Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.

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

Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.

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.

An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.

Order doesn't come by itself.

The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.