Fermat's Last Theorem.

[d000hg]

It's also quite possible he thought he had a proof but was wrong. Prrofs get published and dis-proved sometimes.

[OwlHoot]

The prize for Beal's conjecture might be worth a crack though. Something to do in the evenings when you're working away from home anyway.

Those Clay problems are obviously mind-bogglingly hard. In many cases just reading the problem statement is enough to bring one out in hives.

But there are many unsolved problems (like Fermat's Last Theorem in a way I suppose) which are ridiculously easy to state, but have resisted all attempts to solve them. Here are a couple to work on in that B&B (and one could easily quote a dozen like them) :

* The Erdos-Straus Conjecture Prove that for every integer n > 1 there exist positive integers x, y, z such that 4/n = 1/x + 1/y + 1/z

* The (or a) Ramanujan conjecture: If 2^t and 3^t are both integers for some real t > 0, prove that t is an integer.

The first is a complete mick-taker, because it looks so easy, and it is easy to find solutions with at least one of x, y, z negative, and very easy to prove it for _most_ n; but some values always slip through the net!

But the second is like an impenetrable glass cliff-face. It's no exaggeration to say that hardly any progress has been made on it, which is all the more incredible when one thinks of all the amazing things that _have_ been proved.

[xoggoth]

Didn't threaded explain the proof of Fermat's last theorem to us in layman's terms a couple of years ago?

Umpteen years ago somebody on TV did explain relativity really well by walking two different ways round a triangle. Fermats theorem could probably be done with a whippet and a bowl of custard or maybe prunes would be better.

[DimPrawn]

It all sounds quite tedious to me.

[OwlHoot]

It all sounds quite tedious to me.

How about if all the amounts were in pounds and percentages ?

[Freamon]

Simon Singh's book is pretty good.

[DimPrawn]

How about if all the amounts were in pounds and percentages ?

Now yer talking!

[NotAllThere]

There isn't a prize AFAIK but you would probably make a name for yourself. There are some prizes on offer from the clay maths institute for some other unsolved problems.

It seems likely that if a simple proof existed Fermat would have written it down somewhere else and/or it would have been found already. A lot of very smart people had a crack at it in the intervening 300 odd years. So my guess is that he realised his idea was flawed.

Ian Stewart wrote an accessible book on maths. He talked about a theorem that was proved in many pages of complex maths. Then some guy came along with a completely different argument, and proved it with simple, easy to understand maths, taking about half a page. ( Sorry, can't find the book, so can't tell you which theorem it was).

[doodab]

Ian Stewart wrote an accessible book on maths. He talked about a theorem that was proved in many pages of complex maths. Then some guy came along with a completely different argument, and proved it with simple, easy to understand maths, taking about half a page. ( Sorry, can't find the book, so can't tell you which theorem it was).

In this case it seems that all the simple lines of argument have been explored, but it might happen that some future maths will come along and simplify things.

[BlasterBates]

In this case it seems that all the simple lines of argument have been explored, but it might happen that some future maths will come along and simplify things.

But if that is the case why hasn't anyone at least come up with a plausible "flawed" proof to show what Fermat might have done. His proof must have appeared to be good at least superficially.