other accessible sources, I'd take it out from the external links section. If another better source can be cited for any particular claim, I'd cite that one instead of Mathworld. Any claim sourced to Mathworld should be double checked in better sources anyway, as it's often a bit sloppy. At that point you can just cite the other source you found. –jacobolus (t) 05:04, 7 March 2024 (UTC)
 * @Jacobolus Ahh. I see. What I meant is not for Arithmetic, but for whole articles in general. An example is GA Malfatti circles, or GA Square pyramid in which two MathWorlds being used in external links. Should they (as well as the rest of them, if possible) be excluded in this case? How did one know that whether some kind of website or any sources will be included as external links? Dedhert.Jr (talk) 05:44, 7 March 2024 (UTC)
 * I wouldn't rush out to automatically remove Mathworld from all articles; that would be controversial and probably harmful. But if I'm otherwise looking at an article and its sources, I'll click the mathworld link and review whether it really seems helpful to readers to include, and when it doesn't I just take it out. –jacobolus (t) 05:56, 7 March 2024 (UTC)
 * One example of a mistake in MathWorld, since you're focused on polyhedra: at the time I brought Jessen's icosahedron up to GA status, the MathWorld article gave an incorrect construction based on the coordinates of a regular icosahedron. The current version fixes that.
 * Another example of what I think is a mistake, of terminology for polyhedra: Isohedron describes as a "trapezoidal dodecahedron" (bottom right corner of table) a shape that I think is properly called a "deltoidal dodecahedron" . The trapezoidal dodecahedron is something else, not an isohedron . See Special:Diff/1150447755.
 * Again, it is not hard to find similar mistakes in Wikipedia itself, but that is not the same kind of problem because we don't use Wikipedia as a reference. When we use MathWorld as a reference we need to be careful, more than with some other sources. —David Eppstein (talk) 07:34, 7 March 2024 (UTC)
 * Ahh... I see, then. Just in case, I think I prefer to find better sources for the external links. Dedhert.Jr (talk) 12:32, 7 March 2024 (UTC)
 * Just realized the article Triaugmented triangular prism, where MathWorld says that it is constructed by erecting regular tetrahedron onto each square faces of an equilateral triangular prism. . I remember you have explained this in the edit summary before you nominated it to GA. Dedhert.Jr (talk) 13:54, 28 March 2024 (UTC)
 * Yes, Special:Diff/1112387125. They still haven't fixed that, I guess? —David Eppstein (talk) 17:44, 28 March 2024 (UTC)
 * I wanted to check this against my field of expertise and found this article: https://mathworld.wolfram.com/ProofTheory.html
 * It currently starts with "Proof theory, also called metamathematics", which is just bs. The Wikipedia articles are much better.
 * Metamathematics is much more general, e.g. it includes semantics from model theory, whereas proof theory is syntactic. The latter two fields are subfields of mathematical logic, but metamathematics does not even stop there. It was mostly subsumed by mathematical logic to increase rigor, so I guess this is where the confusion originates.
 * Apart from this mistake, the author seems to know barely anything about proof theory. The description is more one of metamathematics. Formal proofs and their systems, the only things being examined in proof theory, are not even mentioned by name. 134.61.97.95 (talk) 13:13, 18 March 2024 (UTC)
 * I linked to a few other discussions in my general advice essay. MathWorld being untrustworthy for terminology has been an ongoing theme. XOR&#39;easter (talk) 17:20, 6 March 2024 (UTC)

I'd agree with assessment above that Mathworld is a mediocre but usable source and one needs to apply some common sense when using it. But imho it isn't really worse than many other (properly) published mediocre math sources out there such as various small math dictionaries and lexicons. Much of the Mathworld content is also published in book form for by CRC press btw.. For a freely accessible online resource for math history topics the MacTutor History of Mathematics Archive is usually a better alternative.--Kmhkmh (talk) 08:49, 7 March 2024 (UTC)
 * It seems to conflate distinct concepts and to make general statements that are only true in specific contexts. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:33, 7 March 2024 (UTC)
 * While in my experience MathWorld is particularly bad (on terminology issues; the actual math is usually right), even if it were better on that, it would still be a tertiary source, as is MacTutor, as is Princeton Companion (at least arguably), and as are "various small math dictionaries and lexicons". We should really strain to avoid using tertiary sources when good secondary sources are available.  (Though it's reasonable to point readers to a link inside a tertiary source in "Further reading", as an aid to readers who want to look something up quickly.) --Trovatore (talk) 22:44, 7 March 2024 (UTC)

While often very useful, I wouldn't characterize MathWorld as a WP:RS. I would presume that for "basic" stuff it would be relatively accurate, but less so the farther afield one goes. I personally wouldn't use it to cite something I didn't already know to be true. Paul August &#9742; 15:53, 18 March 2024 (UTC)

Draft:Orientational terms
I have the opposite of the usual problem. We have articles on technical concepts of orientation in math and science, but no article on the basic concept of "some things have a top and bottom and front and back". I'm trying to write something that is very everyday life/explain it like I'm five-oriented. Who's good at that? BD2412 T 02:47, 19 March 2024 (UTC)


 * Take a look at . –jacobolus (t) 07:13, 19 March 2024 (UTC)
 * The challenge, I think, is describing what it means for something to be the front or back of an object without just repeating that it is in front, and without using more complex and technical terminology to describe the relation. The anatomy article may at least provide some inspiration. BD2412  T 15:10, 19 March 2024 (UTC)
 * I had similar challenges when editing Shape. It can help to look at how the brain psychologically maps out directions; a quick google search brought this up as an example, it may be worth pursuing this vein of research further:
 * [Https://econtent.hogrefe.com/doi/abs/10.1027/1864-9335/a000065?journalCode=zsp https://econtent.hogrefe.com/doi/abs/10.1027/1864-9335/a000065?journalCode=zsp] Brirush (talk) 16:03, 19 March 2024 (UTC)
 * Excellent, thanks. This is very useful, and I can see how challenging it would be to write a topic like Shape. BD2412  T 17:42, 19 March 2024 (UTC)

I have worked the draft up some. What do you think? BD2412 T 20:11, 29 March 2024 (UTC)

Piecewise
I'm confused by 's recent move of Piecewise to Piecewise-defined function. Shouldn't we have an article about the general concept "piecewise" (when applied to some property of a function, rather than a definition), which subsumes piecewise linear function, piecewise constant function, piecewise continuous function, piecewise differentiable function, etc.? (The last 2 links redirect to Piecewise-defined function which I consider misleading since the properties are independent of the way in which a function is defined.) - Jochen Burghardt (talk) 11:11, 29 March 2024 (UTC)


 * I agree, and I have reverted back to the previous title. D.Lazard (talk) 11:46, 29 March 2024 (UTC)
 * I have rewriten the lead for making clear that "piecewise-defined function" and "piecewise property of a function" are essentially the same concept. Much further work would be useful for this article. D.Lazard (talk) 12:36, 29 March 2024 (UTC)
 * Someone should write something about the higher dimensional case, especially surface interpolation and connections with many areas (e.g., computer graphics). Tito Omburo (talk) 15:06, 29 March 2024 (UTC)
 * Higher dimensional examples are significantly more complicated/diverse; I'm not sure if the name "piecewise" is ever used for this per se, but perhaps. E.g. in the 2-dimensional case there are some such functions based on regular square or triangular grids, some based on arbitrary triangulations or division into assorted rectangles, and some based on arbitrary divisions into regions of other shapes. –jacobolus (t) 17:17, 29 March 2024 (UTC)
 * This concept is not only about functions. See piecewise linear manifold and piecewise linear curve, for instance. —David Eppstein (talk) 19:13, 29 March 2024 (UTC)
 * Generally adjectives make bad article titles (see also WP:NOUN). In mathematics specifically, they often seem to be explanation-of-jargon articles, which in my opinion we should generally not have.  I'm not convinced there's a good rationale to explain all the different mathematical uses of "piecewise" in a single article.  A blurb in glossary of mathematics might be OK, and the search term could redirect there. --Trovatore (talk) 19:50, 29 March 2024 (UTC)

Since the article, as it now stands, is only about piecewise defined functions, it should be moved to Piecewise-defined function and then a new Piecewise disambiguation page should be created, with links to Piecewise-defined function, Piecewise linear manifold, and other "piecewise" things. Michael Hardy (talk) 02:24, 30 March 2024 (UTC)


 * I disagree: The lead of the article defines and is linked to piecewise linear function, and I have just added in this article a hatnote linking to piecewise linear (disambiguation). As Piecewise linear manifold is about a very advanced matheatical concept, one can presume that interested readers will not search for "piecewise", and that the new hatnote is sufficient. D.Lazard (talk) 11:05, 30 March 2024 (UTC)
 * Piecewise linear 2-manifolds, as polyhedral surfaces, are actually a quite familiar and not very advanced concept. Similarly piecewise linear curves are commonplace and familiar. It is only in higher dimensions that they get more advanced. —David Eppstein (talk) 20:06, 30 March 2024 (UTC)
 * Moreover, all articles whose name begin with "piecewise" refer to the same meaning of this adjective. In this case, WP:DABCONCEPT discourages to create a dab page, and recommends an article on the general concept (WP:Broad-concept article). D.Lazard (talk) 11:25, 30 March 2024 (UTC)
 * The big risk with "broad-concept articles" is that we might be abstracting out a "broad concept" on our own, that sources have not isolated as a particular object of study. We are not supposed to do that.  Can you find sources that bring together all these meanings of "piecewise" in a single place?  If not, then we shouldn't either. --Trovatore (talk) 18:36, 30 March 2024 (UTC)