Benoit Mandelbrot: The Mathematician Who Developed Fractal Geometry
Benoit Mandelbrot was a French-American mathematician and a pioneer in the development of fractal geometry, which revolutionized the study of the shape and form of rough, irregular, fragmented objects and surfaces in nature that repeat themselves on different levels of scales. He is best known for the ‘Mandelbrot Set’, his mathematical formulae which produces an instantly recognizable pattern of intricate curlicues. As a result of his influential research and intellectual contributions, Mandelbrot has had a major impact on fields of science including mathematics, physics, engineering, finance, biology, economics, architecture and art. He is often referred to as the “Father of Fractals”.
Early Life & Education
Benoit Mandelbrot was born in Warsaw, Poland on November 20th, 1924, to a Lithuanian Jewish family. His family moved to France in 1936, and he was educated at the Lycée Rolin in Paris until the start of World War II. During the war, Mandelbrot studied under Pasteur-Fourastié as a teenage refugee at the University of Paris and obtained certificates in engineering mathematics and research.
He was granted an academic degree from the University of Paris in 1945, then received a PhD in Mathematical Science from the University of Paris in 1952. He continued his education at the California Institute of Technology and the Institute for Advanced Study at Princeton.
Work on Fractal Geometry
Mandelbrot’s research into fractal geometry began during his doctoral studies and initially resulted in a paper on long-range correlations that he submitted to the French Academy of Sciences in 1952. He continued to focus on the study of fractal configurations and published his research in 1958 in the paper ‘How Long is the Coast of Britain?’ which helped define fractal geometry.
During the 1960s, Mandelbrot worked closely with the IBM Corporation to develop fractal geometry by computing models of natural objects with computers. He was accompanied on this project by Paul R. Hansma and Benoit B. Mandelbrot, and together they produced the first digital images of fractals which further increased the study of geometry.
Mandelbrot’s most famous work, ‘The Fractal Geometry of Nature’, was published in 1982 and this groundbreaking text remains one of the most influential works in the study of geometry. He went on to publish another seven books, making him one of the most prolific authors in the field.
Influence on Science & Mathematics
Mandelbrot believed that many of the features of the universe and nature, including cloud shapes and shorelines, are fractal and he developed the concepts of ‘fractal dimension’ and ‘fractal transformations’ to try and explain the phenomenon. His research into fractal geometry has had major implications in a wide range of fields including architecture, finance, engineering, physics, biology and economics.
In particular, his work had an impact on mathematics. He was the first to introduce the concept of iteration and helped develop chaos theory by describing chaotic and random systems with simple equations. Through his research, he also highlighted the limitations of Euclidean geometry and of measuring the lengths of coastline.
Awards and Recognition
Mandelbrot received numerous awards for his research including the Wolf Prize in Physics in 1993, the US National Medal of Science in 2001, and the prestigious Kyoto Prize for Basic Science in 2006. He was appointed Professor of Mathematical Sciences at Yale University in 1987 and held several visiting professor positions including one at Harvard University. Many of his pioneering works were included in ‘The Best Writing on Mathematics’ edited by Mircea Pitici.
In 1984, Mandelbrot was awarded the Feltrinelli Prize from the Italian National Academy of Sciences and he also received France’s highest civilian honor, the Legion of Honor, in 1999. In 2020, Google Doodle commemorated Mandelbrot’s 96th birthday, recognizing his legacy of work which transformed mathematics and science.
Mandelbrot conducted much of his most influential work during the final three decades of his life and inspired many of the current fractal-based disciplines in mathematics. In his later years, he established the field of fractal finance, which explores the way principles of chaos theory and fractals can be applied to stock analysis.
Mandelbrot died in Cambridge, Massachusetts on October 14th, 2010. His work remained a source of inspiration to mathematicians, scientists and engineers across many disciplines, and his revolutionary approach to understanding the complexity of nature is a lasting legacy to him.