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"HERE IS A mathematician's nightmare I heard in the 1980s when that irritating, unconforming, self-regarding provocateur Benoît Mandelbrot was suddenly famous - fractals, fractals everywhere. The mathematician dreamed that Mandelbrot died, and God spoke: "You know, there really was something to that Mandelbrot." Sure enough. Mandelbrot created nothing less than a new geometry, to stand side by side with Euclid's - a geometry to mirror not the ideal forms of thought but the real complexity of nature. He was a mathematician who was never welcomed into the fraternity ("Fortress Mathematics," he said, where "the highest ambition is to wall off the windows and preserve only one door"), and he pretended that was fine with him. When Yale first hired him to teach, it was in engineering and applied science; for most of his career he was supported at I.B.M.'s Westchester research lab. He called himself a "nomad by choice." He considered himself an experienced refugee: born to a Jewish family in Warsaw in 1924, he immigrated to Paris ahead of the Nazis, then fled farther and farther into the French countryside."

"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." "