"The thought that one unifying idea should continue forever is simply not realistic and therefore not to be hoped for, but I think that for quite a number of years still, perhaps if I am lucky to the end of my life, because I would hate to see that stop in my lifetime, those questions will become very active and still somewhat separate, as different branches of learning become accustomed to them. I cannot imagine that this idea would vanish, not because I am so proud of what I've been doing all my life, but because this is not an artificial thought coming from nowhere in no time and vanishing again rapidly in no time. It has in every one of its manifestations profound roots in the history of the various sciences and the various manners of human enterprise and those roots will not be broken. The continuity of these thoughts will continue, and if any substitute comes, if any other name comes, which is possible, the ideas will remain."

“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...”