And so I got interested in that and invited Mehta to come here to Princeton and work with me, and so Mehta and I wrote a series of papers which occupied us for several years and we were able to go a lot further. The most interesting thing that came out of that was in effect a sort of a general classification of all the possible ensembles. Whereas Wigner had just chosen one arbitrarily, we were able to prove that there are in fact precisely three irreducible ensembles in a well-defined mathematical sense; that every possible matrix ensemble with certain properties of invariance is a direct product of irreducible components, and each irreducible component then has to be one of three types. And the three types are what we call orthogonal, unitary and simplectic. And so the orthogonal one is where it is time reversal invariant and integer spin; and the unitary one is where there's no time reversal invariance; and the simplectic is where it's time reversal invariant with half integer spin. And so those are the only three possibilities, and they have very different behaviour as far as the level spacing distributions are concerned. You have always, in all three cases, you have a repulsion between nearest neighbour levels, so they're not randomly distributed, and a strong level repulsion is different in the three cases. It's weakest in the orthogonal case, and then a little bit stronger in the unitary case, and strongest of all in the simplectic case. So we were able to develop this theory of random matrices into a much more general form and also to prove a lot more fundamental properties of the spacing distributions.