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.

That's what I learned from World War II. Things are always more complicated than most people believe.

The technologies which have had the most profound effects on human life are usually simple. A good example of a simple technology with profound historical consequences is hay. ... It was hay that allowed populations to grow and civilizations to flourish among the forests of Northern Europe. Hay moved the greatness of Rome to Paris and London, and later to Berlin and Moscow and New York.

The universe in some sense must have known that we were coming.

Just because you see pictures of glaciers falling into the ocean doesn't mean anything bad is happening. This is something that happens all the time. It's part of the natural cycle of things. We know from measurements that glaciers have been melting for 200 years at least.

A good cause can become bad if we fight for it with means that are indiscriminately murderous. A bad cause can become good if enough people fight for it in a spirit of comradeship and self-sacrifice. In the end it is how you fight, as much as why you fight, that makes your cause good or bad.

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.