Benoit B. Mandelbrot[a][b] (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".

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.

At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.

[11] 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.

[9]: 17 [18] 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.

[9]: 62–63 [19] 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.

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.

[17] 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.

In the late 1980s, Mandelbrot used intra-daily tick data supplied by Olsen & Associates in Zurich[23][24] to apply fractal theory to market microstructure.

[25][26] 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[27] and The (Mis)behavior of Markets.

[28] 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.

"[11] 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.

[11]Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass.

[9]: xi  He began by asking himself various kinds of questions related to nature: Can geometry deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?

His methods of research were both old and new: The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer ... bringing an element of unity to the worlds of knowing and feeling ... and, unwittingly, as a bonus, for the purpose of creating beauty.

[38] 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.

The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox.

[1][50] Reacting to news of his death, mathematician Heinz-Otto Peitgen said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years.

"[52] Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".