“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.”

My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.

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.

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.

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.

Just learning how to read music requires metrics, and I think that helps you with mathematics. A lot of scientists and doctors have a musical background – it’s very interesting.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express.

The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation.

Thus number may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician.

In 2010, my two Harvard mathematician colleagues and I dismantled kin-selection theory, which was the reigning theory of the origin of altruism at the time.

I am not enough of a mathematician to be able to judge either the well-foundedness or the limits of relativity in physics.