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.

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.

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

Then when I reached college, I realized that many people had thought about the problem during the 18th and 19th centuries and so I studied those methods.

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.

There are proofs that date back to the Greeks that are still valid today.