Asking the right questions is as important as answering them
BENOIT MANDELBROTI 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.
More Benoit Mandelbrot Quotes
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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
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Bottomless wonders spring from simple rules, which are repeated without end.
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When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
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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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A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.
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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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I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
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There is a saying that every nice piece of work needs the right person in the right place at the right time.
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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.
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Order doesn’t come by itself.
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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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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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.
BENOIT MANDELBROT