If you're in the business world, that's what's expected: You should go bust and then start again on something else. So it's a much more relaxed kind of a culture. It's also competitive, but not in such a vicious way. I think the academic world is actually much more destructive of young people.

When I listen to the public debates about climate change, I am impressed by the enormous gaps in our knowledge, the sparseness of our observations and the superficiality of our theories.

So long as you have courage and a sense of humor, it is never too late to start life afresh.

The Besicovitch style is architectural. He builds out of simply elements a delicate and complicated architectural structure, usually with a hierarchical plan, and then, when the building is finished, the completed structure leads by simple arguments to an unexpected conclusion. Every Besicovitch proof is a work of art, as carefully constructed as a Bach fugue.

One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.

For me, science is just a bunch of tools - it's like playing the violin. I just enjoy calculating, and it's an instrument I know how to play. It's almost an athletic performance, in a way. I was just watching the Olympics, and that's how I feel when proving a theorem.

The only way to improve the chances for finding winners is to keep all the choices open and try them all.