Rough edges and hidden order: The genius of Benoît Mandelbrot

His unconventional approach was his greatest asset.

This is the start of a series on people that have been prolific in life and made an impact, people in the top 1% who have contributed to the world’s knowledge, but may be little known today – yet should be. See below for others.

Benoît Mandelbrot was not the sort of mathematician you would expect to change the world. With his rumpled suits and the shock of wild, graying hair, he had the look of a man more at home with ideas than people. His thick, oversized glasses gave him an owlish appearance, as if perpetually peering into a universe only he could see. In a way, he was. Mandelbrot saw order where others saw chaos, and patterns where most saw noise. In doing so, he didn’t just revolutionize mathematics, he forever altered how we understand the world around us.

Born in Warsaw in 1924 to a family of Polish Jews, Mandelbrot’s early life was defined by instability. His family fled to France as World War II began to engulf Europe, evading the Nazi occupation. Moving from village to village, hiding in rural France, Mandelbrot lived on the margins of survival, his life filled with uncertainty. Yet, amid this turbulence, his intellectual curiosity never faltered. After the war, he studied at the École Polytechnique in Paris and later at the California Institute of Technology. But even here, Mandelbrot resisted the rigidity of conventional academia. He was always searching for connections in unexpected places, drawn not to the neat, orderly theories of classical mathematics, but to the messy, rough-hewn edges of the natural world.

It was during his time at IBM in the 1950s that Mandelbrot’s revolutionary ideas began to crystallize. The company had piles of data on signal transmission, irregular bursts of activity followed by periods of calm, with no clear pattern in sight. To most, it was noise. But to Mandelbrot, it was something else entirely. He sensed an underlying structure beneath the apparent randomness. And so he began to investigate.

(image from wikipedia - https://en.wikipedia.org/wiki/Benoit_Mandelbrot)

His findings would turn the mathematical world upside down. Mandelbrot discovered that many of the irregular, fragmented shapes in nature, from the rugged outlines of mountains to the uneven contours of coastlines, could be described using a new kind of geometry. These shapes, which he called fractals, had a unique property: no matter how much you zoomed in or out, the shape retained its complexity. It was self-similar, repeating at every scale, like the branches of a tree or the swirling clouds in the sky.

Fractals were everywhere. The jagged coastlines, the rough surfaces of rocks, the irregular branches of a tree, even the capricious fluctuations of financial markets, all could be described by fractal geometry. Nature, in all its ruggedness and irregularity, could finally be quantified. Mandelbrot’s fractals challenged the long-held belief that the world could be understood through smooth curves and simple equations. Instead, he showed that the natural world is rough, and that this roughness is fundamental, not incidental.

Mandelbrot’s insights didn’t just change how we look at nature. His work reached far beyond mathematics. In finance, Mandelbrot’s fractals laid the groundwork for the theory of The Black Swan, popularized by Nassim Nicholas Taleb. Taleb’s concept of rare, unpredictable events that have a disproportionate impact on the world, whether in financial markets, politics, or even pandemics, owes a great debt to Mandelbrot’s understanding of unpredictability and irregular patterns. In a way, Mandelbrot showed us that chaos and unpredictability are not the exceptions to the rule, they are the rule.

Taleb himself acknowledged Mandelbrot’s influence, noting that the financial markets are not governed by neat, Gaussian distributions, as many had long believed. Instead, they follow power laws, irregular bursts of activity that defy conventional risk models. Mandelbrot’s fractals helped reveal this hidden structure in market behavior, suggesting that the events we think of as anomalies, the Black Swans, are not as rare as they seem. They are just part of the complex, unpredictable systems that Mandelbrot spent his life studying.

But Mandelbrot’s legacy extends even further, into the world of artificial intelligence. AI, especially in its modern form, thrives on recognizing patterns within vast amounts of data. Mandelbrot’s fractal mathematics plays a crucial role in this. His work on scaling, self-similarity, and complexity underpins many of the algorithms that allow AI systems to identify patterns in data that are far from linear or straightforward. Machine learning, for example, often deals with problems that are highly complex and exhibit irregular, nonlinear behavior. Mandelbrot’s ideas about fractals help AI systems navigate this complexity, allowing them to detect patterns in chaos and make predictions in the face of uncertainty.

Mandelbrot’s influence on AI goes beyond just the technical. In many ways, his fractals reflect the very way that AI operates: by learning from the fine-grained details of data, AI systems build models that can recognize structure in the seeming randomness of the world. Just as Mandelbrot uncovered the rough, fragmented patterns that govern natural phenomena, AI finds patterns within massive, messy datasets. The algorithms driving advancements in image recognition, natural language processing, and even self-driving cars owe something to the principles Mandelbrot unearthed decades ago.

Yet despite his towering intellect, Mandelbrot remained humble, even playful. His humor was sharp, but never cruel. He loved telling stories, often with a twinkle in his eye, about how his ideas were first dismissed by mainstream mathematicians as outlandish. “I was lucky to be a misfit,” he would say with a grin. He thrived on being the outsider, the one who looked at problems from an entirely different angle. And in many ways, his unconventional approach was his greatest asset. He didn’t see the world as a place that needed smoothing out. He saw it in all its roughness and found beauty in the irregularities.

In the last years of his life, Mandelbrot’s work gained widespread recognition, far beyond the insular world of mathematics. He became something of a scientific rock star, not for his technical expertise, but for the profound implications of his discoveries. He showed us that the universe is far more complex, and far more beautiful, than we ever imagined. He gave us a new way to see the world, one that embraced the rugged, the uneven, the unpredictable.

Benoît Mandelbrot passed away in 2010, but his legacy lives on in every branch of mathematics, finance, AI, and even art. His fractals continue to inspire new generations of scientists, mathematicians, and thinkers. They remind us that there is order in the apparent chaos of the world, that even the most unpredictable systems follow patterns, and that sometimes, the greatest insights come not from smoothing over the rough edges of life, but from embracing them.

Stay curious

Colin

This is part of a series, of people, who have contributed significantly to their field. Whilst they are known within the field, rarely are they known outside the field or widely, yet should be.

Others in the series are Alonzo Church, Eric Kandel, Hermann Ebbinghaus. Many more to follow.