It is in the long run essential to the growth of any new and high civilization that small groups of men can escape from their neighbors and from their government, to go and live as they please in the wilderness. A truly isolated, small, and creative society will never again be possible on this planet.

Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

I think the biggest misconception is that everybody has to learn mathematics. That seems to be a complete mistake.

I just enjoy calculating, and it's an instrument I know how to play. It's almost an athletic performance, in a way. I was just watching the Olympics, and that's how I feel when proving a theorem.

The language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.

When I listen to the public debates about climate change, I am impressed by the enormous gaps in our knowledge, the sparseness of our observations and the superficiality of our theories.

The more I examine the universe and study the details of its architecture, the more evidence I find that the universe in some sense must have known that we were coming.