Science and religion are two windows that people look through, trying to understand the big universe outside, trying to understand why we are here. The two windows give different views, but they look out at the same universe. Both views are one-sided, neither is complete. Both leave out essential features of the real world. And both are worthy of respect.

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 thing that makes me most optimistic is China and India - both of them doing well.

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

I like people who are working on practical things and who are working in teams. It's not so important to get the glory. It's much more important to get something that works. It's a better way to live.

New directions in science are launched by new tools much more often than by new concepts. The effect of a concept-driven revolution is to explain old things in new ways. The effect of a tool-driven revolution is to discover new things that have to be explained.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.