Wikipedia talk:WikiProject Mathematics/Archive/2025/Sep

There is a book by Helena Rasiowa and Roman Sikorski under the title as above (a link to its review in the Journal of Symbolic Logic). It has no entry in Wikipedia. I wonder if it has enough prominence to have one. Any opinions? Alx-pl (talk) 11:24, 4 September 2025 (UTC)

Maybe include it in Metamathematics § Further reading if it is significant enough? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:34, 4 September 2025 (UTC)

Google scholar lists it has having been cited more than 1000 times, so that contributes to its notability. Interestingly, Google scholar lists a single author only: H. Rasiowa. —Quantling (talk | contribs) 15:14, 4 September 2025 (UTC)

There are three more reviews at , Zbl 0122.24311, and MR 0163850. To me, that's enough to make it notable as a book (under WP:NBOOK #1 and WP:GNG) despite the routine nature of having a review in Zbl and MR. —David Eppstein (talk) 20:04, 4 September 2025 (UTC)

Thanks a lot! I will write a draft of an article about the book. Alx-pl (talk) 08:35, 5 September 2025 (UTC)

I just had a crazy idea. Wikipedia articles should have accessible ledes, but on the other hand the lede is supposed to be a faithful summary of the article. These seem to be requirements that are naturally in tension. An "abstract" of an article seems like it could supply more details on the contents, assuming they are highly technical such as many areas of mathematics. This would also give a nice buffer zone between editors that are: pedants (wanting to make sure that the mathematical content is exactly right) - we know who we are - and folks that want to make sure the lede can be read by a well-educated person hitting the "Random Link" button.

Just a wild thought. Anyway, Tito Omburo (talk) 20:41, 5 September 2025 (UTC)

Sorry, your propose is unclear to me. My guess: make the first subsection of a highly technical article be (eg) "Technical abstract", removing the pressure on the intro to be precise and jargony? Johnjbarton (talk) 20:50, 5 September 2025 (UTC)

Basically yes. The abstract summarizes the most important points of the article, while the lede is an accessible overview. These are incompatible in many cases. Tito Omburo (talk) 21:13, 5 September 2025 (UTC)

I have used the opposite idea in some articles: make the first section of the article "Background" and try there to give summaries of other articles critical to understand the content of the article. Johnjbarton (talk) 01:45, 6 September 2025 (UTC)

That's fine, but at odds with guidance that the lede should be readable by an educated person arriving at the page via random article. Tito Omburo (talk) 21:13, 6 September 2025 (UTC)

? How so. Having background information need have no effect on the lede. Johnjbarton (talk) 21:21, 6 September 2025 (UTC)

The lede should be readable by someone who is not going to read the "background" section. Tito Omburo (talk) 22:09, 6 September 2025 (UTC)

I take back what I said. Having background information improves the intro in theory, because summarizing the background in the intro automatically brings the level down. Johnjbarton (talk) 02:30, 7 September 2025 (UTC)

I don't understand how that's supposed to work, but per MOS:Lead section § Content, the lead is supposed to be an "accessible overview", not a "faithful summary". –jacobolus (t) 20:53, 5 September 2025 (UTC)

The first senstence of your link is: "The lead section should briefly summarize the most important points covered in an article, in such a way that it can stand on its own as a concise version of the article." The first section of WP:LEDE is "In Wikipedia, the lead section is an introduction to an article and a summary of its most important contents." This guidance is often incompatible with the requirements of making the lede accessible on a mathematics article. Tito Omburo (talk) 21:10, 5 September 2025 (UTC)

I don't think the goals of giving an "overview" vs. "summary" and making it "accessible" vs. mentioning "the most important points" are incompatible.

There's always tension and some questions of editorial judgment about how comprehensive or how technical a summary the lead is supposed to be, what aspects of a topic should be the focus, which part of the content is "most important", what the broadest intended audience of technical material should be, etc., but with care and discussion I think we can usually come up with something that does a pretty good job of meeting most readers' needs. If pedants are pushing to make the lead so rigorous that non-experts can't make any sense of it anymore, push back and work towards consensus.

Splitting the lead into two alternate versions and aiming one of them at a professional audience seems technically difficult, and I can't imagine quite what you have in mind. I'm also not sure how helpful it would be, even for expert readers. –jacobolus (t) 21:55, 5 September 2025 (UTC)

I think this discussion would benefit from an example or two. Can you think of a mathematics (or physics, chemistry, etc.) article that spans a whole range of intended audiences and where the lead section is seriously inaccessible? Stepwise Continuous Dysfunction (talk) 23:32, 5 September 2025 (UTC)

Eigenvalues and eigenvectors I think the first sentence in unintelligible because it relates the topic to other mathematics which may not be part of the background of a reader. In some sense that cannot be avoided, but the first question a non-mathematician has is "why are these important"? not how are these related to linear transforms or other mathematical concepts. We only get a hint by the third paragraph, "The eigenvectors and eigenvalues of a linear transformation serve to characterize it..." Johnjbarton (talk) 00:05, 6 September 2025 (UTC)

Tito Omburo wrote what I thought was a helpful extra bit of context a couple of years ago special:diff/1185535612, but it has since been removed. There had been a group effort to work on this at Wikipedia talk:Make technical articles understandable#Concrete example: Eigenvectors and eigenvalues. I think the current state is somewhat worse, but it's not too easy a problem, and there's a lot of disagreement between various editors who come to the page. –jacobolus (t) 02:26, 6 September 2025 (UTC)

If you mean an abstract is basically a summary that is commonly found in academic journals, then NO! Background is fine to me, which explains how the topic occurred. Dedhert.Jr (talk) 10:43, 7 September 2025 (UTC)

Exterior algebra, Galois cohomology, Bogomolny equation, Korteweg-de Vries hierarchy, algebraic K-theory, number field, Dehn twist, geometric integration theory, C*-algebra, von Neumann algebra, weak operator topology, Hilbert's nullstellensatz. Are you serious in wanting examples? *Every* mathematics article is an example! But a very specific example is this diff. Tito Omburo (talk) 20:31, 6 September 2025 (UTC)

None of those span "a whole range of intended audiences". With the exception of algebraic number field, I hadn't seen any of them until graduate school. If a high-school student can't follow the entire intro of von Neumann algebra, well, I suppose that might be a problem in principle, but I doubt that trying to finagle it is the best use of our limited time. What I'm looking for is a topic that is studied in some fashion across many levels of education, and where our article about that topic immediately dives into technicalities that only a PhD candidate could understand. You know, "A prime number is a monoid in the category of Eratosthenean multifunctors...", or something like that. Or maybe not that bad, but worse than the introduction of prime number currently is. Stepwise Continuous Dysfunction (talk) 02:49, 7 September 2025 (UTC)

The lead and early sections of Exterior algebra should definitely be made accessible to early undergrads if possible. Likewise for Algebraic number field. Others of these can probably be safely pitched at grad students, though it would be nice if related central topics (linked from the leads of those) like Group representation, Topology, Hilbert space, Functional analysis, Ring theory, Cohomology, Partial differential equation, etc. were made as accessible as possible to an undergraduate audience. –jacobolus (t) 03:21, 7 September 2025 (UTC)

Thanks. That is a good point about the "central topics". Of those, I think Hilbert space and Partial differential equation would be particularly important to get right, since they have cross-disciplinary use. The intro of Topology seems to start easy, then have a harder paragraph, then an easier one. Stepwise Continuous Dysfunction (talk) 16:45, 8 September 2025 (UTC)

These were just some examples, but someone to whom the Bogomolny equation (for example) might be remotely of interest, would be utterly bewildered by our lede, and likewise for the rest of these examples. To say nothing of the "Random article" reader, who is well-educated, perhaps even in mathematics, but not a specialist in Yang-Mills theory. Should someone with a PhD in combinatorics from Harvard University be befuddled by the first paragraph of von Neumann algebra? Even smart people need more context than what we typically provide. Tito Omburo (talk) 22:03, 7 September 2025 (UTC)

It is probably true that "even smart people need more context" than what our articles usually give them. On the other hand, the people who are studying for or have already earned doctorates in mathematics are probably also the ones most inclined to click around and acquire some context from other pages. ("What was the 'weak operator topology'? Oh, right...") I will see if I can devise a gentler opening paragraph for von Neumann algebra, which right now starts with a definition that is "clear" in a mathematician's sense: there is no ambiguity, but also no motivation.

The Bogomolny equations article is a stub with only two paragraphs. It's not really comprehensible to those unfamiliar with gauge theory, but it's a different kind of problem than a longer article with multiple sections and a true intro. Stepwise Continuous Dysfunction (talk) 17:08, 8 September 2025 (UTC)

I guess most of the people involved were tagged, but just in case — from Reflections on Wikipedia Policies:

"First, I am in no way (absolutely not) connected with any of the individuals involved in the discussions I am about to mention."

Malparti (talk) 16:38, 4 September 2025 (UTC)

LOL, bummed that I didn't merit a ping! --JBL (talk) 00:32, 5 September 2025 (UTC)

Guess we will have to wait for the Parabolic subgroup of a Reflection on Wikipedia Policies group writeup.^[sarcasm] Gramix13 (talk) 02:05, 5 September 2025 (UTC)

Those who were involved with the recent Vincenzo Guerriero spamming (@David Eppstein, Malparti, Johnjbarton, and William M. Connolley:) may be interested in this: --JBL (talk) 00:08, 8 September 2025 (UTC)

Well, that's interesting. Is there any off-wiki connection between the spammed authors, Vincenzo Guerriero and Paul Gagniuc? Maybe this really is a publicist run amok, as speculated in the reflection thread. —David Eppstein (talk) 00:31, 8 September 2025 (UTC)

What a twist!

So far, I am not convinced by the "publicist run amok" theory, at least in the case of Gagniuc: as far as I know, they are more subtle than whoever was spamming Gagniuc (e.g, they usually have a ton of rather old accounts which they use do to minor copy-editing for a while before they use them, etc). Also, judging from the length of the various replies, I had the impression that there was something personal.

Here are other conjectures:

• For me, a more plausible explanation would be that whoever had been spamming Guerriero has realized that the references in question have been removed, which has made them mad. However, that person is not entirely stupid and they also realized that re-adding the references would be pointless, and that complaining about their removal would be suspicious and only serve to put their bad deeds in the spotlight.

But, still: they are mad at the situation, so can't just "forget about it". So they spend some time reading the archives of the math project, perhaps looking at contributions by people involved in the discussion. Eventually, they read about Gagniuc and decide to complain about that on the Village Pump — hoping that maybe this will trigger some sort of backlash/criticism against the people who have criticized Gagniuc's book. If this works, (1) they will have some sort of revenge and (2) they might even be able to advocate for reintroducing other references removed en masse by the same people.

As an argument in favor of this theory: look how careful whoever-was-spamming-Guerriero was. Using different accounts, sometimes doing a tiny bit of copy-editing with those accounts before, doing it over several days, etc. It's not quite on par with what I've seen professional publicist do — if the person responsible for the spam was indeed a hired publicist and is reading this: sorry, you suck at your job! — but clearly the person responsible for this is being very careful.

(and another argument: the timing, of course) Malparti (talk) 08:14, 8 September 2025 (UTC)

• Another possibility: those are two independent people, but they use the same VPN provider — maybe advertised by all Youtubers ;). But I guess that most of those IPs are blocked (for instance, I can't edit Wikipedia when I'm on the train because of this), and that anyway checkusers know a lot more about this then I do and recognize those addresses.

I have other conjectures, but those are the two that seem the most plausible to me at the moment. :)

Malparti (talk) 07:53, 8 September 2025 (UTC)

As far as I can tell this post is unnecessary. What is the purpose here? If anything is going to trigger backlash it would seem to me to be additional posts about this topic. So is backlash the goal?

Moreover when I look at the accusations in Wikipedia:Sockpuppet investigations/MegGutman that lead to the block of User:Asocial network all I see is a complaint about the point of view expressed in 9 civil posts. Long-winded, civil posts like the one above. Johnjbarton (talk) 15:33, 8 September 2025 (UTC)

The block seems to be for using the same IP as another user involved in a different sockpuppet investigation, not for the point of view expressed in their long-winded posts. –jacobolus (t) 16:33, 8 September 2025 (UTC)

@Johnjbarton: The goal is to try to understand what is going on with those two clusters of sockpuppets that have been refspamming: most of us assumed that Asocial network belonged to MegGutman; but it turned out to belong to Aftershock81. Some of us find that puzzling, and would like to understand what is happening — perhaps to make sure we don't make quick assumptions next time, perhaps for the sake of curiosity. David Eppstein asked if there was any off-wiki connection between Gagniuc and Guerriero or if maybe a third-party publicist was involved. I provided a (conjectural) alternative explanation. If you are not interested, please feel free to ignore the long-winded discussion.

What triggered the checkuser inspection is neither the length nor the incivility of the posts by Asocial network, but the fact that they were defending a refspammer and proven sockpuppet (and — surprise — it turned out they were themselves a sockpuppet). So I don't understand your comparison. Malparti (talk) 20:13, 8 September 2025 (UTC)

I'm a bit surprised that this is a red link. If someone could write it WP:JWG, either as a standalone article or a section of Wolfram Research / Wolfram Mathematica , that would be great. Headbomb {t · c · p · b} 09:57, 10 September 2025 (UTC)

I've been learning about matrix minors & cofactors recently and trying to develop an intuition for them, and I found some things that have helped a lot, so I wanted to put them into the article for the next person. Unfortunately, despite searching for a good bit, I can't find a good textbook (a little too advanced for some textbooks) or paper (much too simple) to source. I'm sure it's out there, but have no idea how to find it. Here's what I wrote:

"As the determinant has a simple geometric interpretation (the amount by which the matrix scales oriented area), the (i,j) cofactor of a matrix can also be seen to have a relatively simple geometric interpretation. The cofactor matrix of cofactors of a matrix M is the matrix that transforms the (n-1)-vectors (in 3d, bivectors) of a n-dimensional space the same way the matrix transforms vectors. Bivectors can be represented as linear sums of bivectors in the x0 = 0 plane, the x1 = 0 plane, and the x2 = 0 plane; each components of bivector is its oriented area when projected into that plane. The (i,j) element of the cofactor matrix, or the (i,j) cofactor, gives the area in the xj = 0 plane after applying M to a unit xi = 0 bivector, similar to how the determinant gives the volume after applying M to a unit cube. The (i,j) cofactor is equal (up to sign) to the determinant of M with the ith row and jth column removed because the determinant of that submatrix gives the area of xi = 0 (ith row removed) projection of the output of M applied to a unit cube with the xj element removed (jth column removed)."

I would cite this blog for the statements on (n-1)-vector transformation, that being where I found it, but it's obviously not reliable according to the standards, and the author isn't published anywhere I can find. Does anyone know a good textbook to source for this? Also, how is my writing? I'm trying to give other people who just learned what a cofactor is a bit more of a handle on what it means geometrically. Mrfoogles (talk) 18:15, 10 September 2025 (UTC)

Ever heard of name Ivanov? I haven't found the name of this mathematician in Scholar whenever an Ivanov polyhedron reminds me . Dedhert.Jr (talk) 10:39, 7 September 2025 (UTC)

It is a very common Russian name. From the references of that link, you appear to be referring to B. A. Ivanov, of the paper "Polyhedra with faces that are composed of regular polygons", Ukrain. Geom. Sb. 10: 20–34 (1971). I don't know anything more than that data. —David Eppstein (talk) 19:15, 7 September 2025 (UTC)

If you want to search in Russian:

Иванов Б.А. Многогранники с гранями, сложенными из правильных многоугольников, Укр. геометр. сб. Харьков. Изд-во: ХГУ, 1971. No. 10. C. 20-34.

Here's a list of works that cite it in Russian and in English. –jacobolus (t) 19:26, 7 September 2025 (UTC)

A scan of the journal issue can be found here, and Zbl 0231.52004 has a review in English. –jacobolus (t) 02:54, 8 September 2025 (UTC)

One more reply: I actually read that review, and it seems reasonable that we could make at least stub articles about Zalgaller polyhedron and Ivanov polyhedron, or redirect those terms and explicitly mention them in some other article. To quote:

Aside from prisms and anti-prisms, there is a finite set ⁠${\displaystyle S}$⁠ of convex polyhedra, each of whose faces is either a regular polygon or can be divided into such by diagonals. Call diagonals of this last sort conditional edges. A polyhedron from ⁠${\displaystyle S}$⁠ is simple if it cannot be cut into two members of ⁠${\displaystyle S}$⁠ by a plane through its edges or conditional edges. Write ⁠${\displaystyle S'}$⁠ for the subset of simple members of ⁠${\displaystyle S}$⁠. Zalgaller proved that there are exactly 28 members of ⁠${\displaystyle S'}$⁠ which have no conditional edges. [Ivanov] proves that there are exactly 5 members of ⁠${\displaystyle S'}$⁠ which do have conditional edges.

–jacobolus (t) 17:18, 8 September 2025 (UTC)

@Jacobolus. Actually, it might be more reasonable to redirect to Johnson solid since Zalgaller was the one who proved the list of 92 Johnson solids. But if it's a different polyhedron, then otherwise. Dedhert.Jr (talk) 01:34, 11 September 2025 (UTC)

Oh wait nevermind I didn't read the latter. But maybe a better idea is to redirect to Composite polyhedron. Dedhert.Jr (talk) 01:37, 11 September 2025 (UTC)

Okay. I have added three new polyhedra, redirected to what I expected. Dedhert.Jr (talk) 02:26, 11 September 2025 (UTC)

not sure how long this has been broken, maybe the parser behavior changed? currently Hyperpolarized carbon-13 MRI has 2 errors, red bold text Failed to parse (syntax error). with the current parser the error seems to start at special:diff/819925699, previous revision has no error. --Jeremyb (talk) 04:48, 11 September 2025 (UTC)

Hi @Jeremyb-phone,

The problem came from the use of the use of \atop in the <chem> tag. It's a known bug — see https://phabricator.wikimedia.org/T402102 — but there is a quick fix; and someone as already fixed it in the page you linked.

Cheers, Malparti (talk) 09:37, 11 September 2025 (UTC)

Hello, I noticed a possible asymmetry in the integral formula listed in the “Bernoulli polynomials” article:

$${\displaystyle \int _{0}^{1}B_{n}(t)B_{m}(t)\,dt=(-1)^{n-1}{\frac {m!n!}{(m+n)!}}B_{m+n}}$$

Since the integrand is symmetric in n and m, shouldn't the sign factor also reflect that symmetry? Perhaps something like ⁠${\displaystyle (-1)^{n+m}}$⁠ or a symmetric alternative?

I'd appreciate any thoughts or references. Thanks! IgnorabimusX (talk) 12:01, 11 September 2025 (UTC)

There is a reference. The point is that the bernoulli number on the RHS is zero if n and m have opposite parity, so the apparent asymmetry is not actual. Tito Omburo (talk) 12:23, 11 September 2025 (UTC)

I see now — that was my misunderstanding. Thank you for the clarification! IgnorabimusX (talk) 12:40, 11 September 2025 (UTC)

Someone has raised a question about sources in Numerical methods in fluid mechanics that perhaps someone here can address—see Wikipedia:Reliable sources/Noticeboard#Issue with Numerical methods in fluid mechanics. 173.79.19.248 (talk) 10:36, 17 September 2025 (UTC)

Alright. Who wants to review in Wikipedia:Featured article candidates/Cube/archive1 that has already nominated? Dedhert.Jr (talk) 06:17, 23 September 2025 (UTC)

Surely a worthy candidate for at least one citation or two, so that the article doesn't sit in the "Unreferenced" queue...? Thanks in advance, WikiProject Mathematics. Cielquiparle (talk) 04:49, 10 September 2025 (UTC)

Probably formulae in some mathematical topics may support it. Dedhert.Jr (talk) 03:09, 12 September 2025 (UTC)

I added a few. I don't have books at hand for the really basic stuff, and I'm not sure what actually is best to cite in such cases. Stepwise Continuous Dysfunction (talk) 23:29, 12 September 2025 (UTC)

My go-to for really basic stuff is late 19th century / early 20th century mathematics textbooks on archive.org, because (1) they're reliable enough for this, (2) they state the obvious, unlike more advanced mathematics sources, (3) they're free online, and (4) modern textbooks on similar material (for primary or early secondary school students) have a different style where everything is a worksheet and nothing is stated explicitly. —David Eppstein (talk) 06:53, 21 September 2025 (UTC)

That's a good idea. Thanks. Stepwise Continuous Dysfunction (talk) 04:18, 24 September 2025 (UTC)

Also: The internet archive has a (somewhat annoying but serviceable) full text search of the content of all scanned materials. If IA doesn't turn up something, you can also try the full text search at Google Books, at HathiTrust (which mostly searches Google scans), or at Biodiversity Heritage Library. –jacobolus (t) 07:20, 24 September 2025 (UTC)

I have started a discussion at Draft talk:Peter Renz, please take a look.--Toploftical (talk) 12:28, 24 September 2025 (UTC)

Courtesy link: Draft talk:Peter Renz – AllCatsAreGrey ^(talk) 12:52, 24 September 2025 (UTC)

I have been puttering around with a draft broad concept article on "congruence" (as it applies across many fields) for eleven years now, and I am determined to be done with it this month. Any suggestions on finishing it would be welcome! BD2412 T 17:22, 19 September 2025 (UTC)

I would drop the symbol from the lead sentence, since a variety of symbols are used for different concepts of "congruence".

I assume this is supposed to be pitched at a very broad audience. In the mathematical section in particular, I'm not sure how comprehensible it's going to be for non-specialists. It might help to add examples and unpack each concept a bit further. –jacobolus (t) 17:28, 19 September 2025 (UTC)

I am not very familiar with the notion of concept articles — is this article meant to coexist with the disambiguation page, or to replace it?

A few minor remarks on the lead:

• I agree with jacobolus about the symbol (especially since I have personally never used the symbol ${\displaystyle \cong }$);
• The sentence "Congruence is a concept in various fields describing a state of coming together, the state of agreement" reads a bit weird to me.
• I think it is more relevant (and more correct) to say that the word comes from congruentia, which means "agreement". If you read French (or can get it translated), the entry of the French Wiktionary is great: https://fr.wiktionary.org/wiki/congruence — however, if the English word comes directly from Latin, it could be that not all is applicable (e.g, the part about the word regaining popularity in the 19th century because of mathematics). At any rate: if you want to give the verb as the etymon, I believe that the standard practice (?) is to give the English translation in the infinitive (even though the Latin verb is in the first-person singular).

Malparti (talk) 19:36, 19 September 2025 (UTC)

Comment. I am generally skeptical of the value of "concept articles". They are presumptively original research by synthesis. This is a case-in-point: the symbol ${\displaystyle \cong }$ means... basically whatever the author decrees. I am not convinced that an article is appropriate, without a clear unifying secondary source discussing, for example, the role of the symbol in psychology (!), giving due weight to its almost universal use in mathematics. Tito Omburo (talk) 22:34, 19 September 2025 (UTC)

I think such an article can be more useful than a disambiguation page (like Congruence) which doesn't give any explanation or context, and implies that the various linked topics are entirely unrelated. –jacobolus (t) 00:11, 20 September 2025 (UTC)

A paradigmatic broad concept article would be Damage. Of course, we all know what "damage" is, but there are lots of different kinds of damage in lots of different fields (structural damage, economic damage, crop damage, etc.), and there are also things that are clearly not kinds of "damage" that are named that, like films and songs titled Damage, and even comic book villains. The purpose of a disambiguation page is to guide readers when there are unrelated meanings of a term (e.g., damage to an object as compared to a film titled Damage, or Amazon, the company as compared to Amazon, the rainforest). Where the terms are not really ambiguous but are merely different kinds of the same thing, disambiguation is not the ideal process. In the case of "Congruence", there is a common meaning used in different disciplines, and commonly related in the most basic of secondary sources, the dictionary. With respect to the current disambiguation page, since there are no movies or albums or songs or comic book characters by this name (so far as I can tell), that would be overridden in this case. BD2412 T 00:17, 20 September 2025 (UTC)

The first broad concept article was particle, which sort of synthesizes the general concept of particles, e.g. a small object with several properties. Headbomb {t · c · p · b} 01:12, 20 September 2025 (UTC)

I agree with you in a broad sense, but I'm struggling to understand how this article in particular can exist without violating WP:NOTDICT. It seems like the only criteria for being included is having the term "congruence" in the title, and identical concepts would be completely left out. For example, it's not entirely clear how this is different from Equivalence, apart from name.

I agree it's better than a disambiguation page, but it seems at odds with certain policies. Maybe a section on "Definition and related terms" could be added to justify it as an encyclopedic topic? If that's not possible, I don't think this could survive an AFD review. – Farkle Griffen (talk) 18:23, 20 September 2025 (UTC)

Replying to jacobolus, I think the dab congruence is more encyclopedic than a broad concept article. There doesn't need to be something linking disparate uses. A personal essay, sure, but not an encyclopedia article. Tito Omburo (talk) 18:59, 20 September 2025 (UTC)

What on the disambiguation page describes anything other than a phenomenon that meets the dictionary definition of "congruence"? WP:NOTDICT is a prohibition against making a dictionary entry, not against using the dictionary as a source or having an article on a term defined in the dictionary. BD2412 T 20:23, 20 September 2025 (UTC)

My basic prior is that concept articles are original research. I don't think dicdef is useful here, fwiw. More to the point, if reliable sources do not support a general concept, then neither should Wikipedia. Tito Omburo (talk) 20:45, 20 September 2025 (UTC)

The page I see currently at the draft, with sections on "Mathematics", "Mineralogy and chemistry", and "Psychology", looks far more like a disambiguation page than a broad concept article, and I think that's the direction it should head.

Within mathematics, I think the broad concept under which most of these can already be grouped is equivalence relation / equivalence class / partition of a set. We already have three articles on this cluster of topics; why do we need a fourth? —David Eppstein (talk) 20:46, 20 September 2025 (UTC)

"not against using the dictionary as a source or having an article on a term defined in the dictionary."

No one has said anything like that. WP:NOTDICT also explains how concepts should be grouped. Same-concept different-name should be one article. Same-name different-concept articles should be separate. As written, it seems like the only criteria for being mentioned in the article is just "Does the title contain the word congruence?". It's not clear why items in the dab pages Equivalence and Similarity aren't mentioned, even though they fit the definition there. As it stands, it seems more about a word than a concept. – Farkle Griffen (talk) 20:57, 20 September 2025 (UTC)

@Farkle Griffen: Well let's turn that around and ask why we have separate pages for Congruence (geometry) and Similarity (geometry), if the words mean the same thing. None of the titles containing congruence merely reflect similarity or equivalence; they reflect a specifically abstract relationship. That is what our article will be about. BD2412 T 22:20, 20 September 2025 (UTC)

"Congruence" and "similarity" in geometry are technical terms. They exist solely in and of themselves. You could change the names to "Redness" and "Blueness" and it would make no difference to mathematicians.

"they reflect a specifically abstract relationship"

What abstract relationship? In what way is Mood congruence related to Congruence (geometry) and not Similarity (geometry)?

I am not against a broad-concept article on congruence. My objection is that the definition is vague, and the criteria of what meets that definition is unencyclopedic. If such a concept does exist, instead of arguing here, why not spend your time improving the definition? – Farkle Griffen (talk) 23:17, 20 September 2025 (UTC)

That is exactly why I came here seeking input. BD2412 T 23:49, 20 September 2025 (UTC)

I did offer input. You then proceeded to argue with it. – Farkle Griffen (talk) 00:51, 21 September 2025 (UTC)

My apologies for not conveying that I agree with improving discussion of the definition and related terms. There appear to be some Google Scholar articles that examine just these distinctions. BD2412 T 01:00, 21 September 2025 (UTC)

The basic problem with this draft is that it is original research, par excellence. Try stating things in attributive voice, rather than Wikipedia's. The whole thing falls apart. Tito Omburo (talk) 20:40, 21 September 2025 (UTC)

Hopefully, that can be fixed. Improving the draft is the point of the discussion. BD2412 T 20:48, 21 September 2025 (UTC)

I mean, that's my view. Attribute things to sources. Don't do synthesis. I don't think there is an article here. Tito Omburo (talk) 21:39, 21 September 2025 (UTC)

I agree. Apart from probably violating some guidelines, it is not helpful. Anybody who cares about congruence in a particular field will find it in their field, and basically nobody will make use of this "concept page". PatrickR2 (talk) 04:37, 23 September 2025 (UTC)

I would concede at this point that it is turning out to be far more difficult to find sources discussing this as a broad concept than I would have imagined. BD2412 T 01:01, 24 September 2025 (UTC)

"congruence" and "modulo" are used in similar situations, as in "A and B are congruent by [some criterion]" is sometimes describable as "A and B are equal modulo [some criterion]". And there's a general article on the latter: Modulo (mathematics). Perhaps something done in that article is useful in this discussion. (Or not. I may end up owing apologies for dumping this brainstorm on you instead of pursuing this further myself.) —Quantling (talk | contribs) 14:03, 24 September 2025 (UTC)

I was surprised to see that while there is a First uncountable ordinal article, First infinite ordinal is a redirect to Ordinal number. Surely ${\displaystyle \omega }$ is notable enough to warrant an article of its own, a redirect from Smallest infinite ordinal and a link from Omega (disambiguation) § Mathematics. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 15:43, 24 September 2025 (UTC)

Since ${\displaystyle \omega }$ is just the set of natural numbers ⁠${\displaystyle \mathbb {N} }$⁠, I think we already have it covered. JRSpriggs (talk) 17:46, 24 September 2025 (UTC)

Conventionally, sure, but there's a reasonable semantic difference between them. I don't know if there's enough information on ${\displaystyle \omega }$ alone to warrant an article, but I think an argument can be made. – Farkle Griffen (talk) 19:45, 24 September 2025 (UTC)

The article Base flow (random dynamical systems) has been proposed for deletion because of the following concern:

Tagged as Confusing for 16 years. Unreferenced for 15 years. No other language has a reliably sourced article from which to translate. WP:TNT.

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Bearian (talk) 09:50, 23 September 2025 (UTC)

It was deprodded by Preimage with a suggestion of a redirect target ( Random dynamical system#Formal definition ); I agree with the suggestion of blanking and redirecting, so I have done so. 173.79.19.248 (talk) 11:13, 25 September 2025 (UTC)

I found an article called associativity isomorphism, which seems to fall under the definition of "associativity" in the monoidal category. Does pentagon identity redirect to associativity isomorphism, or does it redirect to Mac Lane coherence theorem since pentagon identity is a notion related to the coherence condition? Also, regarding "identities (unit isomorphisms)", does it meet WP:N for creating a standalone article? For example, nLab had a standalone article on pentagon identity, but not on triangle identity. (note: The nLab has an article called "triangle identities", but it's about adjunctions.) Is there a difference in the notability between "associativity" and "identities (unit isomorphisms)"? --SilverMatsu (talk) 04:04, 9 September 2025 (UTC)

Also, although the article only discusses the monoidal category, the phrase associativity isomorphism also appears in the braided monoidal category and the symmetric monoidal category.--SilverMatsu (talk) 07:01, 21 September 2025 (UTC)

I nominated this article to the AfD.--SilverMatsu (talk) 01:33, 26 September 2025 (UTC)

Hi all! Newbie editor here.

I've stumbled across a category called "Category:Non-Newtonian calculus". From what I've been able to gather, there used to be an article about it, but it was deleted for being non-notable, mostly just referencing the content of a single book and being largely authored by one of the book's authors. So, now, there's not really any information on what "Non-Newtonian calculus" refers to as a category anymore.

Inferring that it's meant to include articles relating to the Non-Newtonian calculus, as was described in the deleted article, then I assume the category should be deleted too? I assume that the importance threshold for categories is stricter than that for articles; otherwise, there would be more categories than articles, and that hardly seems productive.

I also noticed one of the pages in the category, Geometric Brownian Motion, has an external link to the website about the "Non-Newtonian calculus" book, link added by the same author of the book. The connection between Non-Newtonian calculus and any of the article's current content seems tenuous at best, but maybe I didn't read the article well enough.

Does any of this merit further attention? MEN KISSING (talk) 02:37, 28 September 2025 (UTC)

I think the category should be deleted. Tito Omburo (talk) 11:41, 28 September 2025 (UTC)

That seems reasonable. Maybe the articles in the category themselves, too, should be reviewed for unwarranted mentions/links of "Non-Newtonian calculus"? I don't want to assume that all references to Non-Newtonian calculus have been added to Wikipedia in bad faith, but it seems possible to me given the AfD discussions and what I could find on the Non-Newtonian calculus website. It's been a few years, maybe there is some merit to the concept now! But maybe there isn't.

The Geometric Brownian Motion page in particular stands out to me. I don't see what about it makes Non-Newtonian calculus a relevant external link, aside from that:

1: It models a process with tiny increments that are multiplicative rather than additive. From what I understand, though, Non-Newtonian calculus is not a widely accepted term for this kind of thing.

2: It references Itô calculus, which is only Non-Newtonian calculus insofar as it is a thing called a calculus which was not invented by Newton. MEN KISSING (talk) 00:02, 29 September 2025 (UTC)

I should clarify: this is just meaningless cruft that somehow persisted after the deletion of the main article. I think it could be uncontroversially be removed by basically any editor who wants to remove it from all pages that link to it. You could do this yourself, for example. (I don't know if anything else is necessary to delete a category, but suspect that empty categories are probably deleted eventually automatically. But removing its visibility from articles that link to it is something anyone can do. I second that decision.) Tito Omburo (talk) 00:11, 29 September 2025 (UTC)

Ah- meaningless cruft, yes. That's the term for what I felt it probably is, but I didn't want to jump right to assuming it's that. Benefit of the doubt and all that.

I could remove the mentions myself, sure. I'll have to come back with a clearer mind before I take a closer look at the mentions across Wikipedia, though. Going through a mental slog currently. MEN KISSING (talk) 00:56, 29 September 2025 (UTC)

I felt like just removing all the articles with the category wouldn't be the proper way to do it, so I didn't do that. I've gone ahead and made a CfD entry for it instead: Wikipedia:Categories_for_discussion/Log/2025_September_29#Category:Non-Newtonian_calculus

It does look like empty categories eventually get deleted, but not automatically. And they tell you not to empty articles just to get categories deleted: Wikipedia:Categories_for_discussion#Ready_for_deletion MEN KISSING (talk) 00:09, 30 September 2025 (UTC)

IIRC at some point some category people got mildly mad at me for emptying out a category that I thought shouldn't have been created in the first place, because there's some kind of process they prefer people follow. YMMV. –jacobolus (t) 00:16, 30 September 2025 (UTC)

It does also seem like a lot of work to get a category deleted, removing the category from every article individually. There's 21 articles in that category. 21 is a big number. The CfD process seemed easy enough? I hope I didn't do it in a catastrophically wrong manner? MEN KISSING (talk) 00:21, 30 September 2025 (UTC)