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Benoit Mandelbrot, a well-known mathematician who was largely responsible for developing the field of fractal geometry and who once worked as an IBM researcher in Yorktown, died Thursday. He was 85 and lived in Cambridge, Mass.

The cause, his wife, Aliette said, was pancreatic cancer.

The Polish-born French mathematician founded the field of fractal geometry about four decades ago, the first broad attempt to quantitatively investigate the notion of roughness. In 2003, a story in The Journal News described fractal geometry as "a way to measure the rough and tumble real world. Nature abounds with complex shapes, from trees to snowflakes to mountains."

Fractals now are used in many fields. Fractal equations help Hollywood computer artists create more realistic landscapes and doctors measure irregularly shaped red-blood cells to develop better medication.

"As a physicist, I was trying to find ways of representing the messiness of nature. How many flat things do we see in nature? Maybe a lake when there is no breeze and no fish, but not many more," Mandelbrot told The Journal News in 2003. "How many flat things do we see in industry? Everything! This cabinet, the wall, and so on. So industry took some very basic shapes which are rare in nature and made them everywhere."

He received the Japan Prize that year, a prestigious award that is described as being second only to the Nobel Prize. It's awarded annually by the Science and Technology Foundation of Japan to scientists whose work has "advanced the frontiers of knowledge and served the cause of peace and prosperity for mankind."

Mandelbrot shaped many of his theories during his time as at IBM's Thomas J. Watson Research Center in Yorktown. Later, he became Sterling Professor Emeritus of Mathematical Sciences at Yale University.

He was born in Warsaw and emigrated to France with his family in 1936 to escape the growing German threat. They eventually settled in Lyon, where they endured World War II.

"I have had a very adventurous life," he told The Journal News in 2003. "I almost perished a number of times in my youth. I survived all kinds of complications. In the war in France I was almost killed by Germans or French police. I was 19 at the time. At 20 I was a war-hardened veteran, even though I had never seen military action, because I happened to have survived."

He is survived by his wife, two sons and three grandchildren.

**The Associated Press contributed to this report.**

# Benoît Mandelbrot, Novel Mathematician, Dies at 85

###### By JASCHA HOFFMAN

###### Published: October 16, 2010

Benoît B. Mandelbrot, a maverick mathematician who developed the field of fractal geometry and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85.

###### Shizuo Kambayashi/Associated Press

###### Wolfgang Beyer

The cause was pancreatic cancer, his wife, Aliette, said. He had lived in Cambridge.

Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.

“Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found,” said David Mumford, a professor of mathematics at Brown University. “He was one of the primary people who realized these were legitimate objects of study.”

In a seminal book, “The Fractal Geometry of Nature,” published in 1982, Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in rigorous and vigorous quantitative fashion.”

For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting a position at Yale University, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.

“He knew everybody, with interests going off in every possible direction,” Professor Mumford said. “Every time he gave a talk, it was about something different.”

Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.

“Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”

In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a “fractal dimension,” an insight that has proved useful well beyond the field of cartography.

Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena.

His influence has also been felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honor.

“I decided to go into fields where mathematicians would never go because the problems were badly stated,” Dr. Mandelbrot said. “I have played a strange role that none of my students dare to take.”

Benoît B. Mandelbrot (he added the middle initial himself, though it does not stand for a middle name) was born on Nov. 20, 1924, to a Lithuanian Jewish family in Warsaw. In 1936 his family fled the Nazis, first to Paris and then to the south of France, where he tended horses and fixed tools.

After the war he enrolled in the École Polytechnique in Paris, where his sharp eye compensated for a lack of conventional education. His career soon spanned the Atlantic. He earned a master’s degree in aeronautics at the California Institute of Technology, returned to Paris for his doctorate in mathematics in 1952, then went on to the Institute for Advanced Study in Princeton, N.J., for a postdoctoral degree under the mathematician John von Neumann.

After several years spent largely at the Centre National de la Recherche Scientifique in Paris, Dr. Mandelbrot was hired by I.B.M. in 1958 to work at the Thomas J. Watson Research Center in Yorktown Heights, N.Y. Although he worked frequently with academic researchers and served as a visiting professor at Harvard and the Massachusetts Institute of Technology, it was not until 1987 that he began to teach at Yale, where he earned tenure in 1999.

Dr. Mandelbrot received more than 15 honorary doctorates and served on the board of many scientific journals, as well as the Mandelbrot Foundation for Fractals. Instead of rigorously proving his insights in each field, he said he preferred to “stimulate the field by making bold and crazy conjectures” — and then move on before his claims had been verified. This habit earned him some skepticism in mathematical circles.

“He doesn’t spend months or years proving what he has observed,” said Heinz-Otto Peitgen, a professor of mathematics and biomedical sciences at the University of Bremen. And for that, he said, Dr. Mandelbrot “has received quite a bit of criticism.”

“But if we talk about impact inside mathematics, and applications in the sciences,” Professor Peitgen said, “he is one of the most important figures of the last 50 years.”

Besides his wife, Dr. Mandelbrot is survived by two sons, Laurent, of Paris, and Didier, of Newton, Mass., and three grandchildren.

When asked to look back on his career, Dr. Mandelbrot compared his own trajectory to the rough outlines of clouds and coastlines that drew him into the study of fractals in the 1950s.

“If you take the beginning and the end, I have had a conventional career,” he said, referring to his prestigious appointments in Paris and at Yale. “But it was not a straight line between the beginning and the end. It was a very crooked line.”

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