“Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.”

Some mathematicians didn’t even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.

Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.

A fractal is a way of seeing infinity.

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.

Order doesn’t come by itself.

My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.

Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.

I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.

The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.

Being a language, mathematics may be used not only to inform but also, among other things, to seduce.

Asking the right questions is as important as answering them

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.

Nobody will deny that there is at least some roughness everywhere

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.

It’s a great life, and Margaret and I are going to stay put above the Arctic Circle where we’re happy.

I’m conscious of a series of circles working its way through my life. And at this particular moment I have come round to the beginning of my writing cycle. It begins with poetry. There’s hardly a day that goes past on which I don’t write poetry.

It’s true that the Federal Reserve faces a lot of political pressure and is unpopular in many circles.

To refrain from storytelling is perhaps one of the highest forms of respect we can pay. Those people, with no stories to circle them, can die without being misunderstood.

It was a real surprise to me to come across the evidence that Christianity might once have been a danced religion. Certainly, some of the early church leaders thought this was great and spoke of what seems to have been circle dancing, perhaps around an altar.

Evolutionary circles are one of the key social forms in which people are connecting and can connect to make a difference throughout the world.

When he gets mad, it’s like he’s in another world. He’ll look at you with those big eyes and they’ll be going around in circles.

[T]here is only one large circle that we march in, around and around, each of us with our own little picture — in front of us — our own little mirage that we think is the future.