Nobody will deny that there is at least some roughness everywhere

Beautiful, damn hard, increasingly useful. That's fractals.

The techniques I developed for studying turbulence, like weather, also apply to the stock market

If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.

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.

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.

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