Fermat’s Last Theorem rules out positive-integer solutions to a raised to n plus b raised to n equals c raised to n for integer exponents greater than two. The discussion contrasts that statement with the Pythagorean theorem and follows the mathematical connections that led to Andrew Wiles’s proof.
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1:40:18>> Uh 1994 proof of verat's last theorem. >> Yes, this starts actually in Berkeley with um Ken Ribbit's proof of the epsilon conjecture. He resolved that Vermont's last theorem, which is a very simple theorem actually. Um it was made about 358 years ago by Vermont. It was noted in the margins of his book that he had already proved it but he's like I don't want to. Classic French. >> May I just say um here here's the theorem. Okay, you got the Pythagorean theorem. >> Yeah. Yeah. >> Which is a square + b²= c2. Um there's plenty of numbers that fit that. For example, 32 + 42= 52. you have 9 + 16
1:40:59equals 25. Now the question is um are there any numbers where a cubed plus b cubed equals cubed. >> Um for that matter are there any such that a to the n plus b to the n equals c to the n as long as n is not one or two? If it's one or two it's like obvious right? Um so >> that's the question. For the longest time the answer was no. >> Okay. There are no triple integers in the infinity of integers such that a cub plus b cubed equals cubed. Isn't that crazy? >> Yeah. Yeah. Yeah. >> But you we couldn't prove it. But it's a hard thing to prove. Turns out the Pythagorean theorem is super easy to
1:41:40prove. People do it in in eighth grade if you if you if you take a good geometry class, right? But this n= 3 n= 4 in all the infinity of numbers, there are no three numbers that you can find that obey that equation. That is for Mat's last theorem. So Ken Ribbit showed that Format's last theorem is the same as if you prove this other um tanama Shimomura while conjecture. He showed that if you prove the Tamyama Shimomura while conjecture then you've proven for the he showed the connection there. Y >> so Andrew Wilds then made it his goal in life to prove the Tammy Tanyama
1:42:21Shimamura Wild conjecture. Okay. And he spent 10 years locked up at Princeton University's math department in his office up there in Finehal doing nothing else >> but this one thing and he got it and in 1994 he finally proved that conjecture which then in turn proves Vermont's last theorem. It also shows that Vermont definitely did not have a proof. >> He was clearly capping. >> Yeah. Yeah. Yeah. >> Right. Because you didn't know about like Galwa groups and this Shimamura wild conjecture and like so much needed to happen to prove Vermont's last theorem that there's no way that Vermont had some trivial proof. And if he thought he did, it was most
1:43:02definitely wrong. wrong.