I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
BENOIT MANDELBROTAn extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
More Benoit Mandelbrot Quotes
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The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.
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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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The Mandelbrot set is the most complex mathematical object known to mankind.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.
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Asking the right questions is as important as answering them
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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.
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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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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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.
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A formula can be very simple, and create a universe of bottomless complexity.
BENOIT MANDELBROT