I just watched "Fermat's Last Theorem" (1996, 48 min) a BBC documentary made by Simon Singh and John Lynch about the mathematician Andrew Wiles' discovery of a proof for Fermat's conjecture from 1637. Being able to watch documentaries online from decades ago is absolutely wonderfull!
The documentary is well worth watching even if, like myself you can't follow the mathematics. The opening scene is of Wiles holding back tears as he tells about the happiest moment in his working life. He spent 7 years working on finding the proof, without anyone knowing. If colleagues had known they would have realised that there must be a reasonable chance that the conjecture could be proven and may have tried finding it too. The race would be on. All the elements for a gripping story are present: emotion, action and high stakes.
Fermat's Last Theorem states: There are no positive integers x, y, and z such that x^n + y^n = z^n \; in which n is a natural number greater than 2. Fermat wrote "I have discovered a truly remarkable proof of this theorem that the margin of this page is too small to contain" (see image). While Fermat says that he has found the proof Andrew Wiles actually produces one. His solution to the problem is very "20th Century" as it builds on the Taniyama-Shimura Conjecture from 1955, and hence cannot be the same as what Fermat had in mind. Fermat's proof is a puzzle still to be cracked.
Something said by Goro Shimura during the documentary grabbed my attention: "It is very difficult to make good mistakes." Good mistakes are gems because they lead to the next step in a process.
I was triggered to watch this documentary by a comment made in another documentary I recently watched "The Four Horsemen" (2007, 120 min). In it Daniel Dennet says "if they begrudge him that this is a proof, it’s a proof". He's talking about Wiles' peers here, also brilliant mathematicians. They are the gauges with which to measure the validity of his work.
Documentary maker's blog item about Fermat's Last Theorem plus link to documentary:
Discussions with Richard Dawkins: Episode 1 The Four Horsemen: