ÐÓ°ÉÔ­´´

What is mathematical creativity?

I firmly believe it is not some magical, mysterious thing, particularly in mathematics, and in other fields too, though I don’t have enough experience of things like poetry or painting to be authoritative. I’m convinced everything can be explained.

How do you analyse it?

It is difficult. The closer you look, the more it seems to dissolve. If you take an idea that seems outstandingly creative, it usually didn’t appear in someone’s head by magic. Some thought process led to it, and this can be broken into smaller ideas until you get down to the lowest level of thought process, which is essentially routine. So if you add up a whole load of routine things, you can somehow end up with something that everyone acknowledges is creative.

So creativity is a procedure or an algorithm?

Yes, but I realise that I’m opening a big can of worms. That statement requires much more justification than I can possibly give in an interview. If I suggest to people that creativity might be algorithmic, they generally say that it cannot be a simple procedure. They are right, it is not a simple procedure. But that doesn’t stop it being a procedure.

How does the creative process happen in mathematics?

There’s a famous passage in the book Littlewood’s Miscellany by the mathematician John Littlewood in which he talks about the different phases of forming a mathematics problem. One of the most important is immersion. You need to spend a long time thinking hard and getting nowhere in the hope that at some later stage you’ll have what feels like a bright idea. Of course, you’d never have had this idea if you hadn’t been through the immersion stage.

What does immersion feel like?

Most of the time it’s very frustrating. You try lots of things that don’t work: 90 to 95 per cent of mathematical research is the process of trying things and discovering that they don’t work. And this is another factor I think is important. Supposing 1 in 100 ideas turns out to work. If all that people see is the 100th idea, they’ll think how extraordinary it was that somebody thought of that. An analogy is videoing yourself rolling four dice and then editing the video to show only the rolls that produce four sixes. It would look rather remarkable.

Has immersion worked for you?

Yes. One example is a theorem of a Hungarian mathematician called Endre Szemerédi that I spent two years thinking about until finally I got a new proof.

Can you break down the creative process that led to this result?

If I go back, I can find explanations for all the new ideas in that proof. When other people saw them, however, the new ideas looked quite novel because a lot of what I’d been doing didn’t make it into the final paper. You cannot just write a big diary of your thought experiences, including your mistakes. It would be too long. Mistakes are an important part of the thought process. It’s a good research strategy to be a little bit cavalier about the details and go back and check them afterwards. It speeds up the process of having ideas.

Immersion sounds similar to obsession.

I think obsession plays an important role. People tend to think of mathematics as some very mysterious thing that is done by people with special brains. But a large part of what makes mathematicians’ brains special is the capacity to become obsessed with a maths problem.

And the reward?

The sort of pleasure you get is like supporting a not terribly good football team. Once in a while the team has some spectacular success that you can live off for several years. In between, you’re yearning for something else to happen. It’s a bit like that.