Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

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

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

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.

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.

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

Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.

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

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.

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.

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