"I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods — but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality."

“Yale Economic Review - Review of The Behavior of Markets”

“I think it's very important to have both cartoons and more realistic structures. The cartoons have the power of representing the essential very often, but have this intrinsic weakness of being in a certain sense predictable. Once you look at the Sierpinski triangle for a very long time you see more consequences of the construction, but they are rather short consequences, they don't require a very long sequence of thinking. In a certain sense, the most surprising, the richest sciences are those in which we start from simple rules and then go on to very, very long trains of consequences and very long trains of consequences, which you are still predicting correctly.”

“People want to see patterns in the world. It is how we evolved. We descended from those primates who were best at spotting the telltale pattern of a predator in the forest, or of food in the savannah. So important is this skill that we apply it everywhere, warranted or not.”

“Georg Cantor claimed the essence of mathematics lies in its freedom. But mathematicians do not pick problems from thin air for the pleasure of solving them. To the contrary, a mark of greatness resides in the ability to identify the most interesting problems in the framework of what is already known.”

“There is no single rule that governs the use of geometry. I don't think that one exists.”

“A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...”