## Archive for **October 17th, 2010**

## Benoît B. Mandelbrot: IBM Fellow and Emeritus Passes At 85

Former IBM Fellow Benoît B. Mandelbrot died Thursday in Cambridge, Massachusetts. He was 85.

Mr. Mandelbrot was best known for his interest and work in fractal geometry, in which he demonstrated how fractals can occur in many different places, from mathematics to nature. Fractals referred to a new class of mathematical shapes whose unevent contours could mimic the irregularities found in nature.

Mandelbrot was born in Poland in 1924, but emigrated to France in 1936 where he came under the tutelage of his uncle, Szolem Mandelbroit, a professor of mathematics at the College de France.

He later attended the Lycee Rolin in Paris until the start of World War II, and ultimately completed his studies at the Ecole Polytechnique before being granted his Ph.D. by the University of Paris.

Though he worked for a time at the Centre National de la Recherche Scientific, his interest in stastical mechanics and mathematical linguistics led him to move to the United States in 1958 and ultimately to join IBM at their Yorktown Heights Research Laboratory, where he remained for 32 years. There, he became both an IBM Fellow and IBM Emeritus.

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. Two key themes, “fat tails” and “self-similar” structure, ran through a multitude of problems encountered in those fields, and permeated much of his work.

By way of example, Mandelbrot found that price changes in financial markets followed a Levy stable distribution, having theoretically infinite variance, and observing stable distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.

**The Mandelbrot Set**

Mandelbrot came to term these observations “fractals” as a way of describing these structures, and later became one of the first users to prove out his theories using computer graphics. He first published his ideas on fractals in 1975 in an article entitled “Les objets fractals, forme, hasard et dimension.” It was published in English in 1977 under the title “Fractals: Form, Chance and Dimension.” He later wrote a book about his findings, *The Fractal Geometry of Nature.*

While serving as the Visiting Professor of Mathematics at Harvard University in 1979, Mandelbrot began studying fractals called Julia sets that were invariant under certain transformations of the complex plane.

This is when he began using computers to plot images of the Julia sets of the formula *z*² − μ. It was while investigating how the topology of those Julia sets depended on the complex parameter μ that he studied the Mandelbrot set fractal that is now named after him.

**IBM: Freedom To Investigate**

IBM presented Mandelbrot with an environment which allowed him to explore a wide variety of different ideas. He was said to speak often of how his freedom at IBM to choose the directions that he wanted to take in his research presented him with an opportunity which no university post could have given him.

After a distinguished 30+ year career at IBM, Mandelbrot moved on in 1982 to become the Sterling Professor of Mathematical Sciences at Yale University.

As well as serving as longtime IBM Fellow at the Watson Research Center, Mandelbrot was also a Professor of the Practice of Mathematics at Harvard University, and held appointments as Professor of Engineering at Yale, of Professor of Mathematics at the École Polytechnique, of Professor of Economics at Harvard, and of Professor of Physiology at the Einstein College of Medicine.

Mandelbrot also received numerous honors and prizes in recognition of his achievements, including the *Barnard Medal for Meritorious Service to Science *and the *Franklin Medal *in 1985.

In 1987 he was honoured with the *Alexander von Humboldt Prize*, receiving the *Steinmetz Medal* in 1988 and many more awards including the *Légion d’Honneur* in 1989, the *Nevada Medal* in 1991, the*Wolf prize for physics* in 1993 and the 2003 *Japan Prize for Science and Technology*.

Mr. Mandelbrot is survived by his wife, Aliette.