I decided, at the end of the year at Imperial College, there was one more problem that I tried to solve as a mathematician, which was the Siegel conjecture, and that was a very famous conjecture in the theory of numbers about approximability of irrationals. And it said if you have any algebraic number which is not rational, so simply a root of an algebraic equation with integer coefficients, a real algebraic number, and you have a rational p over q, then the theorem says that the difference between the irrational and the rational approximation can't be smaller than 1 over q 2, independent of the degree of the algebraic number. So that was the Siegel conjecture, and it was finally proved by Roth about 10 years later, for which Roth got a Fields Medal, I think. Anyway, it was a major accomplishment. So that was what I set myself up as a goal, to prove that conjecture, and I failed and I didn't find the way, and that was what persuaded me that I wasn't really a mathematician. I couldn't solve that problem which would have been really an important contribution to mathematics. It was clearly crying out for somebody to prove it, and in that year in London I didn't prove it. I managed to make only a slight improvement on what was already known. So I decided, well, I might as well do physics and which is at least as interesting and more important.