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The Mandelbrot set is the most complex mathematical object known to mankind.

Benoit Mandelbrot

For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
BENOIT MANDELBROT

Interest Life Thing Wanted
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.
BENOIT MANDELBROT

Lying Mountain Nature Science Tree
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.
BENOIT MANDELBROT

Lists Long Yale
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.
BENOIT MANDELBROT

Lines Looks Shapes Straight
There are very complex shapes which would be the same from close by and far away.
BENOIT MANDELBROT

Complex Far Away Shapes
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.
BENOIT MANDELBROT

Case Dull Self Shape Shapes
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
BENOIT MANDELBROT

Circles Clouds Mountain
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.
BENOIT MANDELBROT

Lines Pieces Self
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.
BENOIT MANDELBROT

Luck Persistence Reward
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.
BENOIT MANDELBROT

Chance Steps Together
I had very, very little training in taking an exam to determine a scientist’s life in France.
BENOIT MANDELBROT

France Littles Training
There is a saying that every nice piece of work needs the right person in the right place at the right time.
BENOIT MANDELBROT

Needs Nice Pieces
A formula can be very simple, and create a universe of bottomless complexity.
BENOIT MANDELBROT

Complexity Formulas Simple
The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
BENOIT MANDELBROT

Chaos Mankind Mathematics
The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
BENOIT MANDELBROT

Choices Discipline Intellectual
I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
BENOIT MANDELBROT

Computer Levels Mathematics

The Mandelbrot set is the most complex mathematical object known to mankind.

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The Mandelbrot set is the most complex mathematical object known to mankind.

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