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

Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.

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.

When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.

I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.

The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.

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

Asking the right questions is as important as answering them

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.

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.