“Being a language, mathematics may be used not only to inform but also, among other things, to seduce.”

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.

Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.

There’s nothing I believe in more strongly than getting young people interested in science and engineering, for a better tomorrow, for all humankind.

Writing a class without its contract would be similar to producing an engineering component (electrical circuit, VLSI (Very Large Scale Integration) chip, bridge, engine…) without a spec. No professional engineer would even consider the idea.

Engineering is too important to wait for science.

Leonardo Da Vinci combined art and science and aesthetics and engineering, that kind of unity is needed once again.

The Reservoir plan is an engineering mechanism applied to the field of economics, and in its essence it has nothing to do with democracy or any other political philosophy.

I kind of think of engineering like the chefs at a restaurant. Nobody’s going to deny chefs are integrally important, but there’s also so many other people who contribute to a great meal.

Death is an engineering problem.

Software engineering economics.