Benoît Mandelbrot
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Reverted edits by [[Special:Contributions/121.223.143.79|121.223.143.79]] to last version by Cydebot (using [[WP:HG|Huggle]])
{{Infobox_Scientist
| name = Benoît Mandelbrot
| image = Benoit Mandelbrot mg 1804b.jpg
| caption = Mandelbrot speaking in 2007 at the [[EPFL]]
| birth_date = {{Birth date and age|1924|11|20|mf=y}}
| birth_place = [[Warsaw, Poland]]
| residence = [[France]], [[United States]]
| nationality = French, American
| ethnicity = [[Lithuanian Jews|Lithuanian-Jewish]]
| field = [[Mathematician]]
| alma_mater = [[École Polytechnique]]<br>[[California Institute of Technology]]<br>[[University of Paris]]
| work_institutions = [[Yale University]]<br>[[International Business Machines|International Business Machines (IBM)]]<br>[[Pacific Northwest National Laboratory]]
| doctoral_advisor =
| doctoral_students = [[F. Kenton Musgrave]]<br>[[Eugene F. Fama]]<br>[[Murad S. Taqqu]]<br>[[Nassim Nicholas Taleb]]<br>[[Daniel Zajdenweber]]<br>[[Yuval Gefen]]<br>[[Adlai J. Fisher]]<br>[[Laurent E. Calvet]]
| known_for = [[Mandelbrot set]]
| prizes = [[Wolf Prize]] (1993)<br>[[Japan Prize]] (2003)
| religion =
| footnotes = nephew of the mathematician [[Szolem Mandelbrojt]].
}}
'''Benoît B. Mandelbrot''' (born [[November 20]], [[1924]]) is a [[Poles|Polish]]-[[French people|French]]-[[Jew]]ish-[[United States|American]] [[mathematics|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 [[multiple citizenship|dual French and American]] citizen and was educated in France. Mandelbrot now lives and works in the [[United States]]. 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]].
==Early years==
Mandelbrot was born in [[Warsaw]] in a [[Lithuanian Jews|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.{{Fact|date=December 2007}} 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.<ref name="wolf">{{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}}</ref>
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 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.<ref name="wolf"/>
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]].<ref name="people">{{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}}</ref>
In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the [[International Business Machines|IBM]] [[Thomas J. Watson Research Center]] in [[Yorktown Heights, New York|Yorktown Heights]], [[New York]].<ref name="people"/> He remained at IBM for thirty-two years, becoming an [[IBM Fellow]], and later Fellow [[Emeritus]].<ref name="wolf"/>
==Later years==
From 1951 onwards Mandelbrot worked on problems and published papers not only in mathematics but also in real-world fields including [[information theory]], [[economics]] and [[fluid dynamics]]. He became convinced that two key themes, [[fat tail]]s and [[self-similar]] structure, ran through a multitude of these problems.
Mandelbrot found that price changes in financial markets did not follow a [[Gaussian distribution]], but rather other [[stable distributions|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.<ref>[http://www.newscientist.com/article/mg15420784.700.html New Scientist, 19 April, 1997]</ref>
Mandelbrot also put his ideas to work in [[cosmology]] and offered in 1974 a different resolution to 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 [[star]]s in the [[universe]] were fractally distributed (e.g., like a [[Cantor dust]]), it would not be necessary to rely on the [[Big Bang]] theory to explain [[Olbers' Paradox]] (a.k.a. the "dark night sky 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.
[[Image:Mandelbrot p1130876.jpg|thumb|Mandelbrot speaking at the École Polytechnique in 2006.]]
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).<ref>''Fractals: Form, Chance and Dimension'', by Benoît Mandelbrot; W H Freeman and Co, 1977; ISBN 0716704730</ref>
In 1979, while on secondment as Visiting Professor of Mathematics at [[Harvard University]], Mandelbrot began to study fractals called [[Julia set]]s 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 ''z''² - 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 ''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'') .
[[Image:Mandelbrot Set - Periodicites.png|100px|thumb|left|Mandelbrot set and periodicities of orbits.]]
In 1982 Mandelbrot expanded and updated his ideas in ''The Fractal Geometry of Nature''.<ref>''The Fractal Geometry of Nature'', by Benoît Mandelbrot; W H Freeman & Co, 1982; ISBN 0716711869</ref> This influential work brought fractals into the mainstream of both professional and popular mathematics.
On his retirement from IBM in 1987, Mandelbrot joined the [[Yale University|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 planet [http://www.fourmilab.ch/cgi-bin/uncgi/Yourtel?elements=27500+Mandelbrot+53600+3.1783258+0.19827090+1.39758+328.88052+40.87663+208.0406000+13.20+0.15+MPO35431&aim=10&z=1&edump=-xe 27500 Mandelbrot] was named in his honour. On [[November 23]] [[1990]], he was made a knight in the French [[Légion d'honneur|Legion of honour]]. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the [[Pacific Northwest National Laboratory]].<ref>[http://www.pnl.gov/news/release.asp?id=141 PNNL press release: Mandelbrot joins Pacific Northwest National Laboratory]</ref> Mandelbrot was promoted to officer of the French [[Légion d'honneur|Legion of honour]]
on [[January 1]] [[2006]].<ref>[http://www.legifrance.gouv.fr/WAspad/UnTexteDeJorf?numjo=PREX0508911D ''Légion d'honneur'' announcement of promotion of Mandelbrot to ''officier'']</ref>
==Mandelbrot, fractals, and the new theme of regular roughness==
Although Mandelbrot coined the term ''fractal'', some objects featured in ''The Fractal Geometry of Nature'' had been previously described by other mathematicians. However; 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 around into essential tools for the long-stalled effort of extending the scope of science to non-smooth parts of the real world. He highlighted their common properties, such as self-similarity (linear, non-linear, or statistical), [[scale invariance]] and (usually) non-integer [[Hausdorff dimension]].
He also emphasized the use of fractals as realistic and useful models of many phenomena in the real world that can be viewed as rough. Natural fractals include the shapes of [[mountain]]s, [[coastline]]s and river basins; the structure of plants, [[blood vessel]]s and [[lung]]s; the clustering of [[galaxy|galaxies]]; [[Brownian motion]]. Man-made fractals include [[stock market]] prices but also [[music]], [[painting]] and [[architecture]]. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional [[Euclidean geometry]].
{{cquote|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. – B.Mandelbrot, introduction to ''The Fractal Geometry of Nature''}}
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|}
<div class="thumbcaption">Images portraying various views of the [[Mandelbrot set]].</div>
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Mandelbrot has been called a visionary.<ref name=RLD>{{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
}}</ref> 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. It sparked a widespread popular interest in fractals as well as contributing to [[chaos theory]] and other fields of science and mathematics.
==Pronunciation==
Benoît is read as "ben-wa" {{IPA|[bənwa]}}. The pronunciation of the name "Mandelbrot", which is a [[Yiddish language|Yiddish]] and [[German language|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.<ref>Recording of the September 11, 2006, ceremony during which senator Pierre Laffitte presented the Officer of the Legion of honour insignia to Mandelbrot</ref>
==Honours and awards==
Partial list of awards<ref name="Vita">{{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}}</ref>
{|
|valign="top"|
* 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
|valign="top"|
* 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 Berggren-Priset
* Władysław Orlicz Prize
* Wolf Foundation Prize for Physics
|}
==See also==
* [[Gaston Julia]], (1893–1978), a French mathematician who devised the formula for the [[Julia set]], to which the [[Mandelbrot set]] is strongly related.
* [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension]]
* [[Mandelbrot Competition]]
* [[Skewness risk]] and [[Kurtosis risk]]
==References==
{{Reflist|2}}
==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 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, March 23, 2006.
==External links==
{{wikiquote}}
{{Commons|Benoît Mandelbrot}}
* [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]
* {{MacTutor Biography|id=Mandelbrot}}
* {{MathGenealogy|id=60791}}
* {{peoples Archive|id=2930|title=Benoît Mandelbrot }}
{{Wolf Prize in Physics}}
{{Persondata
|NAME= Mandelbrot, Benoît
|ALTERNATIVE NAMES=
|SHORT DESCRIPTION= [[Mathematician]]
|DATE OF BIRTH= {{Birth date and age|1924|11|20|mf=y}}
|PLACE OF BIRTH= [[Warsaw, Poland]]
|DATE OF DEATH=
|PLACE OF DEATH=
}}
{{DEFAULTSORT:Mandelbrot, Benoit}}
[[Category:1924 births]]
[[Category:Members of the National Academy of Sciences]]
[[Category:20th century mathematicians]]
[[Category:Alumni of the École Polytechnique]]
[[Category:California Institute of Technology alumni]]
[[Category:Chaos theorists]]
[[Category:French Jews]]
[[Category:French mathematicians]]
[[Category:IBM Fellows]]
[[Category:Japan Prize laureates]]
[[Category:Jewish scientists]]
[[Category:Légion d'honneur recipients]]
[[Category:Living people]]
[[Category:Naturalized citizens of the United States]]
[[Category:Polish Jews]]
[[Category:Polish mathematicians]]
[[Category:Americans of Polish descent]]
[[Category:French people of Polish descent]]
[[Category:Wolf Prize in Physics laureates]]
[[Category:Yale University faculty]]
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