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."

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

Being a language, mathematics may be used not only to inform but also, among other things, to seduce.

I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

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

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

In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.