Yale Bulletin and Calendar

January 17, 2003|Volume 31, Number 15|Two-Week Issue

Benoit Mandelbrot

'Father of fractals' wins Japan Prize

Benoit Mandelbrot, Sterling Professor of Mathematical Sciences, has been awarded the prestigious Japan Prize by The Science and Technology Foundation of Japan.

The international prize recognizes "original and outstanding achievements that contribute to the progress of science and technology and the promotion of peace and prosperity of mankind."

The prize will be awarded at a ceremony hosted by the Emperor of Japan on April 25 during "Japan Prize Week." The prize has been awarded each year since 1985 in two fields: "Science and Technology of Complexity" and "Visualizing Techniques in Medicine." This year, one of the $400,000 awards will be shared by Mandelbrot and Professor James York of the University of Maryland under the former category.

Mandelbrot is known internationally as the "father of fractals." By studying diverse shapes in nature and culture, he saw that the "overwhelming smoothness" paradigm with which mathematical physics had attempted to describe nature was flawed and incomplete. He also discovered that many kinds of "roughness" can be called "pure," insofar as they show the same pattern on all scales. To handle those phenomena, he developed a set of mathematical tools, coined the term "fractal" to denote those rough objects and created an entirely new system of geometry.

Examples of fractals include coastlines, clouds, tree branches, clusters of galaxies and of physical particles, blood vessels and the fluctuations in the stock market. Fractals also occur in music and Dali's paintings. Mandelbrot's revolutionary new paradigm is described as having revealed order and simplicity in systems with a seemingly high degree of disorder, irregularity and complexity. As a result, his multidisciplinary work has influenced statistical physics and also fields as diverse as graphic design, astronomy, meteorology and computer science. In economics a contrast is now drawn between "Brownian" and "Mandelbrotian" models.

He also is credited with reintroducing the eye and experimentation to the study of mathematics. One of his best-known mathematical conjectures is the "Mandelbrot set," which has been described as the most complex object in mathematics.

Computer-generated imagery of the Mandelbrot set and of fractal landscapes have been credited with bridging chasms that separated mathematics, science and technology from one another and from the interests of the general population. Lynn A. Steen, a mathematics professor at St. Olaf College, has noted that "simply put, fractals enable everyone to enjoy mathematics. Nothing else can make such a striking -- and important -- claim." In 1993 the Wolf Prize for Physics cited Mandelbrot for "having changed our view of nature."

"Fifty years ago, when I began to study complexity for its own sake, I was very lonely," says Mandelbrot, who came to Yale in 1987. "Today, it is the theme of this great prize and I am utterly delighted to be chosen as a recipient.

"Early on," he adds, "I became a wanderer by choice between the disciplines, and between theory and applications. Electing to live as a constant maverick, I allowed my interests to move in and out of mathematics, in and out of physics, of economics, or diverse other fields of physical and social sciences, and even music and art. I showed that very simple formulas can generate objects that exhibit an extraordinary wealth of structure. Lately I have also been very active in college and high school education. I feel extraordinarily privileged that my professional life has continued long enough to allow me to merge every one of my activities into a reasonable beginning of a science of roughness."

Born in Poland, Mandelbrot studied at the Ecole Polytechnique in Paris and the California Institute of Technology. He holds a doctorate in mathematics from the University of Paris. From 1958 to 1993, he was with IBM's T.J. Watson Research Center in New York, where he continues as IBM Fellow Emeritus.

His publications include the books "Les objets fractals" and "The Fractal Geometry of Nature." Both books were translated into several languages (including Basque). American Scientist listed one of his books among the top 10 in mathematical/physical sciences in the 20th century.

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