Talk:Fermat's Last Theorem/Archive 8

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Archive 8

Requested move 2 August 2021

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Not Moved (see what I did there?) Consensus is that retaining the caps in the title/name is appropriate at least in this case. (non-admin closure) В²C ☎ 03:03, 11 August 2021 (UTC)

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Fermat's Last Theorem → Fermat's last theorem – Per MOSCAPS' guidance on theories Primergrey (talk) 02:57, 2 August 2021 (UTC)

This is a contested technical request (permalink). McMatter ^(talk)/_(contrib) 15:49, 2 August 2021 (UTC)

• Oppose. The name of the article only makes sense as a proper noun phrase: it is "Fermat's Last Theorem" because that is the name people call it. It is not "Fermat's last theorem" because it is not actually the last theorem proved or stated by Fermat. —David Eppstein (talk) 16:32, 2 August 2021 (UTC)
  • Incidentally, a "theory" (the subject of MOS:DOCTCAPS) is a very different thing from a "theorem" (the subject of this article). —David Eppstein (talk) 17:34, 2 August 2021 (UTC)
  • Whether it was actually his last theorem is sort of moot, as WP:CRITERIA does not include a criterion like "correctness" or "accuracy". Hence why we have article titles like egg cream and Hundred Years' War. Colin M (talk) 00:47, 4 August 2021 (UTC)
    • Does WP:CRITERIA not include any leeway for common sense and logic, or is it a death cult that we must obey even when it makes no sense? If it is not capitalized then it is not a name and we should feel free to reorder it in any ordering that is still grammatical. If it's ok to call it "Fermat's last theorem" then it's also ok to call it "the final theorem of Fermat" or "the last of Fermat's many theorems" or any of those other things that, as non-name phrases, mean the same thing. But those other things are incorrect, so "Fermat's last theorem" is also incorrect. If it's a name, it should be capitalized as a name. If you're going to point to WP:CRITERIA, then I'm going to point right back at MOS:PROPERNAME. Is "FERMAT'S LAST THEOREM" (however capitalized or not) a descriptive phrase, or a proper name? If it's intended as a descriptive phrase, then it's incorrect, and the guidance on naming that you point to does not apply because it's not a name. Therefore, it should not be "Fermat's last theorem", but rather some other descriptive phrase that is actually correct. If it's intended as a name, then MOS:PROPERNAME applies. Therefore, it should not be "Fermat's last theorem", but rather "Fermat's Last Theorem", because that's how we capitalize names. In neither case is "Fermat's last theorem" a valid title for the article. —David Eppstein (talk) 06:48, 4 August 2021 (UTC)
      • If it is not capitalized then it is not a name and we should feel free to reorder it in any ordering that is still grammatical. If it's ok to call it "Fermat's last theorem" then it's also ok to call it "the final theorem of Fermat" or "the last of Fermat's many theorems" or any of those other things that, as non-name phrases, mean the same thing. I don't think this is a sound line of reasoning. Is it okay to call Pascal's wager "Pascal's bet"? Colin M (talk) 16:09, 5 August 2021 (UTC)
    • WP:CRITERIA (it's very first sentence) says:

"Article titles are based on how reliable English-language sources refer to the article's subject".

In this case that means "Fermat's Last Theorem". In any case, WP content policies are not consistent (surprise, surprise), and when they conflict, the core content policies of WP:NPOV, WP:NOR and WP:V take precedence. In this case, these policies again point to "Fermat's Last Theorem". Paul August ☎ 09:00, 4 August 2021 (UTC)

• Oppose I concur with David Eppstein; this is one place where Wikipedia's zeal to decapitalize like it's 1793 just doesn't work. XOR'easter (talk) 17:14, 2 August 2021 (UTC)
• Oppose. Whatever logic (or MOS for that matter) may say, capitalization should be determined by the usage in reliable sources. In this case this tends to be "Fermat's Last Theorem" (e.g. see this Google Scholar search). Paul August ☎ 17:32, 2 August 2021 (UTC)
• Oppose, what they said. Randy Kryn (talk) 17:38, 2 August 2021 (UTC)
• Oppose for reasons given above (and by me further above), unless frequenter uncapitalized usage in reliable sources can be demonstrated. W. P. Uzer (talk) 20:46, 2 August 2021 (UTC)
  • NB: This is not the standard demanded by MOS:CAPS, which says only words and phrases that are consistently capitalized in a substantial majority of independent, reliable sources are capitalized in Wikipedia (emphasis in original). Colin M (talk) 00:25, 4 August 2021 (UTC)
• Oppose Virtually all sources use the capitalised versions, those that don't, like MacTutor, are inconsistent and don't accurately report capitalisation of sources. --Salix alba (talk): 02:57, 3 August 2021 (UTC)
• Oppose the common name uses the current capitalization. User:力 (power~enwiki, π, ν) 03:01, 3 August 2021 (UTC)
• Oppose per User:David Eppstein. It's a theorem named "Fermat's Last Theorem". It's not literally the last theorem Fermat wrote. JIP | Talk 15:39, 3 August 2021 (UTC)
• Oppose. The relevant section of MOSCAPS is MOS:SCIMATH, which explicitly allows for "established exceptions". Based on the capitalization in the preponderance of sources, it appears that FLT is one of those exceptions. --Ahecht (TALK
  PAGE) 18:34, 3 August 2021 (UTC)
• Support The relevant policy here is MOS:CAPS: only words and phrases that are consistently capitalized in a substantial majority of independent, reliable sources are capitalized in Wikipedia. Ngrams shows that in recent years, the capitalized form leads over the uncapped one by about a 3:2 ratio. I don't think 60% is a "substantial" majority. Add to that the fact that ngrams is indexing not just running text but also titles, chapter headings and the like, and so the capitalized form will be artificially boosted. I browsed the first page of google scholar results since 2017. It's tedious work (which is why I stopped after the first page), but I counted 5 that used uppercase in running text and 3 that used lowercase. Colin M (talk) 00:42, 4 August 2021 (UTC)

See my reply to Colin M above. Paul August ☎ 09:02, 4 August 2021 (UTC)

I'm not sure how what you said in that comment disagrees with what I wrote. You quoted the following line from WP:CRITERIA: Article titles are based on how reliable English-language sources refer to the article's subject. How the patterns of usage in RS determine the appropriate name is elucidated across our many more specific naming guidelines and policies. The relevant one here is WP:NCCAPS, which says to capitalize the title how it would be capitalized in running text. When to capitalize terms in running text is explained in MOS:CAPS. The rule given in MOS:CAPS suggests we should use lowercase in this case, based on the available evidence. Colin M (talk) 16:17, 5 August 2021 (UTC)

• Oppose: FLT is generally capitalized as a proper noun in scientific literature, especially within number theory. Yes, this is not universal and there is a minority that (often inconsistently) does not capitalize the two latter terms, but it is a small enough minority for this to be considered an exception for MOS:SCIMATH.
  As an aside, I have even seen a few texts where this capitalization is used (post priori) to differentiate the acronym of Fermat's Last Theorem (FLT) from Fermat's little theorem (Flt or FℓT), although that is more of a play on the "little". — MarkH₂₁^talk 01:38, 5 August 2021 (UTC)

• Support: Both MOS:SCIMATH and MOS:CAPS apply and neither would lead to capitalisation. Per the latter: only words and phrases that are consistently capitalized in a substantial majority of independent, reliable sources are capitalized in Wikipedia. From the n-gram evidence cited above, usage does not reach the threshold of being "consistently capitalized". I note that n-grams tend to over-report capitalisation because it does not distinguish headings and captions (where titles case is frequently used) from running text. Also, per the assessment of Google scholar above, there is also mixed usage that does not meet the threshold of being "consistently capitalized". I also observed that the theorem is frequently abbreviated to FMT FLT. This then begs the question of whether a source is capping it because it is would be capped in normal usage or because the capping uses an editorial style that caps to indicate the derivation of the initalism. I would also refer to WP:SSF. This is literally Fermat's last theorem to be proven.[1] Hence, the name of the theorem is descriptive and onomastically, proper nouns are not (generally) descriptive. Although some editorial styles do capitalise non-proper-noun noun phrases for distinction, WP does not follow this style. Regards, Cinderella157 (talk) 01:15, 6 August 2021 (UTC)

Just because a name could be considered to be descriptive does not mean it is (e.g. Alexander the Great). Paul August ☎ 10:58, 6 August 2021 (UTC)

Doesn't it? Epithet: a byname, or a descriptive term (word or phrase), accompanying or occurring in place of a name and having entered common usage. ... It can also be a descriptive title: for example, Pallas Athena, Alfred the Great ... It is a common misnomer that all things (words or phrases) that might be capitalised are proper nouns. Furthermore, the definition of a proper noun is grammatical and independent of orthography - ie, a word or phrase is a proper noun, not because it is capitalised but because it has certain properties. Fermat's last theorem is literally his last theorem to be proved.[2] Regards, Cinderella157 (talk) 23:15, 6 August 2021 (UTC)

It was called "Fermat's Last Theorem" long, long before it was proved. Strictly speaking, it should have been called a conjecture; the name "Fermat's Last Theorem" was always a convention, used even when it was not descriptive. XOR'easter (talk) 00:21, 10 August 2021 (UTC)

XOR'easter, All other statements that he claimed to be able to prove true had been proven ...[3] Until Andrew Wiles, it was his last unproven theorem, though as noted, it should have been called a conjecture. Enen before Wiles, it was the last to be [yet] proved. Cinderella157 (talk) 01:35, 10 August 2021 (UTC)

• Oppose, use capitalisation as in major relevant sources (use what is in the text, not in the titles or bibliographies, which may follow different conventions). Using Lowercase is Not a Virtue in Itself. —Kusma (talk) 12:59, 9 August 2021 (UTC)

• Oppose. This is properly marked by capitalisation. If another theorem were to be discovered (for all I know it may have been) that Fermat worked on and perhaps even proved after his work on this one, then that other theorem would be Fermat's last theorem but this one will probably forever remain Fermat's Last Theorem. Andrewa (talk) 09:53, 10 August 2021 (UTC)

Andrewa - Ummm, this is attributed Fermat (1607-1665) in 1637. There are a number of other things (including teories|theorems) for which Fermat is known (see List of things named after Pierre de Fermat). Fermat's right triangle theorem was published in 1670 and is the only complete proof given by Fermat. The argument being made is inconsistent with events. You may wish to consider discussion of the entomology of the term herein and the WP guidance (MOS:CAPS and MOS:SCIMATH) that are the criteria for determining if this is "properly marked by capitalisation". Regards, Cinderella157 (talk) 10:25, 10 August 2021 (UTC)

Ummm, that just seems to bear out what I was saying. This may even be a case in which the other policies are not in the best interests of Wikipedia and its users, if so we just need to invoke wp:IAR (also a policy) and do the right thing regardless. Andrewa (talk) 10:39, 10 August 2021 (UTC)

Andrewa, so, the arguement is, because it is the "last" it should be capitalised and this is also the rationale and sound reasoning to WP:IAR? Cinderella157 (talk) 11:11, 10 August 2021 (UTC)

No. It should be capitalised because this is the way in which English marks a name that refers to a particular instance of the description, an instance known by this capitalised name, rather than a mere description. Andrewa (talk) 13:15, 10 August 2021 (UTC)

• Support since the majority of sources treat this as generic/descriptive, without caps, not as a proper name. Most of the capped uses are in books about the theorem, in the typical specialist style of capping what's important to you, and in citations to works on the topic, using title case. The logic of claiming it must be a proper name, when most sources don't cap it, doesn't square with our guidelines as discussed extensively above. Dicklyon (talk) 15:41, 10 August 2021 (UTC)

• Support—you can oppose all you want, but this would be a flagrant violation of MOSCAPS. We can do better still than Colin M's Ngram, linked above, that shows a substantial minority of downcased occurrences. But when we exclude the occurrence of "Fermat's Last Theorum" in titles and subtitles—generally rendered in title case in the literature—we see that more than half are downcased ("Fermat's last theorem has,Fermat's Last Theorem has"), and almost half using "... is". This is a no-brainer. Tony (talk) 00:53, 11 August 2021 (UTC)
  • That link isn't working for me; I just get a "no ngrams to plot" error message. Perhaps the URL was corrupted somehow? At any rate, why are we looking to Google Ngrams? That's a corpus of every book that Google could find, not a corpus of reliable sources. XOR'easter (talk) 01:28, 11 August 2021 (UTC)
• Support. MathSciNet, a database developed by the American Mathematical Society, which is what mathematicians use to search for articles, apparently has a policy of writing it as "Fermat's last theorem". I think that decades ago it was more common to see "Fermat's Last Theorem" in mathematics articles, but the modern trend has been to capitalize less (though I don't know the actual current frequencies). Ebony Jackson (talk) 01:08, 11 August 2021 (UTC)
  • This is the best argument in favor of the move that I've seen so far! But I remain unconvinced. The AMS certainly doesn't apply that policy across all their materials; see [4][5][6][7][8][9][10] for examples up to last year. Nor is it even consistently enforced across MathSciNet; see MRMR4101578 (Finally, the authors show that asymptotic Fermat's Last Theorem holds for a set of imaginary quadratic fields...) or MR4053081 (an asymptotic version of Fermat's Last Theorem over imaginary quadratic fields) or MR3932127 (Epoch-making breakthroughs, including ... Fermat's Last Theorem) or MR2541434 (the modularity strategy adopted by A. J. Wiles in his proof of Fermat's Last Theorem). They may apply it to titles, but not to the actual text of reviews, and by the logic that we shouldn't pay attention to titles, section headings, etc., I think MathSciNet has to go in the "mixed use" bucket overall. As for frequencies changing over time, that's certainly possible, though I haven't had that impression. Anecdotally, the Proceedings of the National Academy of Sciences used upper case this year [11], and Advances in Mathematics did so last year [12]. XOR'easter (talk) 01:45, 11 August 2021 (UTC)

Extended discussion

• Question @Colin M: @Cinderella157: you both seem to be asserting that "Fermat's Last Theorem" is not a proper noun. My question is what are the reliable sources that support this assertion? My experience indicates that the evidence from the usage in reliable sources supports that it is.Paul August ☎ 10:53, 6 August 2021 (UTC)

Paul August, are you then saying it is a proper noun because it is never written in lowercase?Cinderella157 (talk) 23:18, 6 August 2021 (UTC)

Most quality sources use it in uppercase because it is commonly accepted as a proper noun. As for popular culture acceptance see Fermat's Last Theorem in fiction. Randy Kryn (talk) 23:43, 6 August 2021 (UTC)

@Cinderella157: No I'm saying its a proper noun (or perhaps more technically a proper name) because that's the way it is used in most reliable sources (hence its capitalization in those sources). I repeat why are you saying that it is not a proper name? What are the reliable sources that support that assertion? Oh, and by the way it is not called Fermat's Last Theorem because it is the last theorem of his to be proved. It was called that long before Wiles' proof. Paul August ☎ 10:00, 7 August 2021 (UTC)

Paul August, so what is the etymology of the term? It was also his last published, not only his last proven - even before it was proven. And then, there is the citation I have given (not in dispute). The technicality of proper noun|name is a given. Do we agree that WP bases capitalisation on usage rather than definition? The issue is then, the distinction between most and consistently. "Consistently" is almost always v "most", which does not rise to almost always. To your initial question (of sources), I will respond more fully soon. However, the n-gram evidence certainly does not support your assertion nor does the evidence by Colin M per 3:5 in Google Scholar. Notwithstanding that different regions will return different search results, you could dispute Colin's evidence quantitatively by replicating the search and reporting the the results you have found. Both n-grams and Goggle Scholar searches are random samples to the extent that they are independent of us as observers. Asking for proof, by way of specific sources only leads to a citation war that can only ultimately be resolved by examining all of the reliable sources (or who has more access, which is itself a form of bias). Regards, Cinderella157 (talk) 12:01, 7 August 2021 (UTC)

PS per MOS:CAPS, the burden is to prove that it is capitalised "consistently" in sources. The burden does not lie with me to disprove it is not. That is the broad community consensus. What is your quantitative evidence (v an unsubstantiated assertion). Neither you nor any other have produced a quantitative assessment of evidence that would assert that the term is a proper "name" per the WP criteria. Cinderella157 (talk) 12:41, 7 August 2021 (UTC)

Where in MOS:CAPS do you find your bizarre assertion that one side of such debates has the burden of proof and the other doesn't? —David Eppstein (talk) 16:29, 7 August 2021 (UTC)

MOS:CAPS requires us to avoid unnecessary caps and only words and phrases that are consistently capitalized in a substantial majority of independent, reliable sources are capitalized in Wikipedia. Consequently, any use of caps in WP is so burdened. Cinderella157 (talk) 01:51, 8 August 2021 (UTC)

Surely one could equally easily read that passage as demonstrating that moving the page to a different title requires the move proposers to prove that the capitalization does not appear in a substantial majority of reliable sources? It says what needs to be demonstrated, but not who needs to demonstrate it. —David Eppstein (talk) 18:50, 8 August 2021 (UTC)

MOS:CAPS requires us to avoid unnecessary caps in the first instance. Therefore, any decision to capitalise must be defencible in the first instance. Furthermore, capitalising the term in full is contrary to the more specific advice at MOS:SCIMATH. Consequently, the burden is to show why this should be an exception. Cinderella157 (talk) 01:24, 10 August 2021 (UTC)

Paul August, I respond more fully as I undertook above. I have attempted to replicate the analysis of google scholar results since 2017 made by Colin M (above). My search returned 10 hits on the first page. The results are given as follows for usage in running text, with the number indicating the order of hits:

Capitalised

1. Class field theory, Diophantine analysis and the asymptotic Fermat's Last Theorem

2. Local criteria for the unit equation and the asymptotic Fermat's Last Theorem

5. Natural vector spaces (inward power and Minkowski norm of a natural vector, natural Boolean hypercubes) and a Fermat's last theorem conjecture (Google titles for hits do not necessarily follow formatting of the article title used in the link)

6. Germain and Her Fearless Attempt to Prove Fermat's Last Theorem

10. Asymptotic generalized Fermat's last theorem over number fields

Lowercase

4. Refinement of a generalized Fermat's last theorem conjecture in natural vector spaces

7. On the asymptotic Fermat's last theorem over number fields

8. Extension of Fermat's last theorem in Minkowski natural spaces

9. Simple Algebraic proofs of Fermat's last theorem

Term not specifically used

3. Hypercharge quantisation and Fermat's last theorem. Followed links to pdf. Term is only used in article title.

Acknowledging that this is a small but random sample (ie independent of observer selection), the term is capped in only 55% of cases. This is consistent with the n-grams data (a much larger sample) - at about 3:2 for recent usage but also noting that the n-gram search does not distinguish cases (such as headings of references) where we will see title case in use (ie other than running text). The term is clearly not consistently capitalized in a substantial majority of independent, reliable sources. Regards, Cinderella157 (talk) 02:35, 8 August 2021 (UTC)

This search perfectly highlights the problems of using these numerics. Paper 9 is a crank paper on ResearchGate while 4, 5, and 8 are from the same mathematical chemists.

On the other hand, almost all of the landmark paper (in English), major announcement, and most influential/popular expositions about the theorem use the capitalized "Fermat's Last Theorem" (whose is initialism is FLT, not FMT) in the article text, including:

• Ribet (1990)
• Mazur (1991)
• Wiles (1995)
• Coates (1996)
• Cornell–Silverman–Stevens (1997) (e.g. Darmon's chapter)
• Fermat's Last Theorem by Singh (1997) (cf. Fermat's Enigma by Singh (2017))
• Darmon (1999)
• The Fermat Diary by Mozzochi (2000)
• Abel Prize announcement (2016)

Perhaps the only major article in English that uses "Fermat's last theorem" within the article text, to my knowledge, is Frey's 1986 paper.

If you have a broad enough search that it includes unvetted ResearchGate posts, predatory journals, and quantum chemists attempting to generalize or reprove the theorem, sure maybe then the proportion drops to ~60%. Even then, that is still a sufficiently substantial majority to me to match the title with this capitalization. I get that we want to capture general usage in reliable sources (more selective than ngrams) and not just mathematics (less selective than my list) though. If one really wants more numerical data with less noise, maybe a search through the most cited articles (rather than recency) on MathSciNet, ProQuest, or Web of Science would be better. — MarkH₂₁^talk 03:34, 8 August 2021 (UTC)

That's a good point. We should definitely give more weight to high-quality sources. But getting numbers on usage in just high-quality sources is a more labour-intensive undertaking than just running a query against Google Scholar or Ngrams. A good proxy for this might be to just use all the works currently listed in the article's "Bibliography" section? (That way there can be no suspicion of cherry-picking) I just checked the three works there that happened to have full-text links. Two (Amir and Kleiner) capitalize, and one (Stark) uses lowercase.

As for what constitutes a "substantial majority" for the purposes of MOS:CAPS, I think that 60% isn't nearly enough (I would call that more like a thin majority, especially considering the error bars we're dealing with here). Colin M (talk) 15:28, 8 August 2021 (UTC)

MarkH21, those supporting caps have opined this is the form in virtually all sources or [usage] in most reliable sources and that the exception to capitalise is a preponderance of sources. As Colin M points out, the results must be statistically significantly different and they must be different to a "substantial" or very large extent. Furthermore, the reliable source relied upon must be independent [of the subject]. If one purports that we should rely "good quality" sources that are those that have worked on the solution to the theorem, these sources are not independent of the subject. WP:SSF is relevant. We should consider usage in more generalist sources of good quality such as [13][14][15], which are good quality tertiary sources that use lowercase (and were the only such sources I could identify from several search pages). (See also: [16][17][18][19]) It should be clarified that the n-gram viewer uses a corpus of books scanned into Google Books. It is separate from Google Scholar. Neither rely on or report blog pages. Predatory journals are problematic but striking the ResearchGate source from the previous search only raises capitalisation to 63%. An ad hominem argument against quantum chemist just doesn't cut the mustard. One cannot assert that mathematicians are more or less qualified in the field of onomastics. The works in question appear in publications in good standing and I note that capitalisation is more generally a matter of editorial policy than author preference. However, I have also undertaken a review similar to the afore using a google books search - which is the corpus used by the n-gram viewer. Several duplicate hits were observed so data was collected from two search pages and is as follows:

Capitalised

2, 15: Fermat’s Last Theorem (unable to view but I accept MarkH21 reporting capitalisation in this source)

4, 9: Fermat's Last Theorem: The Proof

6: Fermat's Last Theorem: A Genetic Introduction to Algebraic ...

7: Notes on Fermat's Last Theorem

8, 10, 11: Algebraic Number Theory and Fermat's Last Theorem At p. 270, it uses l.c. therefore not consistent usage.

20: Elliptic Curves, Modular Forms & Fermat's Last Theorem Mixed uses with "Fermat's Last theorem" (see p.8)

Lowercase

3, 14: Modular Forms and Fermat’s Last Theorem Mixed use on review. Does not alter proportion of u.c. usage.

5: 13 Lectures on Fermat's Last Theorem

13: Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem No view was avalable. Initial assignment was based on publisher's notes, which were assumed to be consistent with the source. Should be reported as u.c. usage (After viewing another edition of the same work. Cinderella157 (talk) 12:35, 9 August 2021 (UTC)

17: Number Theory Related to Fermat’s Last Theorem Might better be described as mixed. Does not alter proportion of u.c. usage.

18: The Simpsons and Their Mathematical Secrets

19: Fermat's Last Theorem - Finding a New Surprisingly Simple Demonstration? Strike as not being a WP reliable source.

Mixed use

1: Fermat’s Last Theorem for Amateurs

16: Seminar on Fermat's Last Theorem

Not on topic (or insufficient view)

12: The Last Theorem

Review of results. Cinderella157 (talk) 11:44, 9 August 2021 (UTC)

In the sample (which I again acknowledge as small but independent of observer selection), there are fourteen unique sources relevant to the subject. They all appear to be of "good quality", sufficient to be considered reliable sources within WP. The term FLT is capitalised in only 43% of instances. This does not support a conclusion of capitalisation in a substantial majority of sources. It is consistent with the same conclusion being drawn from the n-gram data. The n-gram data previously cited gives about 60% for capitalisation but inherently over-reports capitalisation (by not discriminating headings etc that are not part of running text). The n-gram data therefore suggests about equal usage or at best a slight majority for catitalisation. Objective data (v unsubstantiated opinion) does not support capitalisation of the term per the general advise given by MOS:CAPS. Regards, Cinderella157 (talk) 03:40, 9 August 2021 (UTC)

I am not convinced that you have performed this search competently. I spot-checked one source, the book "Modular Forms and Fermat’s Last Theorem", which you have listed firmly as a "lowercase" example. It is not. For one thing, it is an edited volume, so its individual contributions may have different standards. For another, the first in-text example of FLT that I found, on the table of contents page, chapter 1, section 6, is capitalized, in a context that is clearly sentence-case not title-case. So is the second example, in the first line of the schedule of lectures. Perhaps there are examples of lowercase deeper within the book; I stopped checking because it was already clear that your conclusions are based on airy nothing. Unless you can somehow demonstrate that this is a fluke and that the rest of your searches are much more accurate, I am led by AGF to the conclusion that you are being misled by bad data. —David Eppstein (talk) 06:16, 9 August 2021 (UTC)

@Cinderella157: Being independent sources is not a problem for peer-reviewed articles and books from academic presses by mathematicians who worked on Fermat's Last Theorem. FLT is a mathematical statement that was studied by mathematicians for hundreds of years, not a person or an organization that is connected to these modern mathematicians, the referees, not the publishers. Wiles's 1995 Annals of Mathematics paper is not an independent reliable source for Wiles's proof of Fermat's Last Theorem but it is for Fermat's Last Theorem itself. Otherwise it's like saying that peer-reviewed academic books and papers by physicists cannot be considered as independent for articles about gravity if those physicists have studied gravity. Nevertheless my previous list of examples, I had also included expositions and articles by people not involved in the actual proof. These are the highest quality academic sources on a highly technical subject.

Adding to David Eppstein's comment, only four chapters (1, 18, 19, 21) of the book Modular Forms and Fermat’s Last Theorem really directly discuss FLT, and three of these (1, 19, 21) use the capitalized version in-text. Your list also includes another crank work at book 19: Fermat's Last Theorem - Finding a New Surprisingly Simple Demonstration? is from the self-publishing platform Lulu.com, has not gone through any review process, and claims to give a simple proof of FLT (Chapter 3). Especially for famous accessible mathematics problems that attract thousands of bogus "proofs" (like FLT, the Riemann Hypothesis, or Goldbach's conjecture), these Google Books and Google Scholar searches always going to be poor. — MarkH₂₁^talk 06:47, 9 August 2021 (UTC)

Good analysis. Wanted to point out that Lulu publications are not allowed as Wikipedia sources. Randy Kryn (talk) 11:32, 9 August 2021 (UTC)

Chiming in to concur that Fermat's Last Theorem - Finding a New Surprisingly Simple Demonstration? is a crank work. Also, The Last Theorem is a novel by Arthur C. Clarke and Frederik Pohl; it capitalizes the term. For example, they begin a nonfiction postscript by writing, We felt it would be useful to give more details of what Fermat's Last Theorem was all about, but we could not find an earlier place for this discussion that did not wound, almost fatally, the story's narrative pace. XOR'easter (talk) 19:26, 9 August 2021 (UTC)

MarkH21, there is a distinction between what are the best sources for an article's content and those which are best for determining matters of style and in this particular case, a matter of orthography. Your response appears to conflate the two. While the subject is highly technical and within the domain of the discipline of mathematics, the question to be addressed here is one of onomastics and orthography, neither of which lay within the domain of mathematics. The article subject is quite widely mentioned in good quality reliable sources outside the specialist sources. WP:SSF specifically warns of the tendency of a specialist field to capitalise terms closely tied to the field compared with the same usage more generally. Consequently, a reliance on specialist sources to determine empirically a matter of capitalisation will tend to skew the result toward capitalisation. Those sources closely dealing with the proof of the theorem are probably not sufficiently independent of the subject to determine a matter of orthography. Hence, we might expect a higher proportion of capitalisation in specialist journal sources compared with good quality generalist sources making editorial style decisions at arms-length from the subject. Cinderella157 (talk) 03:09, 10 August 2021 (UTC)

Is that supposed to be your excuse for relying on crankery? That experts can't be relied on to be expert on their subject and so we must look to what the ignorant have to say instead? —David Eppstein (talk) 03:56, 10 August 2021 (UTC)

"Specialist" is just another way to say relevant and reliable. It's the people doing the "highly technical" writing who know what they're talking about. And it's those people who are well-informed enough to make orthographic choices that best reflect the meaning of their statements. As has already been explained above, "independent of the subject" is a red herring. It's not like the FLT is a company that pays people to write about it, for heaven's sake. Also, WP:SSF is an essay, not a guideline and definitely not policy. It has no community consensus behind it. XOR'easter (talk) 17:45, 10 August 2021 (UTC)

Per the adendum to the results above, having pointed out that Elliptic Curves, Modular Forms & Fermat's Last Theorem (source 20) is self-published, and not a WP:RELIABLESOURCE, it is struck from the analysis (as was Simple Algebraic proofs of Fermat's last theorem, when that was pointed to not being a reliable source. The novel, The Last Theorem was excluded from the sample set because it could not be viewed. On the basis of the statement by XOR'easter, it can be identified as a capitalised source. There is no net change in the number of unique reliable sources from the twenty initial hits.

Modular Forms and Fermat’s Last Theorem is an edited volume and on review, there is mixed use - ie, the term is not consistently capitalised in this source. Assessment was based on a search for the term which generally returned snippets. Just as FLT is capped in the TOC in a heading in sentence case, It is also uncapped in several examples of references also written in sentence case. I looked for instances in running text. The search results within a source are not presented in page order. I acknowledge I missed some cases of caps among the clear examples of l.c. Chapter 1 uses caps, Ch 18 uses l.c, Chapter 19, by Rosen is mixed use: As is well known the study of Fermat's last theorem for exponent .... There is one instance of FLT (in full) capped in the chapter by Damon which is on p.549 in chapter 21. Of the four chapters cited as directly discussing FLT, only half use caps consistently. FLT appears throughout the source and not just in these chapters. Reclassification of the source to mixed use does not alter the proportion of sources that consistently capitalise the term. On closer inspection of source 20, there are instances of "Fermat's Last theorem theory", which makes it mixed usage. A different version of source 13 could be viewed and it is reclassified as capped. The term is capped in seven out of fourteen unique reliable sources - ie 50% of the time. Thankyou to those of you that have helped to improve this assessment. Cinderella157 (talk)

"Fermat's last theory"?? With a Y? And with the "Last" capitalized but the "theory" not? Is this a typo on your part, a typo on the book's part, or are you trying to contribute to editing mathematics on Wikipedia without even knowing the difference between a theory and a theorem? —David Eppstein (talk) 16:56, 10 August 2021 (UTC)

The preview that I can see says Fermat's Last theorem, which is a bizarre mix I don't think I've seen anywhere else; the immediately preceding sentence uses Fermat's Last Theorem. Call it a typo in the book. Incidentally, both of the sources I provided here capitalize it. XOR'easter (talk) 17:54, 10 August 2021 (UTC)

Other "capped" uses that are not in specialist writings: the Associated Press; the New York Times [20]; the Guardian [21][22]; Time [23]; the Telegraph [24]; the Washington Post [25]; the Irish Times [26][27]. There's also The Man Who Loved Only Numbers, written by a journalist and science popularizer rather than a mathematician. XOR'easter (talk) 19:13, 10 August 2021 (UTC)

Very interesting. While I generally deplore linguistic prescription I have long thought that Wikipedia should make better use of capitalisation. Unfortunately most of those here have learned nothing more about markings and proper nouns and proper names since they left primary school, so our consensus on such matters tends to be rather ill-informed. We should for example call pseudonaja textilis the Eastern Brown Snake, because not all Eastern snakes that are brown are this species... and for that matter, in spring these snakes tend to be quite black in colour (and in a very bad mood) when they come out of hibernation. (And pseudonaja may mean phony snake but they are quite real enough. And some say the head looks small... no, the head is large but the neck is larger. It is a very powerful, venomous and dangerous snake indeed, and perhaps we could even do without it in the wild at least.) Anyway, one of my more Quixotic beliefs perhaps, but I'm very interested in the discussion above. Andrewa (talk) 10:19, 10 August 2021 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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