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Mandelbrot, "The Fractalist"

"I realized that mathematics cut off from the mysteries of the real world was not for me, so I took a different path," he writes. He wanted to play with what he calls "questions once reserved for poets and children."

He prized roughness and complication. "Think of color, pitch, loudness, heaviness and hotness," he once said. "Each is the topic of a branch of physics." He dedicated his life to studying roughness and irregularity through geometry, applying what he learned to biology, physics, finance and many other fields.

He was never easy to pin down. He hopscotched so frequently among disciplines and institutions -- I.B.M., Yale, Harvard -- that in his new memoir, "The Fractalist," he rather plaintively asks, "So where do I really belong?" The answer is: nearly everywhere.

As "The Fractalist" makes plain, Mandelbrot led a zigzag sort of life, rarely remaining in one place for long. He was born in Warsaw to a middle-class Lithuanian Jewish family that prized intellectual achievement. His mother was a dentist; his father worked in the clothing business. Both loved knowledge and ideas, and their relatives included many fiercely brainy men.

The family fled to Paris in 1936, in time to escape Hitler's advances. Looking back on dear friends who didn't make it out, he laments their procrastination. Some, he writes, "had been detained by their precious china, or inability to sell their Bösendorfer concert grand piano, or unwillingness to abandon the park view from their windows." He'd learned a lesson about not being tied down.

He communicates the reverence he felt toward men like Norbert Wiener, then a professor at M.I.T., and John von Neumann, then a professor at the Institute for Advanced Study at Princeton. Mandelbrot perceived them, he writes, "as made of stardust." He refers to von Neumann, more than once, as Johnny. He quotes a friend who called Mandelbrot and his wife's first automobile, a grasshopperlike Citroën 2CV, "the Platonic essence of a car."

Beautiful minds don't always write beautiful books. Life isn't fair that way. But "The Fractalist" evokes the kinds of deceptively simple questions Mandelbrot asked -- "What shape is a mountain, a coastline, a river or a dividing line between two river watersheds?" -- and the profound answers he supplied.

Memoir of a Scientific Maverick
By Benoit B. Mandelbrot
Illustrated. 324 pages. Pantheon Books. $30.


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