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Benoit Mandelbrot : a life for fractals

Christophe LETELLIER

Benoît Mandelbrot who developed the field of fractal geometry and applied it to physics, biology, finance and many other fields, died on October 14, 2010 in Cambridge, Massachusset, from a pancreatic cancer. He was 85. Benoît Mandelbrot was born on November 20, 1924, to a Lithuanian Jewish family in Warsaw. In 1936 his family fled the Nazis, first to Paris and then to the south of France, where he tended horses and fixed tools [1].

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Benoît Mandelbrot with his wife, Aliette, and his son, Laurent.

After the war he enrolled in the École Polytechnique in Paris, where his sharp eye compensated for a lack of conventional education. His career soon spanned the Atlantic. He earned a master’s degree in aeronautics at the California Institute of Technology, returned to Paris for his doctorate in mathematics in 1952, then went on to the Institute for Advanced Study in Princeton, N.J., for a postdoctoral degree under the mathematician John von Neumann.

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B. Mandelbrot

After several years spent largely at the Centre National de la Recherche Scientifique in Paris, Mandelbrot was hired by I.B.M. in 1958 to work at the Thomas J. Watson Research Center in Yorktown Heights, N.Y. Although he worked frequently with academic researchers and served as a visiting professor at Harvard and the Massachusetts Institute of Technology, it was not until 1987 that he began to teach at Yale, where he earned tenure in 1999.

Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature. In a seminal book, The Fractal Geometry of Nature, published in 1982, Mandelbrot defended mathematical objects that others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in rigorous and vigorous quantitative fashion.”

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Mandelbrot set

For most of his career, Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting a position at Yale University, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.

Mandelbrot traced his work on fractals to a question he first encountered as a young researcher : how long is the coast of Britain ? The answer depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline. In the 1950s, Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a “fractal dimension,” an insight that has proved useful well beyond the field of cartography.

Over nearly seven decades, working with dozens of scientists, Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena. His influence has also been felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honor.

[1] Adapted from Jascha Hoffman, Benoît Mandelbrot, Novel Mathematician, Dies at 85, New York Times, October 16, 2010.

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