Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory..

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

Asking the right questions is as important as answering them.

The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'..

Unfortunately, the world has not been designed for the convenience of mathematicians..

Although computer memory is no longer expensive, there's always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a m….

If 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; i….

Engineering is too important to wait for science..

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

I didn't want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to ….

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal..

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree..

Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar agai….

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name ….

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, o….

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

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and frag….

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

Think not of what you see, but what it took to produce what you see..

There are very complex shapes which would be the same from close by and far away..

One couldn't even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn't expect….