Benoit Mandelbrot

Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath who focused on practical science, particularly what he called "the art of roughness" in physical phenomena and "the uncontrolled element in life." He called himself a "fractalist" and is known for founding fractal geometry, a field for which he invented the term "fractal" and built a theory of "roughness and self-similarity" in nature.

At age 11, in 1936, Mandelbrot and his family left Warsaw, Poland, for France. After World War II, he studied mathematics, earning degrees from universities in Paris and the United States, plus a master's in aeronautics from the California Institute of Technology. He held dual French and American citizenship and spent most of his career in both countries. In 1958, he started a 35-year stint at IBM, where he became an IBM Fellow, and took occasional leaves to teach at Harvard University. There, after publishing a study of U.S. commodity markets focused on cotton futures, he taught economics and applied sciences.

Thanks to access to IBM's computers, Mandelbrot was among the first to use computer graphics to generate and display fractal geometric images, which led to his discovery of the Mandelbrot set in 1979–1980. He demonstrated that simple rules could produce visual complexity. He argued that things often seen as "rough," "messy," or "chaotic"—like clouds or shorelines—actually had a "degree of order." His math- and geometry-based work touched fields including 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.

Late in his career, Mandelbrot became the Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. He also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, the Institute for Advanced Study, and the Centre National de la Recherche Scientifique. Over his career, he received more than 15 honorary doctorates, served on many science journals, and won numerous awards. His autobiography, *The Fractalist: Memoir of a Scientific Maverick*, was published after his death in 2012.

Born Benedykt Mandelbrot into a Lithuanian Jewish family in Warsaw during the Second Polish Republic, his father was a clothing trader and his mother a dental surgeon. For his first two school years, he was privately tutored by an uncle who hated 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, at age 11, his family fled Poland for France. This move, World War II, and the influence of his father's brother—the mathematician Szolem Mandelbrojt, who had moved to Paris around 1920—kept him from a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he wrote.

Mandelbrot attended Lycée Rollin (now Collège-lycée Jacques-Decour) in Paris until World War II began, when his family moved to Tulle, France, and he enrolled at Lycée Edmond Perrier. Rabbi David Feuerwerker of Brive-la-Gaillarde helped him continue his studies. Much of France was under Nazi occupation, and Mandelbrot recalled this period. In 1944, he returned to Paris, studied at Lycée du Parc in Lyon, and from 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 the California Institute of Technology, earning a master's in aeronautics. Returning to France, he obtained his PhD in Mathematical Sciences at the University of Paris in 1952.

From 1949 to 1958, Mandelbrot worked at the Centre National de la Recherche Scientifique. During that time, he spent a year at the Institute for Advanced Study in Princeton, New Jersey, 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 stayed 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 also in applied fields like information theory, economics, and fluid dynamics. He viewed financial markets as an example of "wild randomness," marked by concentration and long-range dependence, and developed original approaches for modeling financial fluctuations. Early in his work, he found that price changes in financial markets did not follow a Gaussian distribution but instead Lévy stable distributions with infinite variance. For instance, 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. This work from the early 1960s used daily cotton price data from 1900, long before he introduced the word "fractal." In later years, after the concept was established, he continued to explore these ideas.