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

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.

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.

Some mathematicians didn't even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.

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

If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).

Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.