In the back of the taxi some years ago, Benoît Mandelbrot was at work. We had an appointment in Manhattan together, and the Polish-born, Franco-American mathematician did not like the geometry of the route the taxi driver was taking.
“Why don’t you go down Second Avenue?” he asked the driver. Cross on 25th, he ordered. Go left at Park—no, not here. It was a running commentary, and was causing a small explosion in the front seat. But Mandelbrot didn’t care.
“Look, it’s just a matter of elegance,” he explained. “I’d like him to do it with a minimum of motion—an elegant solution. ” I joked that he was trying to solve a “travelling salesman” problem—one of mathematics’ most famous puzzlers—in the back of a cab. “I already solved it,” he chuckled.
That was vintage Mandelbrot: an indomitable will, leavened with some humor, pushing into other people’s business. He died Oct. 14 in Cambridge, Massachusetts, at the age of 85. In life he was the archetypal campaigner—the scientist who, when his reason convinced him of a fact, would not back down. This was the man, after all, who fought the cliquish math world for half a century to earn respect for the branch of mathematics he created, fractal geometry, who made a career of tweaking posh academic noses, who hit 75 before earning tenure at Yale, and who, as early as 1962, argued that the math on Wall Street would lead to the kind of financial disaster that hit in 1987 and again in 2008.
His larger legacy is as an example of the kind of independent, inter-disciplinary researcher that is all too rare—and all too necessary—in the big business of science that characterizes our age. These days, science is huge, with expenditures totaling $935 billion in the developed world alone in 2008, according to the Organisation for Economic Cooperation and Development. It is powerful, shaping fundamental policy debates from climate change to economic management. And it is divided into thousands of narrow specialties—each one a small world of received wisdom, rigid hierarchies, and strict entry requirements.
In that realm, a number theorist is not welcome to publish on high-energy physics, and a biochemist is not often invited to a conference of economists—however much their tangential perspectives on the topic might possibly stimulate new thinking.
Mandelbrot built a career fighting against that trend towards specialization. He was a mathematician who told hydrologists how to build dams, and a computer scientist who studied financial markets. He analyzed the noise on telephone lines, the branching of bronchia in the lungs, the shape of coastlines and clouds, the distribution of word frequencies in literature and of stars and galaxies in the universe.
That’s not to say he didn’t have a method. Wherever there was a phenomenon with large amounts of data and huge variation from one point in the data to another—a stock market chart, an electrocardiogram readout, a telescope’s output—he had a mathematical tool to study the irregularity: fractal geometry.
A fractal, a term he coined while leafing through one of his sons’ Latin grammars (it comes from the word for “broken”), is a shape or pattern that repeats over and over at different scales in the same object or set of data—the way that broccoli florets are a small-scale image of the whole vegetable, for instance, or the way stars cluster into galaxies that in turn group into galaxy clusters, or the way the fluctuations of stock prices during an hour can, statistically speaking, look similar to the way they move around in a day or a month. Today, this math is used in data-compression algorithms on the Internet, in computer graphics, and in financial-market analysis, among many other fields. It is also familiar to millions, either through the Mandelbrot Set, a psychedelic-looking mathematical shape that appears on many screen-savers and T-shirts, or through the lessons now incorporated into numerous high school and college math courses.
Mandelbrot’s work thus makes our world better and easier in countless ways. But in his day he was a trouble-maker, particularly for economists. While working at IBM, he began to look at the way financial markets work. He concluded that the observed data didn’t fit the theories of academic economists: their mathematical formulae were based on a series of embedded assumptions that were plainly false. Sure, the equations were easy to use and produced decent results most of the time. But when they failed—which was more often than the experts liked to admit—crashes and bankruptcies ensued. Recently, in the aftermath of the 2008 crash, Mandelbrot’s views have seemed more prescient than ever. Said one Nobel-winning economist, the late Paul A. Samuelson: “On the scroll of great non-economists who have advanced economics by quantum leaps, next to John von Neumann we read the name of Benoit Mandelbrot.” (The Nobel Prize committee never agreed.)
The world’s problems seem to grow by the year—energy supply, climate, pandemics, financial turmoil. We still need specialists, but we also need creative agitators who cross from one field to another, fertilizing ideas and shaking up the received wisdom. Now more than ever, we need scientists like Mandelbrot.
Richard L. Hudson was co-author of a book with Mandelbrot, “The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Reward” (Basic Books, 2004).This article © Dow Jones & co. Inc.