Benoît B. Mandelbrot (born 20 November 1924) is a French and American mathematician, best known as the father of fractal geometry. He is Sterling Professor of Mathematical Sciences, Emeritus at Yale University; IBM Fellow Emeritus at the Thomas J. Watson Research Center; and Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was born in Poland. His family moved to France when he was a child, and he was educated in France. He is a dual French and American citizen. Mandelbrot now lives and works in the United States.
Mandelbrot was born in Warsaw in a Jewish family from Lithuania. Anticipating the threat posed by Nazi Germany, the family fled from Poland to France in 1936 when he was 11. He remained in France through the war to near the end of his college studies. He was born into a family with a strong academic tradition—his mother was a medical doctor and he was introduced to mathematics by two uncles. His uncle, Szolem Mandelbrojt, was a Parisian mathematician. His father, however, made his living trading clothing. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies. In 1944 he returned to Paris. He studied at the Lycée du Parc in Lyon and in 1945-47 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. From 1947 to 1949 he studied aeronautics at California Institute of Technology. Back in France, he obtained a Ph.D. in Mathematical Sciences at the University of Paris in 1952.
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 then Lille, 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 thirty-two 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. He became convinced that two key themes, fat tails and self-similar structure, ran through a multitude of problems encountered in those fields.
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.
Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' Paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.
In 1975, Mandelbrot coined the term fractal to describe these structures, and published his ideas in Les objets fractals, forme, hasard et dimension (1975; an English translation Fractals: Form, Chance and Dimension was published in 1977). Mandelbrot developed here ideas from the article Deux types fondamentaux de distribution statistique (1938; an English translation Two Basic Types of Statistical Distribution) of Czech geographer, demographer and statistician Jaromír Korčák.
The Mandelbrot set and periodicities of orbits.
While on secondment as Visiting Professor of Mathematics at Harvard University in 1979, 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 of the formula z² − μ. While investigating how the topology of these Julia sets depended on the complex parameter μ he studied the Mandelbrot set fractal that is now named after him. (Note that the Mandelbrot set is now usually defined in terms of the formula z² + c, so Mandelbrot's early plots in terms of the earlier parameter μ are left–right mirror images of more recent plots in terms of the parameter c.)
In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature. 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".
Upon his retirement from IBM in 1987, Mandelbrot joined the Yale Department of Mathematics. At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences. His awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003, and the Einstein Lectureship of the American Mathematical Society in 2006. The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Knight in the French Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was promoted to Officer of the French Legion of Honour in January 2006. An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises. 
Fractals and regular roughness
Although Mandelbrot coined the term fractal, some of the mathematical objects he presented in The Fractal Geometry of Nature had been described by other mathematicians. Before Mandelbrot, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to non-smooth objects in the real world. He highlighted their common properties, such as self-similarity (linear, non-linear, or statistical), scale invariance, and a (usually) non-integer Hausdorff dimension.
He also emphasized the use of fractals as realistic and useful models of many "rough" phenomena in the real world. Natural fractals include the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies; and Brownian motion. Fractals are found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry:
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.
Fractal geometry is useful to accurately describe the development and resulting shape of many growth processes evident in nature, both organic and inorganic. Mandelbrot's work has changed the way researchers in many fields both perceive and characterize the phenomenon of natural growth.
Mandelbrot has been called a visionary and a maverick. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.
Honors and awards
A partial list of awards received by Mandelbrot:
* 2004 Best Business Book of the Year Award
* "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", a 1967 paper by Mandelbrot
1. ^ Benoît is pronounced [bənwa] in French. The English pronunciation of the name "Mandelbrot", which is a Yiddish and German word meaning "almond bread", is given variously in dictionaries. The Oxford English Dictionary gives /ˈmændəlbrɒt/ MAN-dl-brot; Merriam-Webster Collegiate Dictionary and the Longman Pronouncing Dictionary give /ˈmændəlbroʊt/ MAN-dl-broht; the Bollard Pronouncing Dictionary of Proper Names gives the pseudo-French pronunciation /ˈmændəlbrɔː/ MAN-dl-braw; and the American Heritage Dictionary gives /ˈmɑːndəlbrɒt/ MAHN-dl-brot. When speaking in French, Mandelbrot pronounces his name [mɑ̃dɛlbʁot]. (Source: recording of the September 11, 2006, ceremony at which Mandelbrot received the Officer of the Legion of honour insignia.)
* The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, by Benoît Mandelbrot and Richard L. Hudson; Basic Books, 2004; ISBN 0-465-04355-0