Mathematician Profile# Benoit Mandelbrot: Simplifying the Rough and Messy Universe

January 3, 2022

*By Lillie Therieau *

Benoit Mandelbrot saw the harmony and beauty in the messier parts of the universe, applying his theory of fractal geometry to make sense out of chaos.

Benoit started his work on fractals focused on market fluctuations and economics, though he later realized that it could apply to a variety of natural phenomena on Earth and in space. Today, he is remembered for his creativity and visionary mind, as he used early computer visualizations to completely revolutionize natural geometry.

However, he first had to fight through a frequently interrupted education, as well as survive with his Jewish family in hiding during WWII. Learn about the amazing and unlikely life of Benoit Mandelbrot in this installment of our Mathematician Profiles series.

Benoit Mandelbrot was born in Warsaw, Poland, in 1924. His father was a clothing merchant and his mother was a dental surgeon. During his elementary school years, he was also tutored privately by one of his uncles. His uncle disagreed with the routine and memorization of traditional education, so much of his tutoring took the form of non-traditional learning activities like playing chess and examining maps of the world. However, by 1936 his family felt as though they had to leave Poland. They were wary of the war brewing on the horizon, so the Mandelbrot’s decided to follow Benoit’s uncle, Szolem Mandelbrot, a mathematician who had moved to France.

In France, Benoit attended a high school in Paris, until the beginning of WWII. His family relocated to Tulle, France, where a local Rabbi secretly helped him continue his education. Over the next several years, the Mandelbrot's lived in constant fear. As practicing Jews, they were always on guard, terrified that someone in their town would turn them into the Nazi-occupied French government.

However, the family escaped the fate of many other French Jewish families unscathed. In 1944, Benoit traveled back to Paris to continue his formal education. In 1945 Benoit entered the École Polytechnique, where he studied until 1947. Benoit then earned his Master’s degree in aeronautics at the California Institute of Technology in 1949. After his stint in America, Benoit again returned to Paris where he received his Ph.D. in Mathematical Sciences at the University of Paris.

*Photo of Benoit Mandelbrot, via **Yale*

Benoit was a researcher at the Centre National de la Recherche Scientifique from 1949 to 1958, where he was able to travel and collaborate with many other scientists and mathematicians. In 1955, Benoit married Aliette Kagan and moved to Geneva, Switzerland with her. In Geneva, Benoit worked at the International Center for Genetic Epistemology, studying the origin and development of human knowledge. In 1958, the married couple moved to America, where Benoit began working at IBM as a researcher. He would work at IBM for 35 years, becoming an IBM fellow and then a fellow emeritus.

During his years at IBM, Benoit published papers in a variety of different fields, including economics, fluid dynamics, and mathematics. In 1987, IBM ended its pure research division, so he left and took a teaching position at Yale University. In 1999, Benoit became a tenured mathematics professor, at the age of 75. Benoit died at the age of 85 of pancreatic cancer in Cambridge, Massachusetts.

Benoit’s most notable work was in the field of economics and market fluctuations. He was responsible for several very unique approaches to economics, including fractal geometry and wild randomness. Benoit saw financial markets as wild phenomena, which often seem random rather than stable.

From his studies of financial data and historical trends, Benoit realized that markets did not follow a typical Gaussian probability distribution model. Instead, they followed a Lévy stable distribution model with infinite variance. This means that there was much more variation and fluctuation present in markets than economists had previously allowed for. Though the Lévy stable distributions still followed a linear progression, the lack of a finite parameter led to a seriously complex boundary.

*A Fractal, via **Wikipedia*

In the 1970s, Benoit was able to dive much more deeply into his financial theories by using IBM computer processing software to examine vast quantities of financial data at once and to better visualize this new theory. The use of the software led him to the realization that some geometric forms, called fractals, are rough at all scales. No matter how far you were to “zoom in” or “zoom-out”, the forms never get simpler. They are effectively patterns nested within each other such as fern leaves in nature.

Like the fluctuations of markets, many naturally occurring phenomena had some level of fractal geometry, including the clustering of galaxies, a rocky coastline, music, blood vessels, and the internal structures of plants. Benoit called this his theory of roughness. He believed that fractals could help to simplify the superficially messy objects in science. The rougher and messier a thing, the larger the degree of fractal geometry it represented. In fact, Benoit believed that fractals were a much more intuitive and common geometric occurrence than traditional Euclidean geometry.

Benoit wrote several books and many papers about fractals, his theory of roughness, and its economic implications. He won the Wolf Prize for physics in 1993, thanks to these very same discoveries. Benoit had a passionate and accessible writing style and supplemented his papers and books with many detailed illustrations. This allowed his work to rise to mainstream prominence and to be read by many non-specialists.

In 1990, Benoit was named a Chevalier in the French Legion of Honor. In 2006, he was promoted to the rank of Officer. Today he is remembered as a pioneer and a visionary creative. He used intuition, computer visualizations, and a multidisciplinary sensibility to discover fractal geometry and to realize its numerous applications to the broader universe. Fittingly, today he has a small asteroid named in his honor.

This article is the sixth in our series exploring the lives and achievements of famous mathematicians throughout history. (Our last article was about the British mathematician Ada Lovelace!)

Through the lives of these brilliant folks, we hope you’ll find connections, inspiration, and empowerment.