For much of my life there was no place where the things I wanted to investigate were of interest to anyone.

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated.

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

A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale.

The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may not be true. And that idea is still unproven. It is the foundation, what started me and what everybody failed to **** prove has so far defeated the greatest efforts by experts to be proven.

A formula can be very simple, and create a universe of bottomless complexity.

Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.