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Solving Fermat: Andrew Wiles

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Re: Solving Fermat: Andrew Wiles

#11

Post by placebo »

WD-42 wrote: post #7
albert_e wrote: post #2

This was an excellent introduction to this topic: https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem_(book) by Simon Singh But I am not sure if the book covers the mistake and later correction. It has been more than a decade since I read the book (and became a fan of the author).

It does. That’s all part of the drama. One of the best books I’ve ever read.

Agreed. I bought it at the airport for a transatlantic flight the year it came out and started reading before lift off. Completed it before landing. Best flight ever.

Re: Solving Fermat: Andrew Wiles

#14

Post by NiloCK »

Recent LLM dingers like the Jacobian Conjecture counterexample have challenged the efficient mathematics hypothesis. The JC counterexample was so small in degree and coefficient. It should have been a "low fruit" in the scheme of things, but alas, unpicked for 50+ years with considerable attention from good mathematicians.

With respect to FLT, my hopes have modestly increased that a truly marvelous demonstration of this proposition does in fact exist, that Fermat actually had it, and that it may someday be recovered!

edit: some emphasis on modest. But let me be romantic here!

Re: Solving Fermat: Andrew Wiles

#15

Post by tonyedgecombe »

albert_e wrote: post #2

This was an excellent introduction to this topic: https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem_(book) by Simon Singh But I am not sure if the book covers the mistake and later correction. It has been more than a decade since I read the book (and became a fan of the author).

The BBC did an episode of Horizon on it.

https://www.bbc.co.uk/iplayer/episode/b0074rxx

Re: Solving Fermat: Andrew Wiles

#16

Post by HarHarVeryFunny »

matthewfelgate wrote: post #5

I have a truly marvellous comment on this, which this comment box is too small to contain.

FWIW, it seems pretty clear that while Fermat briefly thought he had a proof, he fairly quickly realized it was flawed since he never mentioned this publicly and later went on to develop a proof just for the simple n=4 case.

In 1847 Gabriel Lami presented a claimed (simple) general proof to the French Academy of Sciences, only for the flawed assumption in it to be pointed out immediately at the end of his presentation! This may have been the same proof that Fermat had in mind.

Re: Solving Fermat: Andrew Wiles

#17

Post by clircle »

NiloCK wrote: post #14

Recent LLM dingers like the Jacobian Conjecture counterexample have challenged the efficient mathematics hypothesis. The JC counterexample was so small in degree and coefficient. It should have been a "low fruit" in the scheme of things, but alas, unpicked for 50+ years with considerable attention from good mathematicians. With respect to FLT, my hopes have modestly increased that a truly marvelous demonstration of t…

efficient mathematics hypothesis? What's that?

Re: Solving Fermat: Andrew Wiles

#19

Post by fancyfredbot »

clircle wrote: post #17
NiloCK wrote: post #14

Recent LLM dingers like the Jacobian Conjecture counterexample have challenged the efficient mathematics hypothesis. The JC counterexample was so small in degree and coefficient. It should have been a "low fruit" in the scheme of things, but alas, unpicked for 50+ years with considerable attention from good mathematicians. With respect to FLT, my hopes have modestly increased that a truly marvelous demonstration of t…

efficient mathematics hypothesis? What's that?

It's a pun on "efficient markets hypothesis".

The efficient markets hypothesis says the market prices incorporate all available information and there's no such thing as a cheap stock, so there's no easy money to be made by trading.

The math equivalent is presumably that all easy problems have been solved and all open problems should be very very hard. This has turned out not to be the case as LLMs have found simple counterexamples to long held conjectures.

Re: Solving Fermat: Andrew Wiles

#20

Post by mathisfun123 »

fancyfredbot wrote: post #19
clircle wrote: post #17

Earlier quoted context omitted.

efficient mathematics hypothesis? What's that?

It's a pun on "efficient markets hypothesis". The efficient markets hypothesis says the market prices incorporate all available information and there's no such thing as a cheap stock, so there's no easy money to be made by trading. The math equivalent is presumably that all easy problems have been solved and all open problems should be very very hard. This has turned out not to be the case as LLMs have found simple c…

They're the same thing; knowledge markets are markets.
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