Benoit Mandelbrot, outsider 'fractal' maths theorist, dead at 85

Benoit B. Mandelbrot, the hard-working, Warsaw-born outsider in the esteemed circles of mathematics who eventually was embraced at Yale University for his innovative development of "fractals," died earlier this week in Cambridge, Massachusetts, at the age of 85. The opening line to an article he wrote entitled, "Uncle and Nephew," which appeared in The Scientist in 1987, seems appropriate to reference now. 

"No one influenced my scientific life more than the uncle I knew best," Mandelbrot wrote. "He was a noted mathematician who reached the top of French academia, the Collège de France, when he was thirty-eight and I was thirteen. So I always knew that science is not just recorded in dusty tomes, but is a flourishing enterprise, and the option of becoming a scientist was familiar to me for as long as I can remember. I might now, following the usual pattern, continue with fond reminiscences of teachers and postdoctoral mentors. But, in fact, I seem to have fled from teachers and mentors, and even existing disciplines. No wonder that my scientific life ran against every pattern. The wonder is that it developed at all."

Mandelbrot, who died of pancreatic cancer, worked for decades as a researcher for IBM in New York, where he elaborated on his theory to explain the complexities of uneven surfaces, such as clouds, launching the first broad investigation to quantify "the ubiquitous notion of roughness."

The ideas may sound complex, but are outlined by Mandelbrot, Michael Frame, and Nial Neger in papers posted online at Yale -- the "first course in fractal geometry for students without especially strong mathematical preparation, or any particular interest in science."

The researchers, including Mandelbrot, note: "fractals seem to be a an easy concept for kids," as this drawing by a fourth grader illustrates.

Nonetheless, Mandelbrot's career was an unusual struggle.

As he concluded in his 1987 article, "There was no competition to fend off, which is perhaps why (if there is truth in what I am told) I handle today’s competition with a notable lack of skill. Being 'peerless' was a great frustration. As in sports (and science has taken on altogether too many features of a spectator sport), there is no first without a second, no glory in the sole entrant’s winning a race. I also gave wide use to 'self-similar'; it turns out that this term has been used before, on one single occasion. And, of course, I coined 'fractal'. This notion used to be implicit – in other words, it did not exist – until I made it into a topic of wide interest. Around it, I conceived and developed a new geometry of nature, and implemented its use in diverse fields. Not only does it give fresh meaning to the 'unreasonable effectiveness of mathematics in the natural sciences (Wigner),' but it twins it with the new theme of the 'unreasonable visual beauty of the shapes of mathematics.' Thus, conceptual beauty, practical usefulness, and the pleasure of the eye are brought together most unexpectedly. If the German language were not so reluctant to use kunst freely, this opera-lover would describe his life effort as a Gesamtkunstwerk."

Images: Mandelbrot in 1960 (top) and 1997 (bottom)