Benoit Mandelbrot

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Benoit Mandelbrot : biography

20 November 1924 – 14 October 2010

Lebanese author and professor Nassim Nicholas Taleb states that Mandelbrot "had perhaps more cumulative influence than any other single scientist in history, with the only close second, Isaac Newton." Taleb adds, "He was the only teacher I ever had, the only person for whom I have had intellectual respect. But there was something else that made him magnetic: he was a raconteur with a profound sense of historical context…."Taleb, Nassim Nicholas. James Gleick, author of the best-selling book, Chaos: Making a New Science, explains further:

Chris Anderson, curator of TED conferences, described Mandelbrot as "an icon who changed how we see the world". The President of France at the time of Mandelbrot’s death, Nicolas Sarkozy, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions". Sarkozy also added, "His work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot’s obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry."

Early years

Mandelbrot was born in Warsaw into a Jewish family from Lithuania. His family had a strong academic tradition — his mother was a dental surgeon, although his father made his living trading clothing. He was first introduced to mathematics by two of his uncles, one of whom, Szolem Mandelbrojt, was a mathematician who resided in Paris. "The love of his mind was mathematics," writes Mandelbrot, in his autobiography.

Anticipating the threat posed by Nazi Germany, the family fled from Poland to France in 1936 when he was 11. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family then moved to Tulle, France. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies.Hemenway P. Divine proportion: Phi in art, nature and science. Psychology Press, 2005 ISBN 0-415-34495-6 Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period:

In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc in Lyon, and in 1945 to 1947 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master’s degree in aeronautics. Returning to France, he obtained his Ph.D. degree in Mathematical Sciences at the University of Paris in 1952.

Research career

From 1949 to 1958, Mandelbrot was a staff member at the Centre National de la Recherche Scientifique. During this time he spent a year at the Institute for Advanced Study in Princeton, New Jersey, where he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva, Switzerland, and later to the Université Lille Nord de France. In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow Emeritus.

From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics.

Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having theoretically infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.

As a visiting professor at Harvard University, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set fractal that is now named after him. In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature., by Benoît Mandelbrot; W H Freeman & Co, 1982; ISBN 0-7167-1186-9 This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".