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

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.

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

Always try the problem that matters most to you.

I know it's a rare privilege, but if one can really tackle something in adult life that means that much to you, then it's more rewarding than anything I can imagine.

I never use a computer.