David: For you, is mathematics something discovered or invented?

GC: You know, there is mathematics that, as Ulam puts it, fills in much-needed gaps. There are pieces of mathematics and when you find them, they seem sort of inevitable afterwards – they weren’t in advance – and when you find a thing like that, then it seems more real, then it seems that you’re discovering it. But let’s face it, from a practical point of view we’re inventing it as we go.

But it’s true that on good days, when you’ve found something that you really love, you say, ‘Oh, my God.’ You have a feeling of inevitability that you’re discovering something, that there’s this beautiful thing out there that it really doesn’t feel like any mortal could have invented it. It seems to be something from the Platonic universe of beautiful ideas or from God’s mind. Who knows?

So that’s if you’re very lucky. The whole thing seems so beautiful and so natural and so fundamental that you say, ‘How come I didn’t see it before? How come nobody saw it before?’

That’s a very wonderful feeling, I have to say. But it took ten years to get there because the mathematics was clumsy and awkward, as new mathematics always is. Then people polish it for 300 years... But discovering mathematics is messy, like making love; it’s messy.

David: But the outcome…

GC: The outcome can be…

David: Extremely pleasurable!

GC: Yeah, and it can also be a baby, another human being, who can be a great artist or something. But there are wonderful moments when, yes, you have this feeling, and then moments like that you say, ‘Well, it wasn’t me. I didn’t discover this. This idea exists out there independently of me and maybe it wanted to use me to express itself.’

But maybe it’s a way of fooling ourselves. But this is the kind of thing that helps you to do good mathematics. You have to be inspired. It’s profoundly emotional. I mean, the best mathematics is an art. It’s totally creative. You have to throw your whole personality at it. And it may be that you discover something because you’re crazy. You were the right crazy person to come up with this crazy idea, but other crazy people don’t find anything because their craziness isn’t in sync with the next discovery that had to be made.

David: I was fascinated when you said, ‘Sometimes you feel like the idea just needed you.’

GC: It needed people to express it. It wanted to incarnate, so to speak.

David: Well, I sometimes think that ideas are like a seed.

GC: Absolutely.

David: And that the mind is like a garden. So when people say, ‘I did this,’ I always think to myself that it would be like a little lump of dirt saying to you, ‘Look at the flower I made.’

GC: I absolutely agree with you, David. I remember Benoit Mandelbrot was in a documentary as he was dying, and you could barely hear his voice – they had to put subtitles – and he was saying, ‘I discovered a beautiful world.’

It feels like it’s out there, and you feel very lucky to have stumbled on it. But I don’t think you can take the credit. It’s like climbing mountains: you climb a mountain to get a better view, to see further, and one always feels that there are other mountain ranges that are higher. In the distance you can see still higher mountains, and the ranges never stop and it always gets higher. The further you see, the more you realise that there are.

So, for example, I’ve worked on Omega, but what is consciousness? What is the mind? How does the brain work? Can you prove that Darwinian evolution works? Where do new species come from? I mean, there’s endless questions, and each question just opens more questions.