If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
BENOIT MANDELBROTI had very, very little training in taking an exam to determine a scientist’s life in France.
More Benoit Mandelbrot Quotes
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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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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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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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 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 formula can be very simple, and create a universe of bottomless complexity.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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Think not of what you see, but what it took to produce what you see.
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I don’t seek power and do not run around
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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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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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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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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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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Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.
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In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
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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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There are very complex shapes which would be the same from close by and far away.
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My fate has been that what I undertook was fully understood only after the fact.
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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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A fractal is a way of seeing infinity.
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I 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.
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I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not – for the job that I should spend my life in.
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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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For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
BENOIT MANDELBROT