What did it feel like proving Fermat’s last theorem after searching for a proof for so long?
It’s just fantastic. This is what we live for, these moments that create illumination and excitement. It’s actually hard to settle down and do anything – [you’re] living on cloud nine for a day or two. It was a little difficult at first to go back to the normal working life. I think it was hard to go back to normal problems.
.. Now what you have to handle when you start doing mathematics as an older child or as an adult is accepting this state of being stuck. People don’t get used to that. Some people find this very stressful. Even people who are very good at mathematics sometimes find this hard to get used to and they feel that’s where they’re failing. But it isn’t: it’s part of the process and you have to accept [and] learn to enjoy that process. Yes, you don’t understand [something at the moment] but you have faith that over time you will understand — you have to go through this.
.. It’s like training in sport. If you want to run fast, you have to train. Anything where you’re trying to do something new, you have to go through this difficult period. It’s not something to be frightened of. Everybody goes through it.
.. What I fight against most in some sense, [when talking to the public,] is the kind of message, for example as put out by the film Good Will Hunting, that there is something you’re born with and either you have it or you don’t. That’s really not the experience of mathematicians.
.. Sometimes I put something down for a few months, I come back and it’s obvious. I can’t explain why. But you have to have the faith that that will come back.
.. The way some people handle this is they work on several things at once and then they switch from one to another as they get stuck.
.. Once I’m stuck on a problem I just can’t think about anything else. It’s more difficult. So I just take a little time off and then come back to it.
.. I really think it’s bad to have too good a memory if you want to be a mathematician. You need a slightly bad memory because you need to forget the way you approached [a problem] the previous time because it’s a bit like evolution, DNA. You need to make a little mistake in the way you did it before so that you do something slightly different and then that’s what actually enables you to get round [the problem].
So if you remembered all the failed attempts before, you wouldn’t try them again. But because I have a slightly bad memory I’ll probably try essentially the same thing again and then I realise I was just missing this one little thing I needed to do
.. I think that’s sometimes a little frustrating for mathematicians because we’re thinking in terms of beauty and creativity and so on, and of course the outside world thinks of us as much more like a computer. It’s not how we think of ourselves at all.
.. Do you think maths is discovered or invented?
To tell you the truth, I don’t think I know a mathematician who doesn’t think that it’s discovered. So we’re all on one side, I think.