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Exiles in Pursuit of Beauty

The uncle I knew best was a noted mathematician, who reached the top of the French academia when he was 38 and I was 13. His example showed that science was not fully recorded in dusty tomes but was a flourishing enterprise, and becoming myself a scientist was always a familiar option. This might have set me now on the usual pattern of fond reminiscences of teachers and postdoctorate mentors. But, in fact, I seem to have fled from teachers, mentors and existing disciplines. As a result, no one i

By | March 23, 1987

The uncle I knew best was a noted mathematician, who reached the top of the French academia when he was 38 and I was 13. His example showed that science was not fully recorded in dusty tomes but was a flourishing enterprise, and becoming myself a scientist was always a familiar option.

This might have set me now on the usual pattern of fond reminiscences of teachers and postdoctorate mentors. But, in fact, I seem to have fled from teachers, mentors and existing disciplines. As a result, no one influenced my scientific life more than this uncle. The wonder is not, perhaps, that my scientific life ran against pattern, but that it ran and developed at all.

While still an adolescent, my uncle had fallen in love with a certain branch of mathematics, and he remained utterly faithful to it throughout his life. He left Poland for France at age 20, not for political or economic reasons but as an "ideological" refugee, moved by repulsion for the excessively abstract "Polish mathematics" then in the process of being invented by a man named Waclaw Sierpinski, and by attraction for the Poincaré school that ruled in Paris in 1920. As a postdoc (the function was being invented), he was close to Hadamard and Volterra, that day's most influential mathematicians in Paris and Rome. We later joined him as economic refugees from the depression in Poland, so that the clash between Sierpinski and my uncle concerning ideals in mathematics (and other matters!) had the unanticipated eventual merit of saving our lives.

Before the Paris fashion in mathematics came under the rule of the so-called Bourbaki school, with its own version of abstraction, my uncle had become thoroughly rooted. A dry spell for him could come and go, but he never wavered in his faith: Harmonic analysis as defined in a very classical way was for him the embodiment of truth, beauty and poetry. At age 74, he succeeded to the Académie des Sciences fauteuil that had been Poincaré's, then Hadamard's.

While I was fond of my uncle, many aspects of his story repelled me intensely, somehow. My uncle, in turn, always felt that I had squandered my intellectual gifts. Lately, however, it is becoming clear to me that in some essential ways we were alike.

To begin with the obvious differences, while the course of my uncle's life was straight as an arrow, the externals of mine were to appear as continually broken. Bourbaki made me, in turn, an "ideological" refugee, from Ecole Normale in 1945 and from France in 1958, fleeing toward the concrete. But by a profound irony, whose works were to become one of my most fertile hunting grounds for tools? Those of Waclaw Sierpinski!

While my uncle's peers, teachers, students and other companions at work were few, they were a close club. But I eventually managed to thrive as a scientist without either joining an existing club or feeling I must create my own for my few formal students. This made me "always dependent on the kindness of strangers."

To my uncle, opinion outside his club did not matter, and the idea of acting to draw new members was anathema. Even his formal Closing Lecture at the College de France was addressed to the specialist. But to me, the opinion of kind strangers never ceases to matter. My books appear to be widely popular and influential, but the continual feedback I receive from readers and listeners is somehow disconnected, and my uncle would have found it insufferably haphazard.

Now to the ways in which my story should have enchanted my uncle, and the stark scholars and judges among our ancestors. I, too, follow one single star with unwavering intensity. Also, several active and well-known individuals have led society to expect that I would match them in welcoming occasions to comment about every topic, but I am not a dilettante. My domain of competence is broad and odd-shaped, but has clear-cut limits I refuse to cross.

For many long years, the star I followed was barely distinct. I was hardly able to describe to myself, much less to friend or foe, why it deserved being followed. All I could say is that, to me, certain problems had the same "taste," and that I felt better, while crossing yet another boundary between fields, to be in hot pursuit of a congenial problem that would provide technical cover or excuse. In due time, of course, these likes have expanded and jelled. They are now a significant part of a cluster of related investigations that include the search for order in chaos and the study of scaling in nature, two subjects pursued by many scientists today. During along earlier period after earning my Ph.D. in 1952, however, no other individual with skills and energy to spare was giving more than a passing nod to what I was calling the "study of erratic natural phenomena."

There was no competition to fend off, which is perhaps why (if there is truth in what l am told) I handle today's competition with a notable lack of skill. Being "peerless" was 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.

The old Latin-based "erratic" was far weaker than its Greek-based synonym "chaotic," and it would not have traveled as well and as far, but it may have been less unacceptable at the time. My work also gave wide use to "self-similar," though it turns out that this term has been used before on a single occasion. And, of course, I coined "fractal" for a notion that used to be implicit—in other words, did not exist—but that I made 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 plastic beauty of the shapes of mathematics."

Thus, this opera-lover is blessed with seeing conceptual beauty, practical usefulness, and the pleasure of the eye brought together most unexpectedly.

The author of The Fractal Geometry of Nature (1982), B.B. Mandelbrot is with the IBM Research Center as IBM Fellow, and with the Mathematics Department at Harvard as Professor of the Practice. The book Mathematical People (Birkhauser, 1985) carries a long interview with him, and The Beauty of Fractals (Springer, 1986) includes an autobiographical contribution by him.

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