Brilliant mathematician and the “father of fractals” – Benoît Mandelbrot – died on Thursday, October 14th at the age of 85. His contribution to science range alongside the works of Isac Newton, Albert Einstein and Stephen Hawkins.
“If you take the beginning and the end, I have had a conventional career… But it was not a straight line between the beginning and the end. It was a very crooked line.”
(Benoît Mandelbrot. 1934 – 2010)
Benoît B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, at the age of 85. Mandelbrot was seen as an outsider by the scientific community, but his work stands out as one of the most important contributions over the last 50 years.
His death was caused by pancreatic cancer, his wife, Aliette, says, according to the New York Times.
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.
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.
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.
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.
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.”
“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, He was one of the primary people who realized these were legitimate objects of study.”
David Mumford, professor of mathematics at Brown University
“He doesn’t spend months or years proving what he has observed. And for that Dr. Mandelbrot has received quite a bit of criticism. But if we talk about impact inside mathematics, and applications in the sciences,he is one of the most important figures of the last 50 years.”
Heinz-Otto Peitgen, professor of mathematics and biomedical sciences at the University of Bremen.
Related by The Swapper:
Mandelbrot & Market Behavior: The Fractals of Life (Published October 2010)
Here’s a video of Mandelbrot’s TED 2010 talk.