Benoît Mandelbrot, whose keen intellect has opened our eyes and minds to fractals, visited ICTP last autumn to share his insights into his unique world of shapes and images.

Mr. Fractal

Last November Benoît Mandelbrot, a maverick scientist and the 'father of fractals,' celebrated his 80th birthday at ICTP. It was his fifth visit to the Centre. Participating in the Conference on Practical Applications of Fractals, he brought with him copies of his latest book, The (Mis)behavior of Markets (Basic Books, 2004), written with Richard L. Hudson, former managing editor of the Wall Street Journal European Edition.
The application of fractal geometry to modern financial theory is just the latest and perhaps most provocative and controversial area in which fractals have been used. Indeed it's fair to say that Mandelbrot has been an intellectual provocateur virtually his entire life. Born in Poland and educated in France, he derived a deep interest in numbers, patterns and graphs from his uncle, a mathematician. Yet he describes his unique abilities as a 'mysterious gift' that has shaped his thinking since his youth: "I was 19 and when a professor described a mathematical problem, I saw pictures in my mind, and the pictures instantly suggested the solution to the problem."
After World War II, professors told him that abstract mathematics drove scientific understanding and that pictures had nothing to do with mathematics. "I was publicly insulted by people who said that what I was doing was an intellectual scandal," Mandelbrot now recalls with a sly smile.
The journey from pictures to fractals and from fractals to mathematics was clearly mapped out in Mandelbrot's mind at an early age. Against the advice of professors and colleagues, he left École Normale Supérieure for Polytechnique and soon began to study the bizarre shapes of nature, whose parts often mimic the whole. This concept of 'self-similarity' can be applied to a coastline, a leaf, a cloud. In 1958, Mandelbrot settled in the United States where he has lived and worked ever since: first at Caltech in Pasadena, California; then at the Institute for Advanced Study in Princeton, New Jersey (where he studied with the renowned mathematician John von Neumann); the Massachusetts Institute of Technology (MIT); Harvard; and Yale. He eventually landed a job at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York.
Mandelbrot coined the word 'fractal' from the Latin word 'fractus' ('broken') to describe his new geometry of nature. In 1975, he wrote his best-known book, Les objets fractals. The expanded English version was published in 1982 under the title The Fractal Geometry of Nature.
In 1987, Mandelbrot was appointed Sterling professor of mathematical sciences at Yale. By then, fractal geometry was recognised as a respectable branch of mathematics, explaining the shapes of the clouds as well as the distribution of galaxies in the universe. It also received notoriety in circles beyond science---for example, in computer animation (helping to create alien landscapes in Star Wars movies) and ultimately as a model of price changes in financial markets. The public, however, best knows fractals as a kaleidoscope of images and bright colours that helped define 'pop art' in the 1970s and 1980s---images and bright colours that are, in essence, pictures of the Mandelbrot set. In 1993, Mandelbrot was awarded the prestigious Wolf Prize for Physics for "having changed our view of nature."
Today Mandelbrot lives in the leafy suburb of Scarsdale, just north of New York City, where he continues to revel in his maverick ways as the world's 'hippest' mathematician. He remains as dedicated as ever to writing, speaking and travelling widely to explain his once iconoclast but now increasingly mainstream concepts. His friends say he is a living symbol of the richness of complexity and interdisciplinary thought. His critics assail the supreme confidence that lies behind his staunch defence of his work.
"I have been a lone rider so often and for so long that I'm not even bothered by it anymore," he says in the opening pages of his latest book. Adds his co-author Richard Hudson: "As a mathematically minded friend put it, he moves 'orthogonally' to every fashion."

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