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Benoit Mandelbrot, pioneer in fractal geometry, dies at 85

Benoit Mandelbrot, left, accepts the Japan Prize in 2003 with James A. Yorke of the University of Maryland for their work on chaos theory.
Benoit Mandelbrot, left, accepts the Japan Prize in 2003 with James A. Yorke of the University of Maryland for their work on chaos theory. (Shizuo Kambayashi)

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By Martin Weil
Washington Post Staff Writer
Monday, October 18, 2010; 1:46 AM

Benoit Mandelbrot, 85, a groundbreaking mathematician who sought in his work to confront the rough structure of the real world rather than settle for the smooth approximations upon which much science is based, died Oct. 14 in Cambridge, Mass., where he lived. He had pancreatic cancer.

Dr. Mandelbrot was known as a maverick who went his own way in the world of science, frequently crossing the boundaries between disciplines to make important contributions to chaos theory and become a pioneer in what is known as fractal geometry.

He was admired for his original and productive mathematical approaches to problems in disparate areas such as the distribution of galaxies, the turbulent flow of fluids and the behavior of financial markets.

There was much chaos in his own life. He was born in Warsaw into a Jewish family who fled in the 1930s to France for what they hoped would be safety from the Nazis.

As it turned out, Dr. Mandelbrot survived World War II in Nazi-occupied France and was admitted to the best French schools. He went on to hold dual citizenship in France and the United States and to do much-honored work in both countries.

Shunning academic conventions, he became a self-described "wandering scientist," making forays into physics, math and economics, pursuing what he described as "unpredictable interests."

Once, he said, a top American university made him a "very glamorous offer" that was withdrawn "the next day," when the dean became concerned about his excursions outside his academic discipline.

A touchstone of his work and thought was his recognition that an ocean shoreline was not depicted accurately by bold lines of maps and illustrations. Observed sufficiently closely, shorelines were almost intractably irregular, with a small-scale jaggedness that defied any simple depiction or measurement.

For Dr. Mandelbrot, that unruliness was a challenge to create new mathematical techniques for describing it, accounting for it, teasing out the hidden regularities that might exist within it.

His scientific life, he said, was "one long, ardent pursuit of the concept of roughness.''

The rough-smooth pairing was to him one of nature's essential dualities. It was to him another of those principal attributes of reality - hot and cold, bright and dark, strong and weak, heavy and light, that underlay much of science.

His achievements included the development of fractal and multifractal geometry, a geometry that promises an accurate, orderly way of dealing with disorder.


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