Benoit Mandelbrot

After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM, where he became an IBM Fellow, and periodically took leaves of absence to teach at Harvard University. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences. Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the Mandelbrot set in 1979-1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess", or "chaotic", such as clouds or shorelines, actually had a "degree of order". His math- and geometry-centered research included contributions to such fields as statistical physics, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, economics, geology, medicine, physical cosmology, engineering, chaos theory, econophysics, metallurgy, and the social sciences. Toward the end of his career, he was the Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique. During his career he received over 15 honorary doctorates, served on many science journals, and won numerous awards. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012.

Benoit Mandelbrot studied at lycée du Parc, École polytechnique and California Institute of Technology. Training under Gaston Julia is recorded. Eugene Fama is recorded as having studied under Benoit Mandelbrot. The recorded working language is French and English. The field of work recorded is fractal. Employment is recorded with IBM, Yale University and Institute for Advanced Study. Works named in the authority record are Mandelbrot set, Fractals: Form, Chance and Dimension, The Fractal Geometry of Nature and Zipf–Mandelbrot law. Distinctions recorded are Officer of the Legion of Honour, IBM Fellow, William Procter Prize for Scientific Achievement and Wolf Prize in Physics.

• Name — Benoit B. Mandelbrot • Birth Name — Benedykt Mandelbrot • Born — 20 November 1924 • Birthplace — Warsaw, Poland • Died — 14 October 2010 • Place of death — Cambridge, Massachusetts, U.S. • Fields — * Mathematics • Aerodynamics • Thesis Title — Contributions à la théorie mathématique des jeux de hasard • Thesis Url — https: hal.science/hal-04092602 • Thesis Year — 1952 • Doctoral Advisor — Paul Lévy • Doctoral Students — * L. E. Calvet • Ken Musgrave • Murad Taqqu • Known for — * Mandelbrot set • Chaos theory • Fractals • Zipf–Mandelbrot law • Awards — Légion d'honneur (Chevalier 1990Officier 2006) • Workplaces — * Yale University • IBM • PNNL

Benedykt Mandelbrot was born into a Lithuanian Jewish family in Warsaw during the Second Polish Republic. His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me." In 1936, when he was 11, the family emigrated from Poland to France. The move, World War II, and the influence of his father's brother, the mathematician Szolem Mandelbrojt (who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes. Mandelbrot attended the Lycée Rollin (now the Collège-lycée Jacques-Decour) in Paris until the start of World War II, when his family moved to Tulle, France, where he enrolled in Lycée Edmond Perrier. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies. Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period: Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her... We escaped this fate. Who knows why? In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc in Lyon, and in 1945 to 1947 attended the prestigious École Polytechnique, where he studied under French mathematicians Gaston Julia and Paul Lévy. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics. Returning to France, he obtained his PhD degree 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 (to collaborate with Jean Piaget at the International Centre for Genetic Epistemology) and later to the Université Lille Nord de 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 35 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.

Mandelbrot saw financial markets as an example of "wild randomness", characterized by concentration and long-range dependence. He developed several original approaches for modelling financial fluctuations. In his early work, he found that the price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having 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. The latter work from the early 60s was done with daily data of cotton prices from 1900, long before he introduced the word 'fractal'. In later years, after the concept of fractals had matured, the study of financial markets in the context of fractals became possible only after the availability of high frequency data in finance. In the late 1980s, Mandelbrot used intra-daily tick data supplied by Olsen & Associates in Zurich to apply fractal theory to market microstructure. This cooperation led to the publication of the first comprehensive papers on scaling law in finance. This law shows similar properties at different time scales, confirming Mandelbrot's insight of the fractal nature of market microstructure. Mandelbrot's own research in this area is presented in his books Fractals and Scaling in Finance and The (Mis)behavior of Markets.

As a visiting professor at Harvard University, Mandelbrot began to study mathematical objects 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. While investigating the topology of these Julia sets, he studied the Mandelbrot set which he began visualizing in late 1979 and first published on in 1980. • Illustration — Mandelbrot speaking about the Mandelbrot set, during his acceptance speech for the Légion d'honneur in 2006 In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas in the French book Les Objets Fractals: Forme, Hasard et Dimension, later translated in 1977 as Fractals: Form, Chance and Dimension. According to computer scientist and physicist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics... to areas that had barely seen the light of serious mathematics before". Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals": Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesque broccoli are two examples from nature." He points out an unexpected conclusion: One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot. Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s psychedelic art with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist Johannes Kepler, who calculated and described the orbits of the planets. • Illustration — A Mandelbrot set Mandelbrot, however, never felt he was inventing a new idea. He described his feelings in a documentary with science writer Arthur C. Clarke: According to Clarke, "the Mandelbrot set is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence": the name Mandelbrot, and the word "mandala"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas. 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". In 1987, Mandelbrot joined the Department of Mathematics at Yale, while continuing as an IBM Fellow until his fellowship ended in 1993. He joined the Department of Mathematics at Yale, and obtained his first tenured post in 1999, at the age of 75. He invited his colleague Michael Frame to work at Yale and co-published various articles with him. At the time of Mandelbrot's retirement in 2005, he was Sterling Professor of Mathematical Sciences.

• Fractals: Form, Chance and Dimension, 1977, 2020 * • Mandelbrot, B. (1959) Variables et processus stochastiques de Pareto-Levy, et la repartition des revenus. Comptes rendus de l'Académie des Sciences de Paris, 249, 613–615. • Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79–106. • Mandelbrot, B. (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517–543. • Mandelbrot, B. (1964) Random walks, fire damage amount and other Paretian risk phenomena. Operations Research, 12, 582–585. • Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E, 1997 by Benoit B. Mandelbrot and R.E. Gomory • Mandelbrot, Benoit B. (1997) Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, Springer. • Fractales, hasard et finance, 1959–1997, 1 November 1998 • Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976) (Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot * • Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot) 14 December 2001 by Benoit Mandelbrot and F.J. Damerau • Mandelbrot, Benoit B., Gaussian Self-Affinity and Fractals, Springer: 2002. • Fractals and Chaos: The Mandelbrot Set and Beyond, 9 January 2004 • Mandelbrot, Benoit B. (2010). The Fractalist, Memoir of a Scientific Maverick. New York: Vintage Books, Division of Random House. • The Fractalist: Memoir of a Scientific Maverick, 2014 •; (2006) • Heinz-Otto 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. (re-published by Films for the Humanities & Sciences) * • "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature", NOVA, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.

The indie music satirist Jonathan Coulton's song, "Mandelbrot Set", is dedicated to Mandelbrot, who at the time of the song's release "is still alive and teaching math at Yale." The song incorporates the concepts and images associated with order out of chaos. Mandelbrot Set, you're a Rorschach Test on fire You're a day-glo pterodactyl You're a heart-shaped box of springs and wire You're one badass fucking fractal And you're just in time to save the day Sweeping all our fears away You can change the world in a tiny way The (Mandelbrot Set) song's pre-chorus describes a mathematical equation that is not the Mandelbrot set, to which Coulton has said, "if any of you are mathematicians and you're just waiting anxiously to come up to me afterwards and point out the fact that the equation is not quite right, that I actually described a Julia set, and not a Mandelbrot set, I already know that shit." Mandelbrot appears in the Epstein files. Less than two years removed from his initial sentencing in Florida, in an email exchange Epstein offered $50,000 for Mandelbrot's papers. Mandelbrot ultimately postponed selling his papers, giving his declining health as reason. A meeting was scheduled in Cambridge on Sept. 12, 2010. The pair were also photographed together at some point at Epstein's New York City home.

The authorities additionally record the headings Mandelbrot, B. B, Benoît Mandelbrot and Benoit B. His recorded languages were French and English. He married Aliette Kagan. Other recorded relations include Szolem Mandelbrojt.

Benoit Mandelbrot worked in fractal. He was employed by IBM, Yale University, Institute for Advanced Study, University of Lille and National Center for Scientific Research. He belonged to College of 'Pataphysics, National Academy of Sciences, American Academy of Arts and Sciences, American Association for the Advancement of Science and Institute of Mathematical Statistics.

Benoit Mandelbrot is recorded as having received Officer of the Legion of Honour, IBM Fellow and William Procter Prize for Scientific Achievement.