I'm not the sort of person who does my mathematics writing on paper. I do that at the last stage of the game. I do my mathematics in my head. I sit down for a hard day's work and I write nothing all day. I just think. And I walk up and down because that helps keep me awake, it keeps the blood circulating, and I think and think.

I dislike frontiers, political or intellectual, and I find that ignoring them is an essential catalyst for creative thought. Ideas should flow without hindrance in their natural course.

Would you rather be deaf or blind?

There is no clear-cut distinction between example and theory

No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the 'square root' of geometry and, just as understanding the square root of -1 took centuries, the same might be true of spinors.

If theory is the role of the architect, then such beautiful proofs are the role of the craftsman. Of course, as with the great renaissance artists, such roles are not mutually exclusive. A great cathedral has both structural impressiveness and delicate detail. A great mathematical theory should similarly be beautiful on both large and small scales.

In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.