“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.”

The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.

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.

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.

All we really want in the end is to be connected once again with the Truth of our being, to realize what it is that wears this mask of self.

When you realize what you are now, the issue of death will solve itself.

I think it’s a response in our minds to perfection. It’s too bad, people not realizing that their minds expand beyond this world.

Inspiration is there all the time. For everyone whose mind is not clouded over with thoughts whether they realize it or not.

Realizing that anyone can do it is the first step.

When I was younger, I felt like I could say anything and it was funny.

You’ve got mountains of your own, I’ll bet on it. Take heart. Be encouraged. Remain steadfast.

Growing up in New York, I was sort of shocked when I realized that my children are Californians.