Talk:Fermat's Last Theorem

Renewed interest from serious mathematicians

This section 2.5 is only reported by the NY Times and Wiles has had no comment on it. Saying there was renewed interest from serious mathematicians due to Vaughn seems inconsistent with the sections immediately above where there is clearly work being performed on it all through the centuries including just before Vaughn's money became involved. — Preceding unsigned comment added by 75.80.196.159 (talk) 22:56, 16 February 2022 (UTC)

Section about Harvey Friedman's grand conjecture

There is a short section in the article beginning with While Harvey Friedman's grand conjecture implies ... It strikes me as irrelevant, and honestly, rather stupid. It contrasts with the rest of the article which is so well written and sourced. I propose to delete the section. Can I get some support from mathematicians? --Herbmuell (talk) 21:11, 14 May 2022 (UTC)

It was added in 2010 by R.e.b. (Special:Diff/373497345), whose taste in mathematical interestingness I tend to trust more than those of most other editors, even the ones who frequently edit mathematics articles here. The issue of whether FLT has an elementary proof is still as far as I know unresolved and directly relevant to the question of whether Fermat himself could have had a proof (the previous sentence in the article). See also McLarty 2010 (doi:10.2178/bsl/1286284558), Grosholz 2017 (doi:10.1007/978-3-319-46690-3_5), and McLarty 2020 (doi:10.1007/978-3-030-19071-2_44-1) on exactly this issue, and especially the final section "The Wide-Open Question" of McLarty 2020. —David Eppstein (talk) 21:59, 14 May 2022 (UTC)

Okay, David, thanks for your reply. There is no information about R.e.b. on his user page, contrary to your page. This grand conjecture is very broad, it's not in formal mathematical language, so it's impossible to prove or disprove. It smacks of talk of mathematicians over a cup of coffee. But no problem, we disagree on this, and you have done much more reading than I, so we let the section stand as it is. --Herbmuell (talk) 09:34, 15 May 2022 (UTC)

I believe that the program of reverse mathematics makes this quite a precise and formal conjecture, not vague. Unfortunately Wikipedia rules prevent me from saying more about why I trust R.e.b.'s judgement on this sort of thing. —David Eppstein (talk) 18:22, 15 May 2022 (UTC)

Popular culture: verbiage

There is far too much verbiage about minor Star Trek episodes. I'm removing the obvious excess. People who want to save it should move it to Fermat's Last Theorem in fiction. Here is the deleted material.

• Also in a Simpsons episode, "Treehouse of Horror VI", in the "Homer³" segment, an equation appears on the blackboard that reads 1782¹² + 1841¹²=1922.^12. This is another equation that appears to be a counterexample to Fermat's Last Theorem, but is also wrong. This equation does, however, similar to the one found in "The Wizard of Evergreen Terrace", appear correct if entered in a calculator with 10 significant figures. David Cohen is the Simpsons writer responsible for these appearances of false counterexamples to Fermat's Last Theorem.

• In "The Royale", a 1989 episode of the 24th-century-set TV series Star Trek: The Next Generation, Picard tells Commander Riker about his attempts to solve the theorem, still unsolved after 800 years. He concludes, "In our arrogance, we feel we are so advanced. And yet we cannot unravel a simple knot tied by a part-time French mathematician working alone without a computer." (Andrew Wiles's insight leading to his breakthrough proof happened four months after the series ended.)

Wiles' proof was referenced in the Star Trek: Deep Space Nine season three episode "Facets", where Jadzia Dax says to Tobin Dax that his proof of the theorem was "the most original approach to the proof since Wiles over three hundred years ago".)

Zaslav (talk) 22:30, 21 May 2022 (UTC)

@Zaslav I concur; the trivia referenced directly to a ST episode was the worst. See also the ongoing [[Wikipedia:Articles for deletion/Fermat's Last Theorem in fiction (3rd nomination)]. _{Piotr Konieczny aka Prokonsul Piotrus| reply here} 07:30, 22 May 2022 (UTC)

Despite my keep !vote on the AfD, I also strongly agree with removing self-sourced trivia such as this. Either here or (if kept) at the in fiction article, we should only include material covered in secondary sources that clearly state the significance of the theorem to the work in question. —David Eppstein (talk) 07:46, 22 May 2022 (UTC)

I agree, except for the classic "Simon Flagg" story (!) -- it should be easy for anyone who is motivated to find secondary sources for that story. (By the way, the significance of Fermat's theorem to that work is the most obvious possible.)

I note that many articles have sections of arbitrary trivia of the same nature. It's a bit silly. Zaslav (talk) 22:00, 22 May 2022 (UTC)

In the "Simon Flagg" story it's central to the plot. In the Star Trek one it appears to be just a throwaway remark. I think if we're going to have a section like this here at all, we should swap the Star Trek bit out for The Last Theorem and Arcadia (play) where the connection is again more central. —David Eppstein (talk) 23:33, 22 May 2022 (UTC)

I am disappointed that the example of Wile's proof mentioned in Star Trek Deep Space Nine was removed as it was aired on 12 June 1995, when Wile's proof had only been published in May 1995. This surely shows that the proof of Fermat's Last Theorem was incredibly important to the writers of Star trek who felt it should receive a special mention. Star trek has long been pointed to as an inspiration for young scientists and mathematicians, indeed, Stephen Hawking even appeared in an episode as he was a huge fan. I very much doubt that many young scientists would have read the Annals of mathematics at the time but being informed that the theorum had been proved through Star trek would likely have piqued their interest and led them to find out more about what the characters were talking about. But hey, I guess Star trek isn't for everyone CiaranMacD (talk) 16:07, 13 October 2022 (UTC)

All additions of such material, even in Fermat's Last Theorem in fiction, require in-depth published sources (not merely TV-guide like episode listings) attesting to the significance of the subject to the episode in question, and preferably also explaining why it could not have been possible to substitute some random other unsolved mathematical problem with no change in meaning to the rest of the episode. The section of this article that summarizes Fermat's Last Theorem in fiction should be even more selective. Your addition did none of that. If you want to list TV episodes that mention stuff, maybe TV Tropes would be a better site to edit than Wikipedia. —David Eppstein (talk) 17:06, 13 October 2022 (UTC)

Please delete all of my contributions and my account. CiaranMacD (talk) 04:24, 16 October 2022 (UTC)

I would agree that the Star Trek:Deep Space Nine mention should be returned. As mentioned, it was made only weeks after Wiley's discovery and was significantly pointed out in the episode. Let's return this one. Randy Kryn (talk) 04:30, 16 October 2022 (UTC)

I don't see the point of having a list of some random media mentions here and a list of more random media mentions in the Fermat's Last Theorem in fiction article, without any clear criterion for which ones are important enough to mention here. The paragraph here should be a WP:SUMMARY of the child article, not content fork filtered only by which fans whine the most when their fandom is snubbed. It should certainly not be the case that equivalent content here is both more detailed and less well-sourced than in the "in fiction" article, which was the case in the recent go-round. And judging from our one-sentence description of the episode in the "in fiction" article, it was a throwaway line, not anything intrinsic to the plotline or historically significant as a particularly early piece of Fermat-fiction (as the Simon Flagg piece is), or having any nontrivial mathematical content (as maybe the Simpson's reference does). —David Eppstein (talk) 06:11, 16 October 2022 (UTC)

The relevance: being mentioned on a science fiction show set far in the future just weeks after the discovery occurred, and being added as an iconic event to the already completed script (or possibly the completed show), indicates its importance within society and the structure of mathematics. Randy Kryn (talk) 11:54, 16 October 2022 (UTC)

That gets over the edge into drawing our own new conclusions. I don't think we can make that judgment call. XOR'easter (talk) 14:46, 16 October 2022 (UTC)

You have a point if the conclusion was used in the page text, which it wouldn't be, but in discussion for or against inclusion the point of view seems fine (although I'm not a wikilawyer). Randy Kryn (talk) 14:58, 16 October 2022 (UTC)

If the only grounds for inclusion is our speculation about its possible cultural significance based on guesses about the production schedule of a TV show, then we don't really have grounds for inclusion. XOR'easter (talk) 20:45, 16 October 2022 (UTC)

References

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Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 02:53, 12 March 2023 (UTC)

"It is impossible to separate a cube into two cubes" versus Banach-Tarski paradox?

> "It is impossible to separate a cube into two cubes - Fermat"

The article should clarify for layman readers how that 1670 statement by Fermat can co-exist / reconcile with the Banach-Tarski paradox from 1924? I mean, one may use B-T-P as a workaround: transform the cube into a ball, split that ball up into as few as 5 pieces and re-combine them in a different way, which yields TWO identical copies of the original ball (or abritrarily many copies, per Churkin 2010). Transform those balls into cubes and finished, or not if the logic is broken somewhere? 94.21.229.113 (talk) 23:12, 22 June 2024 (UTC)

One is about integers and the other is about continuous shapes (or, if you prefer, real numbers). They are not very closely related. —David Eppstein (talk) 23:24, 22 June 2024 (UTC)

Is Fermat's copy still around?

I'm finding several different claims that the book was lost right after his death, and all we have a transcripts made by his son, but I also heard claims that the Bibliothèque nationale de France has the original copy with his notes. Any source on either? 2A02:3035:66D:C24F:5D30:1812:F787:BA5B (talk) 16:14, 29 August 2024 (UTC)

Should "Fermat's Last Theorem" be renamed to "Fermat's last theorem" for consistency?

The disambiguation page Fermat's theorem shows that only this article has all words initially capitalized. For example Fermat's little theorem isn't titled Fermat's Little Theorem, and neither is Fermat's theorem on sums of two squares called Fermat's Theorem on Sums of Two Squares. Should this article be renamed to Fermat's last theorem for Wikipedia consistency? GregariousMadness (talk to me!) 16:05, 27 December 2024 (UTC)

This has been heavily discussed, most recently Talk:Fermat's Last Theorem/Archive 8#Requested move 2 August 2021. Have you read those discussions and do you have something different to add than what was already discussed there? But to be brief: This is not actually the last theorem of Fermat, so it does not make sense to use a capitalization suggesting that the phrase is a description. It is not a description; it is a name. In contrast, for the theorem on sums of two squares, the title actually is an accurate description of the theorem rather than its name. —David Eppstein (talk) 16:52, 27 December 2024 (UTC)