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 had this rare privilege of being able to pursue in my adult life, what had been my childhood dream.

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

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

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.

The only way I could relax was when I was with my children.