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Benoît B. Mandelbrot^{[1]} (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.
Early years
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.^{[2]} 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 BrivelaGaillarde, to continue his studies. In 1944 he returned to Paris. He studied at the Lycée du Parc in Lyon and in 194547 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 studied aeronautics. Back in France, he obtained a Ph.D. in Mathematical Sciences at the University of Paris in 1952.^{[2]}
From 1949 to 1957 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.^{[3]}
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.^{[3]} He remained at IBM for thirtytwo years, becoming an IBM Fellow, and later Fellow Emeritus.^{[2]}
Later years
Mandelbrot speaking at the École Polytechnique in 2006, during the ceremony when he was made an officer of the
Legion of Honour.
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 selfsimilar 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.^{[4]}
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).^{[5]} Mandelbrot developed here ideas from the article Deux types fondamentaux de distribution statistique^{[6]} (1938; an English translation Two Basic Types of Statistical Distribution) of Czech geographer, demographer and statistician Jaromír Korčák.
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.^{[7]} 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.^{[8]} Mandelbrot was promoted to Officer of the French Legion of Honour in January 2006.^{[9]}
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 nonintuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the longstalled effort to extend the scope of science to nonsmooth objects in the real world. He highlighted their common properties, such as selfsimilarity (linear, nonlinear, or statistical), scale invariance, and a (usually) noninteger 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.
—Mandelbrot, in his introduction to The Fractal Geometry of Nature
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.
A limb of a maple tree, illustrating organic fractal branching.
Natural water frost crystal growth on cold glass, showing fractal branching growth in a purely physical system.
Mandelbrot has been called a visionary^{[10]} and a maverick.^{[11]} 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 nonspecialists. 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:^{[12]}
 2004 Best Business Book of the Year Award
 AMS Einstein Lectureship
 Barnard Medal
 Caltech Service
 Casimir Frank Natural Sciences Award
 Charles Proteus Steinmetz Medal
 Franklin Medal

 Harvey Prize
 Honda Prize
 Humboldt Preis
 IBM Fellowship
 Japan Prize
 John Scott Award
 Lewis Fry Richardson Medal

 Medaglia della Presidenza della Repubblica Italiana
 Médaille de Vermeil de la Ville de Paris
 Nevada Prize
 Science for Art
 Sven BerggrenPriset
 Władysław Orlicz Prize
 Wolf Foundation Prize for Physics

See also
Notes and references
 ^ 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/ MANdlbrot; MerriamWebster Collegiate Dictionary and the Longman Pronouncing Dictionary give /ˈmændəlbroʊt/ MANdlbroht; the Bollard Pronouncing Dictionary of Proper Names gives the pseudoFrench pronunciation /ˈmændəlbrɔː/ MANdlbraw; and the American Heritage Dictionary gives /ˈmɑːndəlbrɒt/ MAHNdlbrot. 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.)
 ^ ^{a} ^{b} ^{c} Mandelbrot, Benoit (2002), "A maverick's apprenticeship", The Wolf Prizes for Physics, Imperial College Press, http://www.math.yale.edu/mandelbrot/web_pdfs/mavericksApprenticeship.pdf
 ^ ^{a} ^{b} Barcellos, Anthony (1984), "Interview Of B. B. Mandelbrot", Mathematical People, Birkhaüser, http://www.math.yale.edu/mandelbrot/web_pdfs/inHisOwnWords.pdf
 ^ New Scientist, 19 April 1997
 ^ Fractals: Form, Chance and Dimension, by Benoît Mandelbrot; W H Freeman and Co, 1977; ISBN 0716704730
 ^ Jaromír Korčák (1938): Deux types fondamentaux de distribution statistique. Prague, Comité d’organisation, Bull. de l'Institute Int'l de Statistique, vol. 3, pp. 295–299.
 ^ The Fractal Geometry of Nature, by Benoît Mandelbrot; W H Freeman & Co, 1982; ISBN 0716711869
 ^ PNNL press release: Mandelbrot joins Pacific Northwest National Laboratory
 ^ Légion d'honneur announcement of promotion of Mandelbrot to officier
 ^ Devaney, Robert L. (2004). ""Mandelbrot’s Vision for Mathematics" in Proceedings of Symposia in Pure Mathematics. Volume 72.1". American Mathematical Society. http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf. Retrieved 20070105.
 ^ Jersey, Bill (April 24, 2005). "A Radical Mind". Hunting the Hidden Dimension. NOVA/ PBS. http://www.pbs.org/wgbh/nova/fractals/mandelbrot.html. Retrieved 20090820.
 ^ Mandelbrot, Benoit B. (2 February 2006). "Vita and Awards (Word document)". http://www.math.yale.edu/mandelbrot/web_docs/VitaSeveralPage.doc. Retrieved 20070106.
Further reading
 The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, by Benoît Mandelbrot and Richard L. Hudson; Basic Books, 2004; ISBN 0465043550
 A focus on the exceptions that prove the rule, by Benoît Mandelbrot and Nassim Taleb; Financial Times, 23 March 2006.
 HeinzOtto Peitgen, Hartmut Jürgens, Dietmar Saupe and Cornelia Zahlten: Fractals: An Animated Discussion (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. ISBN 0716722135 (republished by Films for the Humanities & Sciences, ISBN 9780736505208)
 A Multifractal Walk down Wall Steet by Benoit Mandelbrot, Scientific American, February 1999 [1]
 "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature", NOVA, WGBH TV, PBS, October 28, 2008.
 The Fractal Geometry of Nature, by Benoît Mandelbrot; W. H. Freeman, 1983; ISBN 0716711869
External links
Persondata 
NAME 
Mandelbrot, Benoît 
ALTERNATIVE NAMES 

SHORT DESCRIPTION 
Mathematician 
DATE OF BIRTH 
20 November 1924 (19241120) (age 85) 
PLACE OF BIRTH 
Warsaw, Poland 
DATE OF DEATH 

PLACE OF DEATH 
