Mandelbrot was born in Warsaw, Poland to a Lithuanian-Jewish family. Anticipating political developments, the family fled Poland to France in 1936 when he was 11. He remained there 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. One, Szolem Mandelbrojt, was a famous Parisian mathematician. His father, however, made his living trading clothing.
Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle. In 1944 he returned to Paris and in 1945-47 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. Then he spent two years at the 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.
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 then Lille.
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 an IBM Fellow, and later Fellow Emeritus.
Mandelbrot and the Mandelbrot setFrom 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 tails 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 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.
In 1975 Mandelbrot coined the term fractal to describe these structures, and published his ideas in Les objets fractals, forme, hasard et dimension (translated into English as Fractals: Form, chance and dimension) in 1977.