Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
BENOIT MANDELBROTIf 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.
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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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.
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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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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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Asking the right questions is as important as answering them
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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I had very, very little training in taking an exam to determine a scientist’s life in France.
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In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.
BENOIT MANDELBROT







