Benoit Mandelbrot

The latter work from the early 60s was done with daily data of cotton prices from 1900, long before he introduced the word 'fractal'.

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.

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?"

Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life".

He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France.

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 1936, when he was 11, the family emigrated from Poland to France.

In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc in Lyon, and in 1945 to 1947 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 earned a master's degree in aeronautics.

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.

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.

Returning to France, he obtained his PhD degree in Mathematical Sciences at the University of Paris in 1952.

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, 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.

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.

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 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 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 and served on many science journals, along with winning numerous awards.

His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012.

Benedykt Mandelbrot was born in 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."