My fate has been that what I undertook was fully understood only after the fact.
BENOIT MANDELBROTI went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
More Benoit Mandelbrot Quotes
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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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Engineering is too important to wait for science.
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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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I’ve been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I’m not a mathematician only. I’m a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.
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Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
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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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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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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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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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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Nobody will deny that there is at least some roughness everywhere
BENOIT MANDELBROT