Recently, I was reading a lecture by Edward Witten at the Clay Mathematics Institute and he touched on the topic of Fermat's Last Theorem. He mentioned how Wiles's tactic to solving it also lead them to discovering a new area of study in the quantum mechanics. After reading that, I started investigating more on the net and found a very intriguing article excerpt by Hitoshi Nishino on the similarity between supersymmetry and Fermat's Last Theorem.

I am assuming that he is talking about the relationship being between Andrew Wiles's solution through the use of a hypothetical elliptic curve and supersymmetry?

A mechanism of supersymmetry breaking in two or four-dimensions is given, in which the breaking is related to the Fermat's last theorem. It is shown that supersymmetry is exact at some irrational number points in parameter space, while it is broken at all rational number points except for the origin. Accordingly, supersymmetry is exact {\it almost everywhere}, as well as broken {\it almost everywhere} on the real axis in the parameter space at the same time. This is the first explicit mechanism of supersymmetry breaking with an arbitrarily small change of parameters around any exact supersymmetric model, which is possibly useful for realistically small non-perturbative supersymmetry breakings in superstring model building. As a byproduct, we also give a convenient superpotential for supersymmetry breaking only for irrational number parameters. Our superpotential can be added as a ``hidden'' sector to other useful supersymmetric models.