Just because we can't find a solution it doesn't mean that there isn't one.

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

The greatest problem for mathematicians now is probably the Riemann Hypothesis.

I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.

But the best problem I ever found, I found in my local public library.

Mathematics... is a bit like discovering oil. ... But mathematics has one great advantage over oil, in that no one has yet ... found a way that you can keep using the same oil forever.

Then when I reached college, I realized that many people had thought about the problem during the 18th and 19th centuries and so I studied those methods.