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.
BENOIT MANDELBROTSome 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.
More Benoit Mandelbrot Quotes
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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
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Bottomless wonders spring from simple rules, which are repeated without end.
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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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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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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Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
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If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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Asking the right questions is as important as answering them
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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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I don’t seek power and do not run around
BENOIT MANDELBROT







