Summary :

It is now well known that Fermat’s last theorem has been proved. Formore than three and a half centuries, mathematicians — from the great names to the clever amateurs—tried to prove Fermat’s famous statement. The approach was new and involved very sophisticated theories. Finally the long-sought proof was achieved. The arithmetic theory of elliptic curves, modular forms, Galois representations, and their deformations, developed by many mathematicians, were the tools required to complete the difficult proof.