I've been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I'm not a mathematician only. I'm a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.
Benoit MandelbrotBoth chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
Benoit MandelbrotIf you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
Benoit MandelbrotIf you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
Benoit MandelbrotI 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."
Benoit Mandelbrot