The language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.

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.

It has become part of the accepted wisdom to say that the twentieth century was the century of physics and the twenty-first century will be the century of biology.

The whole point of science is that most of it is uncertain. That's why science is exciting--because we don't know. Science is all about things we don't understand. The public, of course, imagines science is just a set of facts. But it's not. Science is a process of exploring, which is always partial. We explore, and we find out things that we understand. We find out things we thought we understood were wrong. That's how it makes progress.

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 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.

The biggest breakthrough in the next 50 years will be the discovery of extraterrestrial life. We have been searching for it for 50 years and found nothing. That proves life is rarer than we hoped, but does not prove that the universe is lifeless. We are only now developing the tools to make our searches efficient and far-reaching, as optical and radio detection and data processing move forward.