Comment by techas
14 hours ago
I've always found the story of A. Wiles sad and frustrating. He worked in secret for 7 years. He submitted a (incorrect) proof at year 4 or so. Reviewers found a problem, but he decided kept all secret for many years after. He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem...
I found this behavior against healthy science practices and only driven by ego. Unfortunately, I find this too often at work (working in academia). Most probably I'm too naive...
> He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem...
That's how maths works yes...
What you’re talking about is his proof of (a specialised version) of the Taniyama-Shimura-Weil conjecture[1] which had been proven to imply Fermat’s Last Theorem. The technique he used to prove this was adopted by his students to prove the conjecture in full generality so it now known as the modularity theorem. Given its importance to the Langlands programme it may be that when history looks back on this it will consider this a more important contribution than the fact that it proved FLT even though that is obviously the thing that grabs the headlines, but there’s nothing at all wrong with proving something that implies your goal rather than proving the goal directly. There’s a reason the words “it suffices to show” often turn up in proofs.
[1] https://mathworld.wolfram.com/Taniyama-ShimuraConjecture.htm...
Obviously, he was trying to avoid being labeled as a crank for working on a famous problem like that for so long.
While I can sympathize with this perspective, I don’t think it’s right to call it driven by “ego.” Sometimes one just wants to go at a problem without being second guessed on approaches or led astray with suggestions by others.
> He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem...
I think that was Ken Ribet?
Grigori Perelman and the Poincaré Conjecture is more interesting. IIRC he turned down Millennium and was decidedly not all about the Fields Medal - mostly because Richard Hamilton didn't get credit? Anyway, I am grateful I had the opportunity to learn about Poincaré in college taking a few classes from a professor who was a key contributor to the conjecture and got a Fulbright for it when I was there
Eh, it seems like it's pretty necessary for success on such a problem (but obviously not sufficient). These problems gain a reputation, and you either get judged for it or get too much attention for it.