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).
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.
I'll check that out - I loved his "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography". Excellent introduction to cryptography.
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!
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.
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.
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).
One of the best books I’ve ever read.
https://www.bbc.co.uk/iplayer/episode/b0074rxx
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!
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.
But agreed, that lime green is horrendous.
Posting because he's retiring this year?
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.