Beautiful, damn hard, increasingly useful. That's fractals.

Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics

I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid - a term used in this work to denote all of standard geometry - Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."

I had very, very little training in taking an exam to determine a scientist's life in France.

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.

For most of my life, one of the persons most baffled by my own work was myself.

My fate has been that what I undertook was fully understood only after the fact.