name = Benoît Mandelbrot
caption = Mandelbrot in 2007
birth_date = Birth date and age|df=yes|1924|11|20
France; United States
nationality = French
École Polytechnique California Institute of Technology University of Paris
International Business Machines (IBM)
Pacific Northwest National Laboratory
F. Kenton Musgrave Eugene F. Famaamong others
Wolf Prize(1993) Japan Prize(2003)
Benoît B. Mandelbrot [Benoît is read as "ben-wa" IPA| [bənwa] . The pronunciation of the name "Mandelbrot", which is a Yiddish and German word meaning "almond bread", is given variously in dictionaries. The "Merriam-Webster Collegiate Dictionary" and the "Longman Pronouncing Dictionary" give IPA| [ˈmæn.dəlˌbɹoʊt] (first syllable sounds like "man"; last syllable rhymes with "boat"); the "Bollard Pronouncing Dictionary of Proper Names" gives the quasi-French pronunciation IPA| [ˈmæn.dəlˌbɹɔː] (last syllable rhymes with "draw"); the "American Heritage Dictionary" gives IPA| [ˈmɑːn.dəlˌbɹɑt] (first syllable has the vowel sound of the 'a' in "father"; last syllable rhymes with "pot"). Mandelbrot himself, as most Frenchmen do, pronounces his name as IPA| [mɑ̃dɛlbʁot] (roughly maw-dell-brote) when speaking in French. (Source: recording of the September 11, 2006, ceremony at which Mandelbrot received the Officer of the Legion of honour insignia.)] (born 20 November 1924) is a French mathematician, best known as the father of fractal geometry. He was born in
Poland, but his family moved to France when he was a child; he is a dual French and American citizen and was educated in France. Mandelbrot now lives and works in the United States. He is Sterling Professorof Mathematical Sciences, Emeritusat Yale University; IBM FellowEmeritus at the Thomas J. Watson Research Center; and Battelle Fellow at the Pacific Northwest National Laboratory.
Mandelbrot was born in
Warsawin a Jewish family from Lithuania. Anticipating the threat posed by NaziGermany, the family fled from Poland to Francein 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 famous Parisian mathematician. His father, however, made his living trading clothing.Citation | last=Mandelbrot | first=Benoit | contribution=A maverick's apprenticeship | title=The Wolf Prizes for Physics | publisher=Imperial College Press | year=2002 | url=http://www.math.yale.edu/mandelbrot/web_pdfs/mavericksApprenticeship.pdf]
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 Parcin Lyonand in 1945-47 attended the École Polytechnique, where he studied under Gaston Juliaand Paul Lévy. From 1947 to 1949 he studied at California Institute of Technologywhere he studied aeronautics. Back in France, he obtained a Ph.D. in Mathematical Sciences at the University of Parisin 1952.
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 Studyin Princeton, New Jerseywhere he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva, Switzerlandthen Lille, France.Citation | last=Barcellos | first=Anthony | contribution=Interview Of B. B. Mandelbrot | title=Mathematical People | publisher=Birkhaüser | year=1984 | url=http://www.math.yale.edu/mandelbrot/web_pdfs/inHisOwnWords.pdf]
In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM
Thomas J. Watson Research Centerin 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-similarstructure, 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. [ [http://www.newscientist.com/article/mg15420784.700.html "New Scientist", 19 April 1997] ]
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 Bangtheory 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). ["Fractals: Form, Chance and Dimension", by Benoît Mandelbrot; W H Freeman and Co, 1977; ISBN 0716704730]
While on secondment as Visiting Professor of Mathematics at
Harvard Universityin 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 Juliaand Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets of the formula "z"² − μ. While investigating how the topology of these Julia sets depended on the complex parameter μ he studied the Mandelbrot setfractal that is now named after him. (Note that the Mandelbrot set is now usually defined in terms of the formula "z"² + "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". ["The Fractal Geometry of Nature", by Benoît Mandelbrot; W H Freeman & Co, 1982; ISBN 0716711869] This influential work brought fractals into the mainstream of professional and popular mathematics.
Upon his retirement from
IBMin 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 Prizefor Physics in 1993, the Lewis Fry RichardsonPrize of the European Geophysical Societyin 2000, the Japan Prizein 2003, and the Einstein Lectureship of the American Mathematical Societyin 2006. The small planet 27500 Mandelbrotwas 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. [ [http://www.pnl.gov/news/release.asp?id=141 PNNL press release: Mandelbrot joins Pacific Northwest National Laboratory] ] Mandelbrot was promoted to Officer of the French Legion of Honour in January 2006. [ [http://www.legifrance.gouv.fr/WAspad/UnTexteDeJorf?numjo=PREX0508911D "Légion d'honneur" announcement of promotion of Mandelbrot to "officier"] ]
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 marketprices. 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"
Mandelbrot has been called a visionary.cite web | author=Devaney, Robert L. | title="Mandelbrot’s Vision for Mathematics" in "Proceedings of Symposia in Pure Mathematics". Volume 72.1 | publisher=American Mathematical Society | date=2004 | url=http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf | accessdate=2007-01-05] 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 theoryand other fields of science and mathematics.
Honours and awards
A partial list of awards received by Mandelbrot:cite web | author=Mandelbrot, Benoit B. | title=Vita and Publications (Word document) | date=2 February 2006 | url=http://www.math.yale.edu/mandelbrot/web_docs/VitaSeveralPage.doc | accessdate=2007-01-06]
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", a 1967 paper by Mandelbrot
skewness risk, kurtosis risk
Notes and references
* "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
* " [http://news.ft.com/cms/s/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html A focus on the exceptions that prove the rule] ", by Benoît Mandelbrot and Nassim Taleb; Financial Times, 23 March 2006.
Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupeand 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 0-716-72213-5 (re-published by Films for the Humanities & Sciences, ISBN 978-0-7365-0520-8)
* [http://www.math.yale.edu/mandelbrot/ Mandelbrot's page at Yale]
* [http://www.yaleeconomicreview.com/issues/fall2005/fractalfinance Yale Economic Review - Review of The (mis)Behavior of Markets]
* [http://www.polytechnique.edu/interview.php?id=12 Interview of the École Polytechnique site]
* [http://www.bookrags.com/biography/benoit-b-mandelbrot/ Biography of Mandelbrot]
* [http://mitworld.mit.edu/play/52/ Video stream of Mandelbrot lecturing at MIT]
NAME= Mandelbrot, Benoît
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