Mandelbrot ultimately settled at I.B.M., an association that lasted 35 years. He took frequent leaves, teaching at many colleges, including Yale, where he was a professor for 17 years. He refused to get bogged down solely in math.

“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.”

His work on fractals was inspired, in no small part, by his childhood love of maps; he began to think about creating “random coastlines from a simple formula,” as he put it. The arrival of computer graphics greatly aided his quest. He ultimately described what became known as the Mandelbrot set, famous, he writes, for being “the most complex object in mathematics,” and inspired decades of trippy graphic representations.

Many memoirists write their books too early in their lives. Others, like Mandelbrot, wait too long. “The Fractalist” was composed shortly before he died in 2010 at 85; he never had a chance to make final revisions.

I’m not sure they would have greatly helped. His memoir has a distant quality, a vagueness and rigidity that perhaps came with age. Few of this book’s milieus are evoked with any kind of liveliness or precision. I would have liked to know what it was like to work at I.B.M. during its “Mad Men”-era heyday, for example. But most of what Mandelbrot provides are generalities.