Fermat's last theorem is really a part of the much more difficult (and recently proven) Shimura-Taniyama-Weil conjecture, which makes a more generalized connection between number theory and elliptic curves. The aformentioned conjecture was proven by some of Wiles' students. I don't claim to understand it, but this has been the consensus of the articles I have read on the matter. Fermat's last theorem proves the STW conjecture for specific types of curves.