Real world applications of Fermat's Last theorem

Question

I am trying to edit a high school paper on Wiles and the phases of discovery along the way to his proof are beyond my poor math skills. I would be grateful for a plain English explanation of the Galois Representation, the Kolyvagin-Flach method and the Iwasawa theory, as well as Fermat's Last Theorem ? Or a way to explain how these ideas are applied in the non-pure-math world? I was not even able to find an incomprehensible definition of the Kolyvagin-Flack method. Thank you from one who admires the numerate from afar.

Why Fermat Numbers? By the way, I don't know if such explanation would be able to fit in such a tiny space :3 — LeviathanTheEsper, Mar 20 '17 at 06:46

Stella Biderman · Answer 1 · 2017-03-30T17:31:15.687

1

Unfortunately such an answer is likely impossible, as it is extremely hard to explain en brief. There are entire books devoted to the topic. I think that Fermat's Enigma: the Epic Quest to Solve the World's Greatest Unsolved Problem is a pretty good one, but you're unlikely to condense it to a few pages. Reading it might increase your understanding though.

edited Mar 30 '17 at 17:31

answered Mar 29 '17 at 02:04

Stella Biderman

31,155

score 0 · Answer 2 · answered Nov 09 '21 at 08:13

We waited hundreds of years for a proof of FLT. We will probably wait another hundred years or more than a proof that a normal person can understand.

I downloaded a copy of his proof, and didn’t understand a thing. I only noticed that all the signs that allow me to identify crackpots were missing. It all felt right.

Real world applications of Fermat's Last theorem

2 Answers2