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.

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.

I mean science was blamed for all the horrors of World War I, just as it's blamed today for nuclear weapons and quite rightly.

Many of the technologies that are now racing ahead most rapidly, replacing human workers in factories and offices with machines, making stockholders richer and workers poorer, are indeed tending to accentuate the existing inequalities in the distribution of wealth.

The average student emerges at the end of the Ph.D. program, already middle-aged, overspecialized, poorly prepared for the world outside, and almost unemployable except in a narrow area of specialization. Large numbers of students for whom the program is inappropriate are trapped in it, because the Ph.D. has become a union card required for entry into the scientific job market.

The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily over time. Also, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily over time.

I think it's a big mistake to decide too soon what you're going to do with your life.