The shaping of a great polymathic mind

Benoit B. Mandelbrot was a distinguished polymath of the 20th century, whose childhood and education were particularly noteworthy. His story is both unique and inspiring.

Mandelbrot was an international mathematician and polymath with broad interests in the practical sciences. Having discovered fractals, he created the geometry of non-smooth forms and chaos theory and changed humanity’s view of the world. An opponent of specialization and "nomad-by-desire", Mandelbrot began the great synthesis of the sciences, found mathematical characteristics of the tactile senses, revived experimental mathematics, and uncovered the secret of harmony and beauty. He became the personification of chaos, just as Einstein personified relativity. He showed that chaos and complexity can arise from the operation of simple laws and rules.

The basis of Mandelbrot’s approach was the synthesis of the logical and figurative-artistic perception of the world. His extraordinary geometrical intuition, preserved thanks to the unconventional education he received, was probably the key to his genius contributions. While he is known most widely for his work in mathematics and in finance, Mandelbrot influenced almost every field of modern intellectual activity.?

Benoit Mandelbrot was born in Warsaw in 1924 into an educated and fairly wealthy family, originally from Lithuania. His father was a wholesale clothing merchant, largely self-educated, whose hobby was collecting geographical maps. His mother, a qualified and respected physician, spoke French, German, and Russian in addition to Polish. Mandelbrot recalled: “Both parents worshiped individual achievement, but because of the Depression and the war, they never achieved what they wanted and deserved. So their ambition and high expectations were transferred to me.”?

His childhood education was of a rare type, close to a modern form called “unschooling”. After their previous child died of an epidemic, Mandelbrot’s parents did not want to send him to school, so his uncle, a famous Parisian mathematician, became his tutor and teacher. He taught the boy in a peculiar way, never making him memorize either the multiplication table or the alphabet. As a result, even when he grew up, calculations still gave the famous mathematician some problems. However, Mandelbrot’s uncle trained his nephews' memory and developed independent and creative thinking.

Remembering those years, his uncle wrote that Benoit

"spent his time playing chess, studying maps, and looking at the world around him with his eyes wide open.”?

By his own account, Mandelbrot owes much of his later success to this unconventional method of learning; it allowed him to think in ways that are difficult for someone with a conventional upbringing to comprehend. He turned out to have an excellent spatial imagination, and would solve algebraic problems geometrically.?At the age of nineteen, during a math class at the Lycee du Parc in Lyon, Mandelbrot had a profound realization. His professor was discussing a mathematical problem when Mandelbrot suddenly recognized the ability to transform algebraic concepts into visual images. This epiphany made him realize that the ability to see mathematical concepts as pictures made problem-solving much more intuitive and straightforward.

Typical for a passionate polymath, Mandelbrot’s interests belonged to different and even distant areas of knowledge. So distant, in fact, that they seemed to have nothing in common, except that he practiced them all. Mandelbrot himself, however, was sure that "between his scattered forays into desolate and desolate corners of the undiscovered, there was nevertheless some connection.”

While working at IBM, Mandelbrot went far beyond the purely applied problems of the company. He worked in linguistics, game theory, economics, aeronautics, geography, physiology, astronomy, and physics. He liked to switch from one topic to another, to explore different directions. Later, after the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences at Harvard. Why this change? Mandelbrot himself said: “When I first began studying prices, it wasn't a topic that mathematicians were working on. Purely by accident, I saw a set of data on price changes presented in a lecture and realized they behaved similarly to the geometric models I was already studying.”?and “The techniques I developed for studying turbulence, like weather, also apply to the stock market.”?

Studying the world as a whole, Mandelbrot disregarded the boundaries between the sciences. “I do not believe in specialization," he declared.

“Specialization is the reason for the walls that have been erected between the sciences. Although these walls are higher than they appear, they are merely psychological. I have crossed them an enormous number of times. Now it seems natural to me ... and now these walls no longer exist."?

Researcher V.A. Shlyk mentions: “It seems incredible that a new science with such broad applications could be created by one man. In our times significant advances in science and technology are the fruits of the work of teams. The time of “single encyclopedists” is gone, and specialization has advanced to the point where one person can't even cover the basic ideas of different fields.”

But is this time really gone? And why is it that again and again such people turn up and go against the mainstream, creating new sciences? In the case of Mandelbrot, I wonder how big was the role of the unconventional childhood education in shaping his polymathic mindset?