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.

I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal

Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.

I never use a computer.

We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention.

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

Pure mathematicians just love to try unsolved problems - they love a challenge.