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.

The brain, being analog, is able to grasp images so much better. The brain is just designed for comparing images and some patterns - patterns in space and patterns in time - which we do amazingly well. Computers can do it, too, but not in anything like the same kind of flexibility.

As we look out into the Universe and identify the many accidents of physics and astronomy that have worked together to our benefit, it almost seems as if the Universe must in some sense have known that we were coming.

Lucky individuals in each generation find technology appropriate to their needs.

I'm a mathematician, basically. What I do is look around for problems where I can find useful applications for mathematics. All I do, really, is the math, and other people have the ideas.

We cannot hope to either understand or to manage the carbon in the atmosphere unless we understand and manage the trees and the soil too.

The analogies between science and art are very good as long as you are talking about the creation and the performance. The creation is certainly very analogous. The aesthetic pleasure of the craftsmanship of performance is also very strong in science.