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.
BENOIT MANDELBROTWhen people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
More Benoit Mandelbrot Quotes
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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.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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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.
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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.
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Order doesn’t come by itself.
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I had very, very little training in taking an exam to determine a scientist’s life in France.
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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.
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In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Nobody will deny that there is at least some roughness everywhere
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A fractal is a way of seeing infinity.
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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.
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I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
BENOIT MANDELBROT