If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.

For much of my life there was no place where the things I wanted to investigate were of interest to anyone.

Bottomless wonders spring from simple rules, which are repeated without end.

Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.

The most important thing I have done is to combine something esoteric with a practical issue that affects many people.

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

I've been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I'm not a mathematician only. I'm a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.