Who thinks that Fermat really couldn't prove his Last Theorem, even though he hinted he had so in the margin of one of his papers? Also, has anyone simplified it since it was proven in 1994?

I like to believe he could. Euler had his house searched for the proof. If only they made books with bigger margins.

Apparently there are lots of "proofs" for Fermat's Last Theorem that look correct but actually have quite subtle flaws. (I haven't found any of these by the way.) So my guess is that he thought he'd proved it, but it didn't quite work.

Michael

Well you really can't say because man's mind is most amazing thing !! But I have serious doubts as to his claims.

The reason is that the present proof is far too complex to be written out by a single man in a sudden insight.Also it uses so many things which were really not known in Fermat's time. I believe that whatever was available to Fermat and add to that all the insight shown by him in all his work,
the proof known to him, would not be something that a today's graduate student of maths cannot grasp with a little work. But you see thousands of minds have devoted themselves to the task of prooving this theorem over 300 years and still they can't ...
What seems to be a more rational view to me is that he got the proof for n=3 or perhaps 4 and thought that this would generalize to higher powers.

He certainly proved it for n = 4 (see the last post in this discussion for the proof). Very easy to understand - very difficult to figure out, as usual.

Michael

Thanks for that!! And as I said..it doesn't generalize...

I have seen a few of the proofs dealing with Fermat' Last Theorem, and most of them are flawed disproofs. A typical example involves dividing by zero (diguised cleverly though) to show that 2=1 or something like that. This goes on to show that

zⁿ =yⁿ +xⁿ =y+x²

which has solutions. Perhaps though there are better "proofs" that actually halfway work.

Brad