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.

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.

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

However impenetrable it seems, if you don't try it, then you can never do it.

Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room.

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

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