Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.

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

When people ask me what's my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.

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

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.

An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.