“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.”

Nobody will deny that there is at least some roughness everywhere

The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…

I don’t seek power and do not run around

I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.

A formula can be very simple, and create a universe of bottomless complexity.

In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.

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.

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

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.

There is a saying that every nice piece of work needs the right person in the right place at the right time.

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.

Engineering is too important to wait for science.

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

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 message to everybody else, and the buffer fills

Bottomless wonders spring from simple rules, which are repeated without end.

Part of the middle class promise is that, after a lifetime of hard work, you’ll be able to retire and enjoy the fruits of that labor.

Which is why I think any loving, committed couple — gay or straight — should be able to get married.

We’re all fortunate to be able to be doing this for a living, so we’re just grateful to be here and we just do what we do and we let the people decide.

Each one of us has his own place in the industry. I’ve been able to prove that you don’t necessarily have to be a Khan to be successful!

I’ve been able to work for so long because I think next time, I’ll make something good.

I can control most things, but I don’t seem to be able to control death.

To have the Raiders global, and we’re not going to be able to do that with a half-filled stadium.

I wasn’t really able to love someone but I couldn’t help but want to be loved.