“Fermat’s Last Theorem” Research Summary (Yutaka Taniyama)
Pierre de Fermat’s last theorem states that that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This became one of the most puzzled and complex theorems ever to emerge in the Mathematician world. No one could prove this to be true until British Mathematician Andrew Wiles solved it in 1995. Wiles was first inspired by the Taniyama-Shimura conjecture and used this as a starting point in solving Fermat’s theorem.
The Taniyama-Shimura conjecture was developed by Yutaka Taniyama and Goro Shimura. Although both mathematicians are credited, it was essentially Taniyama who was responsible for the theorem. The Taniyama-Shimura conjecture was a partial and refined case of elliptic curves over rationals.
Yutaka Taniyama was a brilliant mathematician who committed suicide at the age of 31 in 1958. Due to depression of lack of confidence for a happy future, he ended his life. His ideas were often criticized which most likely led to his death. Goro Shimura stated that he was sad when he heard the terrible news, but was more shocked and puzzled more than anything. Shimura’s famous quote after Taniyama’s death stated “He was not a very careful person as a mathematician. He made a lot of mistakes. But he made mistakes in a good direction. I tried to emulate him. But I've realized that it's very difficult to make good mistakes.”
In conclusion, Andrew Wiles would not have been able to prove Fermat’s last theorem had it not been for Taniyama’s conjecture. While there were more formulas and theorems that Wiles mentioned he had used, the Taniyama-Shimura conjecture sparked the flame that drove Wiles to work in secrecy to prove this enigmatic idea known as Fermat’s last theorem. Thus, finally proving the 400 years theorem we come to know as Fermat’s last theorem.
Sources:
http://en.wikipedia.org/wiki/Yutaka_Taniyama http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem http://en.wikipedia.org/wiki/Andrew_Wiles