The great advances in science usually result from new tools rather than from new doctrines.

The more I examine the universe and study the details of its architecture, the more evidence I find that the universe in some sense must have known that we were coming.

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 public knows that human beings are fallible. Only people blinded by ideology fall into the trap of believing in their own infallibility.

I grew up in England at a time when England was winning Nobel Prizes right and left. I mean it was amazing how many Nobel Prizes England was winning in chemistry and physics and biology and all the sciences and at that time the teaching of science in the schools was really lousy.

To me, mathematics is like playing the violin. Some people can do it - others can't. If you don't have it, then there's no point in pretending.

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.