Wikipedia talk:WikiProject Mathematics/Archive/2022/Apr

all square roots of natural numbers, other than of perfect squares, are irrational

"all square roots of natural numbers, other than of perfect squares, are irrational" is said in the article Irrational number can we provide a source for this?Immanuelle (talk) 23:42, 4 April 2022 (UTC)

This is an almost obvious consequence of the fundamental theorem of arithmetic. Suppose that

${\sqrt {n}}={\frac {a}{b}}$

where a/b is in lowest terms. Then

$nb^{2}=a^{2}.$

By the theorem, any prime factor p of b is a factor of the left hand side and thus of the right hand side and thus of a. This contradicts the fact that the fraction is in lowest terms, unless b = 1. That is, unless n is a perfect square. OK? JRSpriggs (talk) 00:02, 5 April 2022 (UTC)

That quote is from the lead. In the body of the body we state that the proof is in Quadratic irrational number. Meters (talk) 00:03, 5 April 2022 (UTC)

It is not an unreasonable request that a claim in a Wikipedia article be given a citation. The article Quadratic irrational number gives the same proof as JRSpriggs, but also without a citation. (It also gives another proof, not relying on any properties prime factorization.) --JBL (talk) 00:47, 5 April 2022 (UTC)

Chapter 4 of Hardy and Wright's "An introduction to the theory of numbers" is a good and standard reference for that, also for some of the other claims in the article. Gumshoe2 (talk) 01:07, 5 April 2022 (UTC)

Citation added MrOllie (talk) 01:08, 5 April 2022 (UTC)

I was tempted to point to Theaetetus (dialogue), but I think the following looks like another more-helpful reference:

Ungar, Peter (April 2006), "Irrationality of square roots", Mathematics Magazine, 79 (2): 147–148, doi:10.2307/27642924, JSTOR 27642924

—David Eppstein (talk) 01:10, 5 April 2022 (UTC)

Fourier series page problems

I'm concerned that Fourier Series, which covers a pretty important topic, has some issues, especially in the lead. It seems to be written with a more pedagogical, occasionally vague and "intuition-building" goal, rather than to summarize. There are objective problems, like the fact that the way the lead refers to images violates MOS:SEEIMAGE, but fixing this would require rewriting the lead wholesale. I'm inexperienced when it comes to fixing larger issues like this and hope someone would help. Wuffuwwuf (talk) 20:05, 5 April 2022 (UTC)

Thanks for calling attention to the Fourier series page. Per WP:NOTTEXTBOOK, we can't hold the reader's hand and lead them step-by-step through the subject (and since that process would be different for every reader, it would be a mistake to try). But per WP:ONELEVELDOWN, that article should at least start with material comprehensible to readers who have seen the prerequisites but not Fourier series themselves. For example, we can reasonably guess that they know what sines and cosines are and have at least a glancing familiarity with calculus. XOR'easter (talk) 06:25, 6 April 2022 (UTC)

Residual Wolfspam

I'm not quite sure which page(s) to raise this question on, since we don't have a WikiProject Grandiose Interdisciplinary Claims, but maybe the community here would be interested. Last year, we had a major operation to clean up Wolfspam — undisclosed paid editing by Wolfram employees. Some residual effects and general hyperbole may still need addressing. In particular, I've been looking lately at our article on A New Kind of Science. The "Contents" section still strikes me as rather vague, in that "created by a fan in the days before Wikipedia had citations" kind of way. It's all but footnote-free; even granting that a book is a valid source for its "plot summary", as it were, there's no indication of where in 1200+ pages the reader should look for a given claim. Further opinions would be welcome. XOR'easter (talk) 19:26, 7 April 2022 (UTC)

This article should do no more than give the reader an idea of what the book is about and where it fits into the academic landscape. IMO, the contents section should be reduced to under 10% of the size, simply describing the topic of the book. Essentially, the following would suffice to replace that section: "In NSF, Wolfram explores, as have many before, examples of how unexpectedly complex behaviour can sometimes arise from simple computational rules. He then attempts to find parallels of this behaviour in several other systems." 172.82.47.18 (talk) 22:55, 8 April 2022 (UTC)

I'd have no objection in principle to a significant shortening. XOR'easter (talk) 08:39, 9 April 2022 (UTC)

Twists of curves

Can someone figure out if Twists of curves has the right article name? None of the sources in the article use the term "twists of curves" at all, and honestly, I find the article extremely technical and understand literally zero percent of it. Ten Pound Hammer • ^{(What did I screw up now?)} 02:57, 10 April 2022 (UTC)

The second line of reference 4 begins, The study of twists of curves is a very useful tool. I don't think there's anything wrong with the current title, strictly speaking, but it could perhaps be changed to "Twists of curves in algebraic geometry" or "Twists of algebraic curves" or something like that. I've no strong feelings on the matter. (It's outside my own specialization.) As for it being "extremely technical", well, when a subject isn't likely to be encountered before graduate school, sometimes that's just the way it goes. In practical terms, it's probably more worthwhile to work on making elliptic curve a comprehensible introduction, as that is a prerequisite and more likely to be encountered. We can't build every niche mathematical topic up from Algebra 101 in its own article. XOR'easter (talk) 03:34, 10 April 2022 (UTC)

The only thing that I see that might be wrong with the article title is potential confusion with Twist (mathematics), which discusses a quantity associated with ribbons (which are essentially curves with additional structure). However, this could probably be solved with hatnoting. Felix QW (talk) 09:47, 10 April 2022 (UTC)

Good point. XOR'easter (talk) 16:29, 10 April 2022 (UTC)

The other issue is that it is plural, for no obvious reason, when one could just as well consider one particular twist rather than the whole family of twists. One possibility would be something like twist (algebraic curve). (The disambiguator needs to be very specific to distinguish it from e.g. twists of modules.) —David Eppstein (talk) 16:30, 10 April 2022 (UTC)

I thought about that and have no problems with it myself but had some vague notion that a style guide somewhere preferred non-parenthetical disambiguations when possible. I could be completely backwards on that, however. XOR'easter (talk) 16:35, 10 April 2022 (UTC)

@XOR'easter: WP:NCDAB. — MarkH₂₁^talk 22:07, 10 April 2022 (UTC)

That was probably it; thanks. XOR'easter (talk) 22:13, 10 April 2022 (UTC)

Or twist of an algebraic curve, then? "Algebraic", to distinguish it from torsion of a curve. —David Eppstein (talk) 18:54, 10 April 2022 (UTC)

Sounds good to me. XOR'easter (talk) 19:29, 10 April 2022 (UTC)

Ditto. --JBL (talk) 20:48, 10 April 2022 (UTC)

I moved boldly Twists of curves to Twists of elliptic curves. This is clearer than Twist of an algebraic curve, since there is no indication in the article that the concept extends to other algebraic curves. D.Lazard (talk) 21:01, 10 April 2022 (UTC)

In the article, no, but it is definitely applied to other related curves; see my remarks in Wikipedia:Articles for deletion/Twists of curves. —David Eppstein (talk) 21:32, 10 April 2022 (UTC)

It did mention hyperelliptic curves briefly, and I've added some further remarks. As I said, though, this is outside my own specialization, and having never tried to explain Galois cohomology before, my brain goes into a 60-hertz hum when I try. XOR'easter (talk) 21:46, 10 April 2022 (UTC)

One part in two million? What's that mean?

In YBC 7289, I've read this sentence.

...a numerical approximation of the square root of two that is off by less than one part in two million.

I still don't get it, even though I had read the cited sources before. My bad for asking this one (if this is kinda silly), cause I don't fully understand it. I appreciate that someone answers this question. Regards, Dedhert.Jr (talk) 07:21, 13 April 2022 (UTC)

The claim is that the clay tablet has a very accurate representation of the square root of 2. That value is around 1.4. Dividing 1.4 by two million gives 7×10⁻⁷. The claim is that 7×10⁻⁷ is the error in the value on the clay tablet. Johnuniq (talk) 07:53, 13 April 2022 (UTC)

Maybe, "is off by less than 0.00005%" is easier to understand, although harder to read. - Jochen Burghardt (talk) 07:59, 13 April 2022 (UTC)

I would expect "off by" to refer to absolute error, not relative error. The value on the tablet is approximately 1.414212962962963. The actual square root of two is approximately 1.4142135623730951. Their difference (absolute error) is approximately $6\times 10^{-7}$. But that doesn't match the quoted phrase, so maybe relative error was intended. —David Eppstein (talk) 08:13, 13 April 2022 (UTC)

I see, thanks. Dedhert.Jr (talk) 08:50, 13 April 2022 (UTC)

Tagged a statement in Sphere packing as dubious

I added a {{dubious}} tag to a statement in Sphere packing#Dense packing and started a discussion at Talk:Sphere packing#FCC and HCP are not both lattices?. Input is welcome. Toshio Yamaguchi (talk) 12:09, 13 April 2022 (UTC)

about Table of congruences

For the Table of congruences, I can find references for each of the content in the article, but I couldn't find any references for the list. --SilverMatsu (talk) 08:50, 11 April 2022 (UTC)

If you mean the first section "Table of congruences characterizing special primes", there is no need for a common reference for that. Each entry refers to another wikipedia article, which is supposed to contain references as needed for that particular entry (example, Wolstenholme's theorem, etc). PatrickR2 (talk) 04:16, 12 April 2022 (UTC)

Thank you your comment. I agree with your comments as to whether a comprehensive reference is required. But I think there is a comprehensive reference somewhere, like the List of definite integrals.--SilverMatsu (talk) 16:19, 13 April 2022 (UTC)

Also, I thought the meaning of the current title of the article was like a tables of logarithms, so I misundersted if the content of the article was something like this link (External link). --SilverMatsu (talk) 03:20, 15 April 2022 (UTC)

Subbase: alternate definition

There are two potential definitions of subbase in topology. The second one seems dubiously sourced. I have started a discussion at Talk:Subbase#Alternate definition section. Would appreciate any input. PatrickR2 (talk) 05:34, 16 April 2022 (UTC)

Are these edits vandalism?

[1] Doug Weller talk 08:05, 16 April 2022 (UTC)

Not really vandalism, if no error has been introduced by these changes (which I have not checked). Certainly WP:disruptive editing, as these changes of variable names would need a careful check by other editors for being sure that no error has been introduced. I have undone these changes, as MOS:VAR applies here. D.Lazard (talk) 08:43, 16 April 2022 (UTC)

Thanks. All of the first editor's edits seem dubious, and he's never edited an article on mathematics again. Doug Weller talk 09:09, 16 April 2022 (UTC)

Delete Complex conjugate vector space?

Complex conjugate vector space makes no sense. A complex conjugate vector space, as defined there, is just a complex vector space. I suggest deleting it. 172.82.47.212 (talk) 19:57, 28 March 2022 (UTC)

Or redirect it to Antilinear map. 172.82.47.212 (talk) 20:17, 28 March 2022 (UTC)

"A complex conjugate vector space" is not a thing; "the complex conjugate of a given complex vector space" is a thing. --JBL (talk) 21:07, 28 March 2022 (UTC)

Could just rename the article Complex conjugate of a vector space and be done with it? The content is important enough to warrant a mention somewhere (although it could be merged into Complex conjugate or Complex vector space). Tazerenix (talk) 10:42, 29 March 2022 (UTC)

Field automorphisms induce vector space automorphisms functorially so maybe merge some of the article content into there? --Fourier-Deligne Transgirl (talk) 08:55, 29 March 2022 (UTC)

Any thoughts on a subtle renaming to Complex conjugate (vector spaces) or similar, with a hatnote from Complex conjugate? Felix QW (talk) 09:18, 29 March 2022 (UTC)

Complex conjugate (vector spaces) must be avoided, as most readers would understand that it is about conjugation in vector spaces, which is defined in complex vector spaces with a canonical basis (matrices, polynomials, ...) and complexified real vector spaces. So, I agree with Tazerenix, including merge suggestion. D.Lazard (talk) 12:44, 29 March 2022 (UTC)

Complex vector space just redirects to vector space, and Complex conjugate is about the basic operation underlying an Antilinear map. Therefore, I prefer to merge into the latter, as suggested by 172.82.47.212. Since the article name "Complex conjugate vector space" is questionable (as discussed above), I suggest not to turn it into a redirect. - Jochen Burghardt (talk) 15:38, 29 March 2022 (UTC)

I actually think it is a mistake that there is no complex vector space article. We do have the complex vector bundle article after all, which discusses the conjugate bundle (vector bundle version of a complex conjugate vector space.) If there is the complex vector space article, stuff like conjugates or anti-linearity can be discussed in natural ways. —- Taku (talk) 19:03, 29 March 2022 (UTC)

Taku, indeed. However, you will concede that the notion of a conjugate complex bundle is indistinguishable from a complex bundle: it is only through the structure that connects them (such as duality) that one can tell that there is any antilinearity involved. I agree with Jochen: delete after merge. 172.82.47.212 (talk) 17:06, 31 March 2022 (UTC)

I have now boldly moved the page as suggested by Tazerenix above, without any prejudice to a separate merger. Felix QW (talk) 10:15, 5 April 2022 (UTC)

I agree to move the page, also I think the inner product space is one of the option for merging.--SilverMatsu (talk) 17:32, 16 April 2022 (UTC)

Examples of differential equations

I don't really know what to make of this page. It seems to be a guided walk-through of how to solve different classes of differential equations rather than a coverage of examples in the sense of the Examples of Markov chains or the Examples of groups. Everything encyclopedic here seems to overlap with the articles for the individual types of differential equation or the Linear differential equation article. I thought I'd check here to see what others think. Options I could see would include blanking and redirecting to Differential equations#Examples or starting the nucleus of an actual page of examples in the spirit of the other pages mentioned above by only retaining the barebones of the oscillating motion example. Felix QW (talk) 10:06, 5 April 2022 (UTC)

A note to anyone reading the above that the page has now been nominated for deletion. Felix QW (talk) 13:39, 5 April 2022 (UTC)

The eventual consensus was to redirect the article to Differential equation#Examples. XOR'easter (talk) 18:03, 16 April 2022 (UTC)

Uncited source of a sentence in Pythagoras

In the sentences as follow:

Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors

didn't have any cited source. And I did the same thing in Indonesian Wikipedia. But someone already reverted my edit and told me that the cited source has already been in a sentence in one of the sections, that is

Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton.

And I'm not very sure that the sentence in an introduction can be the same as that sentence in Numerology. Maybe someone can explain this thing, cause I'm afraid that I misunderstand it. Regards, Dedhert.Jr (talk) 11:41, 20 April 2022 (UTC)

Requested move at Talk:Fixed point (mathematics)#Requested move 8 April 2022

There is a requested move discussion at Talk:Fixed point (mathematics)#Requested move 8 April 2022 that may be of interest to members of this WikiProject. Favonian (talk) 08:34, 23 April 2022 (UTC)

Fellows of the AMS

Looking at some of the current drafts on mathematicians, I have been wondering whether the fellowship of the AMS satisifes Criterion #3 of NPROF. The AMS is certainly a "major scholarly society", but I was wondering whether its own admission that the goals of the fellowship program include "lift[ing] the morale of the profession by providing an honor more accessible than those currently available" means that it is not a "highly selective honour" in the sense of the notes to NPROF#3. Does anyone have any thoughts on this? Felix QW (talk) 08:42, 22 April 2022 (UTC)

If I remember right, they have no membership restriction other than paying their dues. I would not call that selective. JRSpriggs (talk) 10:14, 22 April 2022 (UTC)

AMS Membership is not selective at all. AMS _Fellowship_, on the other hand, is fairly highly selective. I believe it meets WP:NPROF C3. The acid test is that most AMS fellows appear to meet other WP:NPROF notability criteria. Comment that being more accessible than the fancier and fewer-in-number AMS awards does not mean that it is not sufficiently selective for Wikipedia notability. Russ Woodroofe (talk) 10:25, 22 April 2022 (UTC)

I agree with Russ Woodroofe here. XOR'easter (talk) 14:03, 22 April 2022 (UTC)

I think the AMS fellowships are more tied to scholarly achievement and less tied to seniority than some other societies. That's a good thing for whether it counts towards C3; it means that someone named a fellow can be more relied on to have done something important and not just been around a long time. —David Eppstein (talk) 15:57, 22 April 2022 (UTC)

I think it satisfies the criteria, although on the lower margin; of all the standard honors I can think of for professional mathematicians, it is the least selective. Also, if it is to be used to satisfy the criteria, I believe the same principle should apply to analogous honors awarded by other countries' mathematical societies (or similar organizations). Gumshoe2 (talk) 20:29, 22 April 2022 (UTC)

It is not an issue of national parity, but of how selective that individual society is in offering their analogous honors. If they are as selective, then it should probably count for the same reason. If they are not selective in offering this honor, then they should not, regardless of the prestige or national standing of the society. There are several other national-society fellowships (for instance Canadian Mathematical Society [2]) that I think do and should count. I am not entirely convinced that FIMA for the UK is selective enough, though (their criteria [3] speak of seven years of experience as a mathematics researcher, and say nothing about limits on number of fellows as a fraction of total membership, so I think that may be too low a bar). —David Eppstein (talk) 22:28, 22 April 2022 (UTC)

I agree. In part I suppose that what I implicitly had in mind is my belief that US (and British) mathematicians are somewhat disproportionately represented here, even after taking into account that this is the English wikipedia. So I should have instead just said that it would be good to find comparably prestigious honors for mathematicians based in China, Japan, South America, and others. As for those you linked, I would judge the CMS Fellows as a very prestigious list (moreso than AMS), but I actually can't find any publicly available members list for FIMA! Gumshoe2 (talk) 22:59, 22 April 2022 (UTC)

So WP:NPROF specifically gives as an example Fellow of the Institute of Electrical and Electronics Engineers, which is limited to 1/1000 of members per year. According to American Mathematical Society, the AMS has 30,000 members; there were 45 new fellows last year. So that's less selective, but basically comparable. --JBL (talk) 22:29, 22 April 2022 (UTC)

Thank you very much for your thoughts! Felix QW (talk) 08:34, 25 April 2022 (UTC)

Help with Kahn–Kalai conjecture

I've had a go at writing something on the Kahn–Kalai conjecture, but have run out of mathematical knowledge in the relevant field. Hopefully what I have written is not gibberish, but I know when I'm out of my depth. Can anybody more knowledgeable help? — The Anome (talk) 09:14, 27 April 2022 (UTC)

Need to fix Heptadecagon?

This article is very messy due to some animations having a massive scale, so I can't even possibly feel comfortable while reading. Dedhert.Jr (talk) 10:55, 24 April 2022 (UTC)

I agree that the diagrams and animations there are too complex to be helpful towards understanding. Somebody put a lot of work into them, but probably they should be removed. Ebony Jackson (talk) 03:25, 26 April 2022 (UTC)

Maybe the material could be rearranged into a gallery of some sort? XOR'easter (talk) 15:31, 27 April 2022 (UTC)

I have fixed the page in my sandbox, User:Dedhert.Jr/1st sandbox. Also, I added the properties of heptadecagon. Maybe someone can help to fix the words here, and please inform me (by ping) that I'm making mistakes. Regards, Dedhert.Jr (talk) 03:59, 28 April 2022 (UTC)

User script to detect unreliable sources

Main page: User:Headbomb/unreliable

I have (with the help of others) made a small user script to detect and highlight various links to unreliable sources and predatory journals. Some of you may already be familiar with it, given it is currently the 39th most imported script on Wikipedia. The idea is that it takes something like

• John Smith "Article of things" Deprecated.com. Accessed 2020-02-14. (John Smith "[https://www.deprecated.com/article Article of things]" ''Deprecated.com''. Accessed 2020-02-14.)

and turns it into something like

• John Smith "Article of things" Deprecated.com. Accessed 2020-02-14.

It will work on a variety of links, including those from {{cite web}}, {{cite journal}} and {{doi}}.

The script is mostly based on WP:RSPSOURCES, WP:NPPSG and WP:CITEWATCH and a good dose of common sense. I'm always expanding coverage and tweaking the script's logic, so general feedback and suggestions to expand coverage to other unreliable sources are always welcomed.

Do note that this is not a script to be mindlessly used, and several caveats apply. Details and instructions are available at User:Headbomb/unreliable. Questions, comments and requests can be made at User talk:Headbomb/unreliable.

- Headbomb {t · c · p · b}

This is a one time notice and can't be unsubscribed from. Delivered by: MediaWiki message delivery (talk) 16:01, 29 April 2022 (UTC)