Talk:Fermat's Last Theorem/Archive 2

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This archive of Talk:Fermat's Last Theorem covers the 2007 discussions.

All Proofs Proven?!?

The article states before the TOC this:

"All the other theorems proposed by Fermat were proven, either in his own proofs or by other mathematicians, in the two centuries following their proposition. The theorem was not the last that Fermat conjectured, but the last to be proven."

I am curious if anyone could verify whether or not they were ALL proven. I recently read Fermat's Enigma by Simon Singh and I seem to remember reading that some of Fermat's conjectures were disproved. He made a lot in his lifetime and he rarely wrote full proofs, so it would stand to reason that an amateur such as him would occasionally make a mistake. Nthitz 22:13, 7 January 2007 (UTC)

I think I remember that line...I have changed it accordingly.--HereToHelp 00:43, 8 January 2007 (UTC)

There is a difference between statements that Fermat asserted he had proven, and conjectures. For example, Fermat asserted he had shown exactly which primes could be written as a sum of two squares, or as a sum of a square and twice a square; on the other hand, he explicitly conjectured that all Fermat numbers would be prime. The latter conjecture was proven false. It is my understanding that in all cases where Fermat asserted publicly that he had proven or that he could prove a result, the results has in fact been proven. Fermat's Last Theorem was a bit of an oddity not just because it had not been settled, but also because his assertion of proof was a private note to himself, not a public claim. Magidin 20:15, 9 January 2007 (UTC)

usefulness?

i'm sure this is terribly relevant to daily life somehow, but the article doesn't say how. —The preceding unsigned comment was added by 71.103.88.223 (talk) 20:01, 26 January 2007 (UTC).

Like many topics in number theory, Fermat's Last Theorem has little application to the real world. Yet it is quite an interesting problem... Nthitz 20:18, 15 February 2007 (UTC)

It would be nice to show scans of the original bookpage where Fermat scribbled his comment, instead of the printed annotation version currently available. If the original book is lost, it should be noted in the description of the image. 80.202.98.204 18:51, 29 January 2007 (UTC)

Hypothetically...

Hypothetically, what if you had figured out a preposterously simple approach to proving Fermat's last theorem? The problem is - it's preposterously simple and you don't see how all the mathematicians before you could have overlooked it. Nor do you have a strict proof yet. Where would you go to check if this approach had any merit? —The preceding unsigned comment was added by 71.135.62.1 (talk) 01:11, 8 March 2007 (UTC).

Answer: graduate school? CMummert · talk 01:21, 8 March 2007 (UTC)

There is an elementary approach to proving Fermat's last theorem: abc conjecture. Arcfrk 10:39, 10 April 2007 (UTC)

"Fermat's conjecture" re-directing here

Why is this a logical re-direct?? The most logical meaning of the term "Fermat's conjecture" is the statement that 2^(2^n)+1 is prime for all non-negative integers. This definition of the term makes sense in that this conjecture was later disproven. Any debate on the most logical meaning of this term?? Georgia guy 22:40, 18 March 2007 (UTC)

Why not make the redirect into a disambiguation page that links to here and to the article on that conjecture (if there is an article on it)? CMummert · talk 00:54, 19 March 2007 (UTC)

I'm not sure what you, Georgia guy, mean by most logical meaning of. Fermat conjectured a lot of things. Some of these became very famous, the most famous probably being what is now called his last theorem. However, it has not been a theorem until Andrew Wiles proved its correctness, it has been a conjecture.

I support CMummert's idea to make a disambiguation page on this. The page on Erdős' conjectures could work as model for this. — Ocolon 16:08, 19 March 2007 (UTC)

Well, so could the page Fermat's theorem. — Ocolon 16:12, 19 March 2007 (UTC)

External Links

"http://ne-plus-ultra.net/pubs/kisby_fermatarticle_rev.pdf" (Kisby, Adam William (2004). Fermat's Last Theorem Revisited: A Marginal Proof in Ten Steps (PDF). Parody.) seems to be down. Mike wiki 13:34, 22 March 2007 (UTC)

Thank you for pointing at this! It's much appreciated. I recovered the link from web.archive.org and if you're interested in the file you can download it now. — Ocolon 16:56, 22 March 2007 (UTC)

Solution?

1^3 + 2^3 = (cubed root of 9)^3 1+8=(2.08...)^3 9=9

So if FLT was proven, then why would this equation be correct.—Preceding unsigned comment added by 69.14.146.146 (talk)

Because the values of a, b, and c have to be integers…--HereToHelp 00:47, 10 May 2007 (UTC)

Ah. Still, I've pointed out a major flaw in the original wording of Fermat's (unless he does indeed use the word integer in the untranslated version). —The preceding unsigned comment was added by 69.14.146.146 (talk) 00:49, 10 May 2007 (UTC).

Fermat wrote his comment on a copy of the work of Diophantus; in that work, it is always rational and integer solutions that are at issue. That is, there is an underlying assumption that all variables will only take values in the integers and the rationals. His original comment must be taken in the context in which it is written. Magidin 14:45, 10 May 2007 (UTC)

A-Class?

I've been checking some A-Class ratings and nearly passed over this. This article is definitely a great piece of work and may well be A-Class, but I'm not quite convinced that it has nailed it, and suggest it might be worth taking to mathematics A-Class review. So I'm only able to sign it off as B+ for now: someone else can upgrade it if they are more confident. Possibly I am being tough on the article because it is so important, and of such popular interest.

Although referencing is one concern I have, this isn't a dominant criterion for A-Class: more important is completeness. I just think there are more opportunities here to add more mathematical content. For instance, the contributions of Germain and Kummer could be expanded: the latter in particular inspired the development of ring theory, ideals, and the ideal class group. And surely more could be said about the proof — perhaps we should separate the proof from the history of the proof. At present the text seems to imply that Wiles proved the Taniyama–Shimura conjecture, whereas my understanding is that he only proved a special case (which was sufficient for FLT). Geometry guy 18:38, 9 June 2007 (UTC)

Proof

I think, to justify the adjective "well written" (Category:A-Class mathematics articles) the proof section should contain some more mathematics. For example, what does the phrase

"that is, all elliptic curves are also modular forms"

mean? I know elliptic curves and also roughly modular forms, but I cannot make sense of this phrase. If the prahse is correct, please reformulate it in a way understandable not only to a layman, but also to someone who wants to see some math in it, not just prose. Also, references could be more specific, e.g. the paper/book(?) of Hellegouarch is missing. Jakob.scholbach 21:19, 11 June 2007 (UTC)

I agree. I've nominated the article for A-Class review and hope you will be willing to join in and help the article on its way back to A-Class. Geometry guy 21:44, 11 June 2007 (UTC)

I am sorry but I completely disagree with high accolades for this article. My assessment is that it is presently between Start and B-class (frankly, I have seen more developed articles rated Start class by a certain Geometry guy). Already the lead contains questionable statements, the history section is utterly inadequate (for example, Kummer's remarkable achievements get barely a one-line mention; while most of the work on FLT post Kummer is not mentioned at all). The article's only strength seems to be in the Proof section, at least, as far as the History of Wiles' proof is concerned. Even that section is not problem-free, and as has been remarked above, it contains precious little mathematics. Arcfrk 22:34, 11 June 2007 (UTC)

It seems I was right to delist this from A-Class, then! Can you fix any of the problems you mention? Many thanks if you can. Geometry guy 23:02, 11 June 2007 (UTC)

I have been tempted to go for it several times already, but my earnest assessment is that it would take upwards of 50 hours to bring this article to a decent state. The patches can be applied in several places, but it's unlikely that the quality would substantially improve without a major, well planned, and extended effort. Arcfrk 23:18, 11 June 2007 (UTC)

Let's hope WP:WPM/ACR can deliver. Maybe over the next week we can find 10 people to put in five hours overall, at least on average? Geometry guy 23:32, 11 June 2007 (UTC)

Concerning, your (Geometryguy) request: right now I'm busy writing a database for a Bibtex replacement for references. But even if not, I would probably refrain from editing here, as I don't have the number-theoretic knowledge necessary to give the article the more solid math's it needs. One general problem in this Wikiproject, as far as I see, is that lots of articles often only describe vaguely what is meant instead of making it clear. Math is a discipline where the latter is always possible! Probably the reason for this problem is, that one needs to know the subject in question pretty well in order to escape this trap. Jakob.scholbach 05:06, 13 June 2007 (UTC)

I've now pulled out the mathematical content into a separate section, revealing just how little there is there. Hopefully, this will help some editors with more expertise than me to develop this aspect. Geometry guy 14:38, 17 June 2007 (UTC)

In fiction

Does anyone else think the "in fiction" section is rather long and unwieldy? Perhaps a split is necessary? --C S (Talk) 00:00, 17 June 2007 (UTC)

I'd say, leave a couple of them, and move the rest out into a separate article. Also, calling TV series and rock lyrics 'fiction' is stretching it a little bit, I feel. Arcfrk 04:31, 17 June 2007 (UTC)

P.S. Nice edits, by the way! Keep up the good work.

I agree: I hope I haven't damaged these improvements in my own work on the article today. Geometry guy 17:22, 17 June 2007 (UTC)

I might have a proof

I might have a simple proof that seems too babyish to not have been seen before. Where/ Who should I go/apporach in order to test its validity. thanks —Preceding unsigned comment added by 68.209.186.75 (talk) 16:44, 1 July 2007 (UTC)

*Shrug* Maybe go to the newsgroup sci.math. You're certain to get a response. Of course you realize there's virtually no chance of the proof being correct. Probably once someone else gets a look at it they'll see the flaw pretty quickly. Eric119 02:06, 4 July 2007 (UTC)

I also have a marvellous proof, but this talk box is too narrow to contain it. Manning (talk) 18:20, 26 November 2007 (UTC)

The mention of the PBS Nova Special

Hi I'm wondering why the PBS NOVA version of the BBC Horizon's "Fermat's Last Theorem" is mentioned instead of the original version done by the BBC. Timothy Clemans 18:28, 13 July 2007 (UTC)

It's because Wikipedia is essentially an American entity, and as such most of the contributors tend to make the articles US-centric. It's occured to me that despite the fact that the US population is ~5% that of the world and the country has only existed for a little more than 200 years, it features significantly more than it should in the front page articles.Fizzackerly 14:09, 5 October 2007 (UTC)

Rather than complain, why not just fix it? Geometry guy 23:21, 21 October 2007 (UTC)

I'm not complaining, I'm answering the question Fizzackerly 12:08, 22 October 2007 (UTC)

Introductory paragraph

As a non-mathematician I am a bit put off by this article. I feel that the opening section should be far more generalist (given that this is a mathematical theorem with broad public interest) and that its significance (and its misleading name) should be acknowledged from the outset. To me it feels like it dives into the technicalities far too quickly, and leaves precious little content of interest for those who are not mathematically skilled enough to comprehend them. Comments anyone? Manning (talk) 18:18, 26 November 2007 (UTC)

I think the introduction section is fine. The third and fourth paragraphs of the introduction ("Fermat's last theorem is strikingly different and much more difficult to prove than the analogous problem for n = 2..." and "Fermat's last theorem is one of the most famous theorems in the history of mathematics ...") speak to significance. The third paragraph also explains why it is called Fermat's last theorem. It would be more consistent with modern usage to call it "Fermat's conjecture" or "Wiles's theorem" (and both of these names redirect to this article), but the historical terminology is so deeply ingrained that I doubt either of these alternative names will ever be more than pedantic curiosities. I don't see any "technicalities" in the lead section beyond the basic algebra required to understand the statement of the problem. However, if you want to propose a re-write of the introduction, you can put a new version on this talk page for discussion. Gandalf61 (talk) 09:30, 27 November 2007 (UTC)

I'm wondering if link to Exponentiation might help readers such as Manning. Cuurrently if you don't know the notation aⁿ then you are rather stuck. --Salix alba (talk) 11:05, 27 November 2007 (UTC)

Serre Conjecture

I believe Serre Conjecture has been proven more or less true. See the wikipedia article on it. Then please modify this article accordingly. —Preceding unsigned comment added by 68.43.205.215 (talk) 09:15, 4 December 2007 (UTC)

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