Is there math that goes far beyond that which is taught at graduate school? If so, how much? Is it likely that a mathematician will run out of problems to solve and theorems to prove in his or her lifetime?
When Stanislaw Ulam was alive, the rate of theorems that were published per year was 200 000. This, I think, was in the 70s. Today it's a larger number for sure. Now imagine the amount of mathematics there is out there. Just from 1975 to 2011 there were 7 200 000 theorems published.