- Benoît Mandelbrot
Infobox_Scientist
name = Benoît Mandelbrot
caption = Mandelbrot in 2007
birth_date = Birth date and age|df=yes|1924|11|20
birth_place =Warsaw ,Poland
residence =France ;United States
nationality = French
ethnicity =
field =Mathematician
alma_mater =École Polytechnique California Institute of Technology University of Paris
work_institutions =Yale University
International Business Machines (IBM)Pacific Northwest National Laboratory
doctoral_advisor =
doctoral_students =F. Kenton Musgrave Eugene F. Fama among others
known_for =Mandelbrot set
prizes =Wolf Prize (1993)Japan Prize (2003)
religion =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 theUnited States . He isSterling Professor of Mathematical Sciences,Emeritus atYale University ;IBM Fellow Emeritus at theThomas J. Watson Research Center ; and Battelle Fellow at thePacific Northwest National Laboratory .Early years
Mandelbrot was born in
Warsaw in a Jewish family fromLithuania . Anticipating the threat posed byNazi Germany, the family fled from Poland toFrance 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 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 toTulle . He was helped by RabbiDavid Feuerwerker , the Rabbi of Brive-la-Gaillarde, to continue his studies. In 1944 he returned to Paris. He studied at theLycée du Parc inLyon and in 1945-47 attended theÉcole Polytechnique , where he studied underGaston Julia andPaul Lévy . From 1947 to 1949 he studied atCalifornia Institute of Technology where he studied aeronautics. Back in France, he obtained a Ph.D. in Mathematical Sciences at theUniversity of Paris in 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 theInstitute for Advanced Study inPrinceton, New Jersey where he was sponsored byJohn von Neumann . In 1955 he married Aliette Kagan and moved toGeneva ,Switzerland thenLille ,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 Center in Yorktown Heights,New York . He remained at IBM for thirty-two years, becoming anIBM Fellow , and later FellowEmeritus .Later years
From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as
information theory ,economics , andfluid dynamics . He became convinced that two key themes,fat tail s andself-similar structure, ran through a multitude of problems encountered in those fields.Mandelbrot found that price changes in
financial market s did not follow aGaussian distribution , but rather Lévy stable distributions having theoretically infinitevariance . 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 largerscale 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 ofOlbers' 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 thestar s in the universe were fractally distributed (for example, likeCantor dust ), it would not be necessary to rely on theBig 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). ["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 University in 1979, Mandelbrot began to study fractals calledJulia set s that were invariant under certain transformations of thecomplex plane . Building on previous work byGaston Julia andPierre 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 theMandelbrot set fractal 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
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 theWolf Prize for Physics in 1993, theLewis Fry Richardson Prize of theEuropean Geophysical Society in 2000, theJapan Prize in 2003, and the Einstein Lectureship of theAmerican Mathematical Society in 2006. The small planet27500 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 thePacific 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-integerHausdorff 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
mountain s,coastline s andriver basin s; the structures of plants,blood vessel s andlung s; the clustering of galaxies; andBrownian motion . Fractals are found in human pursuits, such asmusic ,painting ,architecture , andstock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditionalEuclidean 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"
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