There are very complex shapes which would be the same from close by and far away.

The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.

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

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.

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.

There is a saying that every nice piece of work needs the right person in the right place at the right time.