“My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.”

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

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 and expecting to found one would have been pure madness.

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

If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.

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

It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.

The techniques I developed for studying turbulence, like weather, also apply to the stock market

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.

The Mandelbrot set is the most complex mathematical object known to mankind.

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; it is a straight line.

Some mathematicians didn’t even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.

Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.

Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.

A fractal is a way of seeing infinity.

The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.

Order doesn’t come by itself.