# Wikipedia talk:WikiProject Mathematics

 This is a discussion page for WikiProject Mathematics This page is devoted to discussions of issues relating to mathematics articles on Wikipedia. Related discussion pages include: /Conventions /Graphics /PlanetMath Exchange /Proofs /Typography /Wikipedia 1.0 Mathematics Portal MoS Mathematics Reference desk (mathematics) (Please ask general questions of interest here). Please add new topics at the bottom of the page and sign your posts.

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## Article and talk page title mismatch for Dual-complex numbers

Currently, the page Dual-complex numbers redirects to Dual-complex number, but Talk:Dual-complex number redirects to Talk:Dual-complex numbers, not vice versa. Either the article and talk page should both be plural, or else, they should both be singular. JBW only moved the talk page back to the plural title, but not the article. GeoffreyT2000 (talk) 21:57, 4 October 2019 (UTC)

Done, moved the singular article title to the plural article title to match the talk page move by JBW. — MarkH21 (talk) 22:06, 4 October 2019 (UTC)
@MarkH21, JBW, and GeoffreyT2000:That seems backwards: compare complex numbers, real numbers, quaternions, etc. --JBL (talk) 22:45, 6 October 2019 (UTC)
You’re completely right. I made the move just to match the talk page without actually looking at the discussion or reason for the talk page move itself. — MarkH21 (talk) 23:32, 6 October 2019 (UTC)

@GeoffreyT2000, Joel B. Lewis, and MarkH21: It seems to me more natural to have "complex numbers", "real numbers", etc, but since, as JBL has pointed out, we have the singular forms, I have moved Dual-complex numbers back to Dual-complex number for consistency. And of course moving just the talk page was a mistake; thank you GeoffreyT2000 for pointing it out. JBW (talk) Formerly known as JamesBWatson 12:41, 14 October 2019 (UTC)

## Map projection

I’ve exhausted my patience for this dispute for the day and so I’m seeking a third opinion here. —Jasper Deng (talk) 09:37, 6 October 2019 (UTC)

Yikes. I have commented there. XOR'easter (talk) 21:30, 6 October 2019 (UTC)
it would have been helpful to include a link to the discussion; for everyone else, it is here. I have also commented. --JBL (talk) 22:43, 6 October 2019 (UTC)
And in all that (still ongoing!) discussion, nobody has raised the vital question of what your favorite map projection says about you. XOR'easter (talk) 01:54, 7 October 2019 (UTC)

## MacCullagh ellipsoid and Galois axis

The article MacCullagh ellipsoid survived a deletion debate last year (at the time, I said that where there might be an argument for a merge-and-redirect, that can be decided at a later date). It has since been moved to MacCullagh ellipsoid and Galois axis, which seems to give undue prominence to the "Galois axis" part, given that it appears to be the pet idea of Semjon Adlaj, himself of uncertain wiki-notability, and not an established term. I may take a crack at sorting all this out myself, but perhaps someone would like to beat me to it. XOR'easter (talk) 23:33, 6 October 2019 (UTC)

Moved back, seems silly when "Galois axis" is defined on "MacCullagh ellipsoids" and is of uncertain notability. — MarkH21 (talk) 21:35, 7 October 2019 (UTC)
The aformentioned article on Adlaj is now at AfD. — MarkH21 (talk) 21:47, 7 October 2019 (UTC)
And now there's an article Galois axis? XOR'easter (talk) 21:29, 10 October 2019 (UTC)

The IP/SPA edit-warring has continued on Galois axis and MacCullagh ellipsoid, so I have taken Galois axis to AfD to end the chance for future edit-warring. The activity has also spread to Tennis racket theorem, j-invariant, and WP:ANI#Please restore the stable version of MacCullagh ellipsoid and Galois axis. Attention appreciated. — MarkH21 (talk) 15:06, 11 October 2019 (UTC)

AfD closed due to some effective edit conflicts with sock disruption. Also forgot to mention the same disruption is also at Pendulum (mathematics).
— Preceding unsigned comment added by MarkH21 (talkcontribs) 15:34, 11 October 2019 (UTC)

The German Wikipedia has a better article on the topic de:Trägheitsellipsoid which seems to be related to inertial ellipsoid. It apparently the geometric location of all angular momenta corresponding to the same rotational energy. --Salix alba (talk): 19:46, 11 October 2019 (UTC)

Yes, in fact that corresponds better to the article Poinsot's ellipsoid, which mentions the inertia ellipsoid and whose existence partially prompted the original AfD. — MarkH21 (talk) 19:55, 11 October 2019 (UTC)

## Three prodded calculus articles

Linearity of integration, Constant factor rule in integration, and Sum rule in integration have all been prodded. Someone who knows more than I about calculus pedagogy might want to evaluate whether they should be saved or let go. —David Eppstein (talk) 04:10, 7 October 2019 (UTC)

At first glance, these would belong on Wikiversity or Wikibooks. They read like course notes I might prepare for a first-year calculus course, not encyclopedia articles. Doubtless many texts cover these properties, but do they need separate articles from those on differentiation and integration? I don't think so.--Jasper Deng (talk) 05:40, 7 October 2019 (UTC)
• These are unsourced pedagogical essays and the content is covered already at Integral. These titles should redirect there. Reyk YO! 09:01, 7 October 2019 (UTC)
• (edit conflict) Maybe not useful for me to add anything more, but I completely agree with the redirect. In particular, to the section Integral#Properties. — MarkH21 (talk) 09:07, 7 October 2019 (UTC)
• Actually I’ll just convert them to redirects now. — MarkH21 (talk) 09:10, 7 October 2019 (UTC)
• Redirecting is a good fix. Thanks. XOR'easter (talk) 17:44, 8 October 2019 (UTC)

## Statement in the lead of the article on infinity

In the article Infinity, there's a statement in the lead: "For example, Wiles's proof of Fermat's Last Theorem uses the existence of very large infinite sets." I don't really know anything about this stuff, and this struck me as rather surprising, so I went to look for more. However, nothing in the article talks about this, and nothing at the article on the proof seems to say anything about this either. I also couldn't find anything after a cursory search. So I really have no idea if this is a valid statement or not; I've tagged it with a `{{cn}}` for now, but if anyone happens to know more about this, please feel free to either set me right, or even excise the statement with extreme prejudice. Thanks, –Deacon Vorbis (carbon • videos) 02:54, 8 October 2019 (UTC)

It’s because Wiles’ proof (and much of the cohomology used in modern number theory) uses Grothendieck universes. Within ZFC, their existence is equivalent to the existence of certain large cardinals. Here is a suitable reference. You (or someone else) can judge whether this is appropriate in the lead there though - I don’t really know much about this kind of stuff. — MarkH21 (talk) 03:18, 8 October 2019 (UTC)
Just my impression but that sentence does look out of place, because in mathematics (or at least in algebraic geometry), one doesn’t worry too much about the set-theoretic issues. Some results might collapse without the existence of a strongly inaccessible cardinal. But they might not (with some care, it is sometimes possible to avoid the use of universe but I think people don’t bother). Determining that is an (interesting or uninteresting) original research and cannot be done in Wikipedia. — Taku (talk) 23:09, 8 October 2019 (UTC)
I added some words there ("in fact", maybe not "in principle"... according to that source); feel free to revert if you dislike it. Boris Tsirelson (talk) 20:30, 11 October 2019 (UTC)
Maybe I shouldn't argue again after writing "feel free to revert if you dislike it", but let me do. XOR'easter's text "For example, Wiles's proof of Fermat's Last Theorem uses the existence of very large infinite sets, though it may happen that another proof that avoids such sets will be found" is deleted by MarkH21 with edit summary "this whole bit feels unnecessary, the sentence is about Wiles’ proof - not all proofs - so there’s no implication about any other proof", logically flawless and nevertheless controversial. A reader (human, not robot) seeing that a famous proof uses (or "is written with the implicit reliance on" according to Takuya Murata) an exotic assumption, probably concludes that this assumption is, or at least is widely believed to be, necessary. Why? First, math textbooks often encourage a student to check that each assumption (of a theorem) is necessary; thus a student may believe that doing otherwise is unprofessional. Second, otherwise, why mention this fact in the lead to "infinity" article? Third, otherwise experts would find (or at least, actively seek; or, at the very least, debate possible existence) of a "better" proof. And really, it is debated (see the source [4]: used "in fact", not "in principle"), which is not even hinted at in our article. Thus is why I feel that our article is a bit misleading (or not neutral). Boris Tsirelson (talk) 17:43, 17 October 2019 (UTC)
I'm neutral on whether the whole sentence should be kept in the lead or not. (I can see Grothendieck universe might be an interesting thing to mention in the lead.) I changed "use" because the meaning of it is very unclear; one can argue that the use of "universe" is a stylistic choice but not a logical necessity (and I don't think we know the answer). I agree the wording I introduced was somehow strange but I couldn't figure out the better one (would be happy to see the others give a shot too). -- Taku (talk) 23:55, 17 October 2019 (UTC)
My feeling is that the mention of large cardinals in the use of a famous theorem is mildly interesting and engaging to any reader, but not essential to the lead. However, further elaboration on the possibility of resolving the reliance on Grothendieck universes (still unknown according to the cited source) seems unnecessary for a brief engaging digression. Since Wiles's proof relies on the existence of Grothendieck universes, and it's unknown whether that reliance may be removed by some other way, it seems completely honest to just say that Wiles's proof relies on it. So the current brief mention seems fine and mildly interesting to me, but I disagree with including a further digression on how it's unknown whether the reliance can be removed. — MarkH21 (talk) 08:43, 18 October 2019 (UTC)
I'd prefer nothing at all to something a bit misleading. Boris Tsirelson (talk) 10:12, 18 October 2019 (UTC)
I introduced this sentence by [this edit]. The purpose of it was to fix a common misconception that infinity would be a philosophical concept in mathematics. IMO, this is important to show that, in mathematics, infinity is no more a philosophical concept, but is, presently, a purely mathematical concept that is mathematically studied, and is widely used across. Looking at many Wikipedia article, such as this one, that are close to the interface between philosophy and mathematics, it appears that my above assertions, which are evidence for most mathematicians, are not widely known outside mathematics community. Thus my edit was a tentative for clarify this. The whole article would need to be clarified from this point of view, but, at least, the lead require to be clear, as many readers look only on it.
IMO, the example of Wiles's proof of Fermat's Last Theorem is essential in the lead, because it the only example that I know that can be used to show to non mathematicians that the manipulation of infinity as a mathematical concept is useful even for problems that seem unrelated. For making clear that this is the purpose of this example, I have completed the sentence by "for solving a long standing problem, which is stated in terms of elementary arithmetic". D.Lazard (talk) 11:28, 18 October 2019 (UTC)
Nice; but it is unfair to implicitly overstate it by exploiting the implicit assumption of some (or many?) readers that "uses" means here "uses in principle" rather than "uses in fact" (these phrases appear in the source [4] because McLarty recognizes this potential for confusion). Till now, no one addresses my "first", "second" and "third" arguments (above). Boris Tsirelson (talk) 11:45, 18 October 2019 (UTC)

## Multiplicative digital root

This looks like OR, spread across 64 different anonymous edits. Opinions welcome. XOR'easter (talk) 17:38, 8 October 2019 (UTC)

Is "not everything in Mathworld is a real thing that should have a Wikipedia article, just delete it" the kind of opinion you are looking for?
More seriously (maybe): I would throw around a bunch of cn tags and start a discussion directly with the IP -- they've been editing from the same address in the same manner for several weeks on a bunch of probably-not-really-notable base-dependent number sequences, perhaps they are amenable to learning about our policies. (The editing reminds me of, but seems more competent than, that of User:Xayahrainie43‎.) --JBL (talk) 00:04, 9 October 2019 (UTC)
Pretty sure they're not the same person as X despite the overlapping interests. —David Eppstein (talk) 04:35, 9 October 2019 (UTC)

## Notability of integer sequences

What makes an integer sequence notable? Is an entry in OEIS or MathWorld enough? Specifically this is a question for the following articles:

but I suspect this to be the case for many other such articles on integer sequences on Wikipedia. They do not have references other than OEIS or MathWorld, if any at all, and are either stubs lacking content other than the information on OEIS or MathWorld, or articles filled with what seems to be original research not found in OEIS or MathWorld. Prova-nome (talk) 04:08, 9 October 2019 (UTC)

We have a guideline on this; see Wikipedia:Notability (numbers). I don't think OEIS or MathWorld by itself is enough, but they can contribute to notability together with academic journal articles and books that discuss these sequences. It's important to follow WP:BEFORE by looking for sources rather than assuming that a badly-written article is also non-notable. Sometimes it also works to search for the OEIS sequence numbers in other sources. The odious and evil numbers are clearly notable; e.g. "odious numbers" has 60 hits in Google scholar, many of which look sufficiently in-depth for both sequences. Factorions have fewer but see JSTOR 3620842 and JSTOR 3620841; that may be enough. I'm not sure about the rest, though. —David Eppstein (talk) 04:18, 9 October 2019 (UTC)
If the sequence has the keyword "dumb" in OEIS, it probably shouldn't be included. And appearing in MathWorld may mean that the idea or the name is solely that of Weisstein or some other MathWorld contributor. I'm not sure about pernicious or polydivisible, although I'm sure pernicious needs to have some trivia removed. — Arthur Rubin (talk) 09:51, 9 October 2019 (UTC)
Agree with David, and Arthur, neither OEIS, nor especially MathWorld, is enough. Paul August 17:09, 9 October 2019 (UTC)
I agree in particular that OEIS alone is not enough. That site has many thousands of integer sequences, and I don't think we should have articles on the majority of them. Many of the articles we do have, for instance polydivisible number may be notable but are also full of original research- much of it banal. Reyk YO! 18:24, 9 October 2019 (UTC)

## Typo in an article (edit request?)

Very unfamiliar with how wikipedia works but this seems to be where to submit this. In this article, under the section "Extensions of the standard dictionary numbers", for the value of 10^51 sexdecillion, it instead says sedecillion. This also does not align with the "Standard dictionary numbers" section of the article with the proper spelling. Pnunya (talk) 16:21, 12 October 2019 (UTC)

Thank you for your comment. It looks like the "Extensions of the standard dictionary numbers" table is based on a different system, in which the prefix se- takes an x before octo but not before deci. XOR'easter (talk) 16:27, 12 October 2019 (UTC)

## De Bruijn index and De Bruijn notation

The current version of the former article links to the latter, with a note: "This notation has little to do with De Bruijn indices, but the name "De Bruijn notation" is often (erroneously) used to stand for it." I do not see how this can be correct - both are ways of representing lambda terms uniquely in terms of alpha-equality, and therefor identical. I'm considering removing this note. Airbornemihir (talk) 11:23, 14 October 2019 (UTC)

Done. Airbornemihir (talk) 11:30, 14 October 2019 (UTC)
Nevertheless, the article began with "Not to be confused with De Bruijn notation. In mathematical logic, the de Bruijn index is a notation..." This was highly confusing. Thus, I have modified the hatnote, and removed the use of "notaation" in the first sentence. In any case, it is wrong to say that De Bruijn index and De Bruijn notation are identical, as the bind variables are named in one case and not in the other. D.Lazard (talk) 13:15, 14 October 2019 (UTC)

## Draft:Multiplicity (statistical mechanics)

Dear mathematicians: Here's a draft article that is within the interest of this WikiProject. Perhaps someone who with knowledge of this field can take a look at it.—Anne Delong (talk) 11:45, 15 October 2019 (UTC)

My first impression is that it is written like an essay and would need cleaning up before it could be suitable as an article. The content appears redundant with diversity index, surprisal, entropy and other existing articles. XOR'easter (talk) 17:25, 15 October 2019 (UTC)

## “Quotient” of functional integrals

Normally, if we write one expression on top of a fraction line and another on the bottom, we evaluate both before dividing. This would yield an indeterminate form when both the numerator and denominator are functional integrals with infinite value. Yet the article on functional integrals states “Most functional integrals are actually infinite, but then the limit of the quotient of two related functional integrals can still be finite”. Huh?

The topic overall needs love. It’s way too hand-way right now.—Jasper Deng (talk) 04:31, 23 October 2019 (UTC)

Apparently, that phrase is like "${\displaystyle f'(x)={\tfrac {dy}{dx}}}$" that hints at ${\displaystyle \lim {\tfrac {\Delta y}{\Delta x}}}$ rather than ${\displaystyle {\tfrac {\lim \Delta y}{\lim \Delta x}}}$. Boris Tsirelson (talk) 05:06, 23 October 2019 (UTC)
And by the way: I just added EoM article to "See also" there. But I was not able to use the Template:SpringerEOM, since its "http:" is obsolete and not working; now must be "https:". Oops, no; "id=" is needed, in addition to "title=". Boris Tsirelson (talk) 06:23, 23 October 2019 (UTC)