Wiles is famous for proving the Fermat’s theorem. He was interviewed on NOVA and has some interesting things to say about creativity, again showing how important it is to think about connections between different areas and the role of rest in creative thinking.
NOVA: On a day-to-day basis, how did you go about constructing your proof?
Wiles AW: I used to come up to my study, and start trying to find patterns. I tried doing calculations which explain some little piece of mathematics. I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about. Sometimes that would involve going and looking it up in a book to see how it’s done there. Sometimes it was a question of modifying things a bit, doing a little extra calculation. And sometimes I realized that nothing that had ever been done before was any use at all. Then I just had to find something completely new; it’s a mystery where that comes from. 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 only way I could relax was when I was with my children. Young children simply aren’t interested in Fermat. They just want to hear a story and they’re not going to let you do anything else.
NOVA: Usually people work in groups and use each other for support. What did you do when you hit a brick wall?
Wiles AW: When I got stuck and I didn’t know what to do next, I would go out for a walk. I’d often walk down by the lake. Walking has a very good effect in that you’re in this state of relaxation, but at the same time you’re allowing the sub-conscious to work on you. And often if you have one particular thing buzzing in your mind then you don’t need anything to write with or any desk. I’d always have a pencil and paper ready and, if I really had an idea, I’d sit down at a bench and I’d start scribbling away.