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.

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.

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

Always try the problem that matters most to you.

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

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