The Mandelbrot set is the most complex mathematical object known to mankind.
BENOIT MANDELBROTThe rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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Think not of what you see, but what it took to produce what you see.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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.
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Asking the right questions is as important as answering them
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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.
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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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One couldn’t even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn’t expect and expecting to found one would have been pure madness.
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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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 way of seeing infinity.
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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 don’t seek power and do not run around
BENOIT MANDELBROT