“Unfortunately, the world has not been designed for the convenience of mathematicians.”

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.

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.

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.

As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.

Mathematicians, like cows in the dark, all look alike to me.