MANDELBROT, BENOIT

MANDELBROT, BENOIT (1924– ), U.S. mathematician, scientist, and educator. Born in Warsaw, Poland, the nephew of the expert in mathematical analysis Szolem Mandelbrojt, Mandelbrot moved to France with his family in 1936. The need to avoid detection during the German occupation of France in World War ii greatly disturbed his education, but he gained admission to the Ecole Polytechnique – one of France's leading science schools – after the occupation ended in 1944. After graduating in 1947, he gained an M.Sc. in aeronautics at the California Institute of Technology. It was in the doctoral thesis he presented for his 1952 Ph.D. at the University of Paris that Mandelbrot first used scaling, a concept that refers to the manner in which the fine details of patterns replicate those patterns' large-scale irregularities. This was to become the unifying theme of his work. He was J. von Neumann's postdoctoral fellow at the Institute of Advanced Study in Princeton when he realized that the *Hausdorff-*Besicovitch fractal dimension is not an esoteric notion of mathematics but can be used to measure roughness numerically. Mandelbrot's interdisciplinary bent led him to join ibm and apply his theories successfully to both the problem of random noise on telephone circuits and that of fluctuations in stock-market prices. In the latter case, he was able to offer a highly effective statistical method for predicting such fluctuations' riskiness over a range of time scales. Over time, his theory of fractals was found to be applicable to a very wide variety of phenomena, from turbulence to the dispersion of blood vessels through the body. Increasingly, it came to be recognized that fractality reveals an important and hitherto unrecognized characteristic of nature and natural development as a whole. The theory exerts a profound influence upon modern scientific theory, helping to provide descriptions of anything from the behavior of the human heart under stress to the shapes of mountains and clouds or the pattern of water seepage into the soil, in addition to forming a key tool in modern chaos theories. Mandelbrot synthesized these view in his book The Fractal Geometry of Nature (1982). The Mandelbrot set that Mandelbrot discovered and that is named in his honor is called the most complex orderly object in mathematics. Many of its properties are understandable even to young students but have not yet been proven rigorously. Early on, Mandelbrot's eclectic and wide-ranging approach meant that he was often regarded with suspicion by a scientific establishment that valued compartmentalization and specialization in a single field, but the undoubted value of his discoveries have led to wide recognition of his importance. He has been ibm Fellow and Sterling Professor of Mathematical Sciences at Yale, has held many visiting positions, and received many awards.

[Rohan Saxena /

Gali Rotstein (2^nd ed.)