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

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.

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.

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.

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.

When I was working in my first job engineering construction, what I liked the most was working with architects and making buildings that had this creative side coming from the architect and that were making them a big success.

I don’t know technology and engineering. I don’t know accounting.

I think a craft becomes an art form when the space of possible solutions becomes so huge that engineering can’t carry you through.

There’s nothing I believe in more strongly than getting young people interested in science and engineering, for a better tomorrow, for all humankind.

Writing a class without its contract would be similar to producing an engineering component (electrical circuit, VLSI (Very Large Scale Integration) chip, bridge, engine…) without a spec. No professional engineer would even consider the idea.

Engineering is too important to wait for science.

Leonardo Da Vinci combined art and science and aesthetics and engineering, that kind of unity is needed once again.

The Reservoir plan is an engineering mechanism applied to the field of economics, and in its essence it has nothing to do with democracy or any other political philosophy.