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### Benoit Mandelbrot

20 Nov 1924 in Warsaw, Poland

E-mail:benoit.mandelbrot@yale.edu

Benoît B. Mandelbrot was born in Warsaw, Poland, the 20th day of November of 1924. At the age of 11, his family emigrated to France (1936), where his uncle, Szolem Mandelbrot, who by then was Professor of Mathematics at the Collège de France, took responsibility for his education. It was him who in 1945 introduced Mandelbrot to Gaston Maurice Julia's "Mémoire sur l'itération des fonctions rationnelles" (1918), a 199 page masterpiece in which the 25 year-old Julia describedthe set J(f) of those z in C for which the nth iterate f(z) stays bounded as n tends to infinity. However, Mandelbrot did not like it, and it was not until some thirty years later (working with his own theories) that he turned his attention to Julia's paper again.

Mandelbrot received his diploma from L'ةcole Polytechnique, Paris, in 1947, his Master of Science in Aeronautics from the California Institute of Technology in 1948, and his Ph.D. in Mathematical Sciences from the University of Paris in 1952.

From 1949 to 1957, he worked at the Centre National de la Recherché Scientific. He also worked as a professor of mathematics in Geneva between 1955-1957, and at L'ةcole Politechnique in 1957-1958. Afterward, he moved to the United States and joined International Business Machines (IBM) in 1958. Working for IBM he became an expert in processes with unusual statistical properties and their geometric features, what later culminated in his well-known and highly admired contributions in fractal geometry.

Mandelbrot's article "How long is the coast of Britain?" published in Science magazine in 1967, can be described as a turning point in science and mathematics, with a high spreading rate to other fields of human experience. In that article, he used the longitude of Britain's coast as an example to illustrate that a coastline does not have a determinable length. More likely, its longitude is relative to the resolution of measurement or scale. That demonstration later gave way to other analogous discussions and explanations regarding other mathematical figures, some of which, as the Koch snowflake, were known since the late nineteenth and early twentieth centuries. Back then, they were called "pathological shapes"; now they were helping to understand some natural phenomena as rivers, clouds, plants, mountain ranges, galaxies, population growth, hurricanes, electronic noise and chaotic attractors. All of them share an outstanding and unifying principle: their general patterns repeat in different scales within the same object. In other words, they are said to be "self-similar".

In the mid-1970s Mandelbrot coined the word "fractal" (from the Latin word "fractus", meaning fractured, broken) to label objects, shapes or behaviors that have similar properties (self-similarity) at all levels of magnification or across all times, and which dimension, being greater than one but smaller than two, cannot be expressed as an integer. Today, it is common to find that concept in such diverse fields as economics, linguistics, meteorology and demography.

Mandelbrot's own work is a case of multidisciplinarity: his doctoral thesis (a mathematical analysis of the distribution of words in the English language, U. de Paris, 1952) combined linguistics with the tools of statistical thermodynamics.

Fractals also moved into the arts, not only advancing some aesthetic principles in fine arts, but also contributing to the study of sound and music theory. Likewise, the rapid development of the computer made possible the fast diagraming of complex iterating processes associated with fractal geometry. The resulting graphs proved to be so eye-catching that quickly captured the imagination of new fractal explorers that promptly established an innovative algorithmic art. Thence, fractals proved useful describing and modeling natural phenomena and became bearers of a fantastic kind of beauty. In the words of Mandelbrot, "Fractal geometry may, therefore, usher a new 'liberal art', one that transcends the boundaries that usually separate the arts and diverse narrow academic disciplines from one another".

Mandelbrot became professor of mathematics at Yale University in 1987. He is Abraham Robinson Professor of Mathematical Sciences, IBM Fellow Emeritus, (Physical Sciences) at theIBMT. J. Watson Research Center, and Professor of the Practice of Mathematics at Harvard. He has also been Institute lecturer at the Massachusetts Institute of Technology (MIT), and Visiting Professor at various institutions, including Harvard (first of Economics, later of Applied Mathematics, Mathematics, and Practice of Mathematics), Yale University (Engineering), the Albert Einstein College of Medicine (Physiology), and the University of Paris-Sud (Mathematics). In 1995, he served as Professeur de l'Académie des Sciences de l'ةcole Polytechnique.

He has received numerous awards, prizes and medals for his contributions, including the "Barnard Medal for Meritorious Service to Science" (1985), the Franklin Medal for Signal and Eminent Service in Science (1986), the Alexander von Humboldt Prize (1988), the Charles Proteus Steinmetz Medal (1988), the "Science for Art" Prize (1988), the Harvey Prize for Science and Technology (1989), the Nevada Prize (1991), the Wolf Prize for Physics (1993), the Honda Prize (1994), the Médaille de Vermeil (1996), the John Scott Award (1999), the Lewis Fry Richardson Medal (1999), the Medaglia della Prezidenza della Republica Italiana (1999), and the William Procter Prize for Scientific Achievement (2002), among other awards, diplomas, grants, decorations and honorary doctorates. He's also a member of the American Academy of Arts and Sciences; the USA National Academy of Sciences; the European Academy of Arts, Sciences and Humanities; the IBM Academy of Technology, and the Norwegian Academy of Science and Letters.

His work was first put forward in the book**Les objets fractals, forn, hasard et dimension** (1975), best known simply as**Les objects fractals**, and more fully in his best-selling book**The Fractal Geometry of Nature** (1982).

**Juan Luis Martيnez****Taken from:**

http://www.fractovia.org/people/mandelbrot.html

**For more information:** http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Mandelbrot.html

http://pegasus.cc.ucf.edu/~janzb/boehme/boehmebib.htm|