Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
BENOIT MANDELBROTFor much of my life there was no place where the things I wanted to investigate were of interest to anyone.
More Benoit Mandelbrot Quotes
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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.
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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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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
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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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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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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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There are very complex shapes which would be the same from close by and far away.
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The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
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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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Some 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.
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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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Although computer memory is no longer expensive, there’s always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills
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If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
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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.
BENOIT MANDELBROT