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I had very, very little training in taking an exam to determine a scientist’s life in France.

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
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.
BENOIT MANDELBROT

Circles Lines Shapes
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
$Benoit Mandelbrot Quote - A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…$

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
BENOIT MANDELBROT

Definitions Scales Science
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
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).
BENOIT MANDELBROT

Nature Past Science
Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
BENOIT MANDELBROT

Fashion Happen Mathematics Strong
$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$

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.
BENOIT MANDELBROT

Chaos Shapes Strong
I was in an industrial laboratory because academia found me unsuitable
BENOIT MANDELBROT

Academia Found Laboratory
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
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
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
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
Think not of what you see, but what it took to produce what you see.
BENOIT MANDELBROT

Produce See Thinking Took
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
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.
BENOIT MANDELBROT

Powerful Science Tool

I had very, very little training in taking an exam to determine a scientist’s life in France.

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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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