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.

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

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

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

There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable

If you look at coastlines, if you look at that them from far away, from an airplane, well, you don't see details, you see a certain complication. When you come closer, the complication becomes more local, but again continues. And come closer and closer and closer, the coastline becomes longer and longer and longer because it has more detail entering in.

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.