What took 365 years to be solved? Who solved it?

Off the top of my head I'm guessing that's about the time frame for Fermat's Last Theorem, a conjecture finally proved about a decade ago by Andrew Weils (sp?). If that's right, I'll try to provide a link or two...

That's right,professor.Thanks.
Andrew Wiles. Source.

It's a great story. In 1637 Fermat stated his theorem (explained below) in the margin of a math book he was reading, then added these words: "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

Whether this "proof in his head" was correct will never be known. From Wikipedia:

quote:

...all the other theorems proposed by Fermat were settled, either by proofs he supplied, or by rigorous proofs found afterwards. Mathematicians were long baffled, for they were unable either to prove or to disprove it. The theorem was not the last that Fermat conjectured, but the last to be proved. The theorem is generally thought to be the mathematical result that has provoked the largest number of incorrect proofs, perhaps because it is easy to understand.

and from MathWorld:

quote:

It was called a "theorem" on the strength of Fermat's statement, despite the fact that no other mathematician was able to prove it for hundreds of years.

In connection with the Pythagorean Theorem of right triangles, most people have seen that 9+16=25 which can be written 3² + 4² = 5², in other words, two squares can sum to another square. There is, in fact, an unlimited supply of integers (whole numbers) x, y, and z such that xⁿ + yⁿ = zⁿ when n=2. (Another example is 5²+12²=13²)

Fermat wondered whether this would work for higher values of n. Are there two cubes that sum to another cube, or fourth powers, etc.? He discovered the answer is no for all n>2. Modern computers failed to find any counterexamples that would disprove the conjecture. Wiles finally published a 200-page proof in 1994. Not exactly "truly marvelous" as promised by Fermat, but it made Wiles a math superstar nonethless.

There was also a PBS Nova episode on FLT.

mozart, one of us is off on the years: 1994-1637=357 years.

{Edited to fix Nova link}

This message has been edited. Last edited by: Professor,

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mozart, one of us is off on the years: 1994-1637=357 years.

Well my source is from "Guinness world record" While yours is from "Wikipedia"( concerning the years ). I have been using numerous times Wikipedia as a source and usually trust them..But let's ask DG which source he would trust more?

The reliable MathWorld (link posted above) says only that Fermat's scribbled note was found posthumously. We aren't entirely sure where Wikipedia got the year 1637 in its article on FLT.

Fermat wrote

I have discovered a truly remarkable proof which this margin is too small to contain.

Fermat almost certainly wrote the marginal note around 1630, when he first studied Diophantus's Arithmetica.
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In August 1994 Wiles addressed the International Congress of Mathematicians but was no nearer to solving the difficulties.

Taylor suggested a last attempt to extend Flach's method in the way necessary and Wiles, although convinced it would not work, agreed mainly to enable him to convince Taylor that it could never work. Wiles worked on it for about two weeks, then suddenly inspiration struck.

In a flash I saw that the thing that stopped it [the extension of Flach's method] working was something that would make another method I had tried previously work.

On 6 October Wiles sent the new proof to three colleagues including Faltings. All liked the new proof which was essentially simpler than the earlier one. Faltings sent a simplification of part of the proof. - Article by: J J O'Connor and E F Robertson for School of Mathematics and Statistics
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This gives us 1994 as the year of solution, as do the all the other sources. But the year of the first attempt, of Fermat's writing the notation in the margin, is uncertain. Using 1630, we have a time period of 364 years. Guinness also gives 1630, while Wikipedia gives 1637. Many sources avoid giving an exact date. Looking around at .edu sites, I found that most avoid an exact date, but of those that do give a year, 1630 appeared more than any later date.

Both Wikipedia and Guinness are excellent sources, but I have seen errors in both. Wikipedia is, and always will be, a work in progress, while Guinness is, in matters like this, more of a collector of established facts.

If I remember correctly, isn't it somewhat of a given that, in general, a mathematician's original output usually takes place by the time he is 30 or so? Assuming that this generalization is relatively valid even for those in the 1600s, if I had to choose a year, I would choose 1630, but I also wouldn't be certain that I was right. I also note that 1630 as the year that Fermat "first studied Diophantus's Arithmetica" was not disputed by any sources that I looked at. Has anyone looked at the date(s) given by the most widely recognized schools of mathamatics?


(Please note that I have avoided giving anything that could be construed as a definitive answer. I'm rather proud of that. )

quote:

isn't it somewhat of a given that, in general, a mathematician's original output usually takes place by the time he is 30 or so?

I heard physicists were finished by forty. 35 years is another cutoff I've read somewhere. Is this is the edge of urban legend? At the bottom of all this paraphrasing, there must be a real quote from a real guy.