Taniyama–Shimura–Weil conjecture

Andrew Wiles proof that all that all rational semi stable elliptic curves are modular which, in particular, implies Fermat's Last Theorem. This is the proof of the Taniyama-Shimura-Weil conjecture which can be found here. Kenneth Alan Ribet is the one who found the link between Taniyama-Shimura-Weil and Fermat's last Theorem. This is contained in his proof of the epsilon conjecture, and thereby proved that Fermat's Last Theorem would follow from the Taniyama-Shimura conjecture.