“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.”

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.

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

It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.

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

I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

The Mandelbrot set is the most complex mathematical object known to mankind.

If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.

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.

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.

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.

If we want users to like our software we should design it to behave like a likeable person: respectful, generous and helpful.

The other one, and probably an equal pleasure, is finding out how I can be helpful and then really being helpful.

It was universal pressure on the regime to secure my release. International pressure was certainly helpful in my release.

It’s been very helpful for my career, but I’m trying to stay on the path I was on before.

Some critics have commented that understanding the specific Brazilian political context of the novel is helpful for reading Quiet Creature. This may be true, but it’s not prerequisite for understanding it.

Dissenting opinions are useful even when they’re wrong. So instead of speaking to highly agreeable audiences, target suggestions to people with a history of originality.

Writing is the process of finding something to distract you from writing, and of all the helpful distractions – adultery, alcohol and acedia, all of which aided our writing fathers – none can equal the Internet.

Your aim will be knowledge and wisdom, not the reflected glamour of fame.