French-American mathematician Benoit Mandelbrot has died of cancer at the age of 85 in Cambridge, Massachusetts.
Mandelbrot was most famously known for his work in exploring the mathematical shapes known as “fractals.” Fractals are shapes that reproduce themselves infinitely–each offshoot of the shape is an approximate miniature of the original shape (including the offshoots). This property (each part being a miniature of the original shape) is called “self-similarity.”
“Fractals are easy to explain, it’s like a romanesco cauliflower, which is to say that each small part of it is exactly the same as the entire cauliflower itself,” Catherine Hill, a statistician at the Gustave Roussy Institute, told the AFP, “It’s a curve that reproduces itself to infinity. Every time you zoom in further, you find the same curve.”
The study of fractals and the mathematics behind them can be traced all the way back to 17th century mathematician Gottfried Leibniz, who contemplated the idea of recursive self-similarity. A few mathematicians after Leibniz dabbled in what we would call fractal geometry after that–including Karl Weierstrass in 1872, who offered a function whose graph would be considered a fractal; and Helge von Koch in 1904, who refined Weierstrass’s definition and came up with a function that produces the Koch curve.
Mandelbrot didn’t start studying fractals and the property of “self-similarity” until the 1960’s, while he was working as a research fellow at IBM. Mandelbrot coined the word “fractal” in 1975, and used a computer to construct visualizations. “Fractal” is technically defined, by Mandelbrot, as an object whose Hausdorff-Besicovitch dimension is greater than its topological dimension, but visualizations mostly focus on the recursive nature of fractals.
In other words, fractals look really cool (especially when you add some color), and so Mandelbrot is considered a stand-up guy in both mathematics and pop culture.
Mandelbrot’s 1982 book titled “The Fractal Geometry of Nature” argued that irregular mathematical objects (fractals) were a reflection of nature. Fractals are found in many parts of nature–in objects such as cauliflower, broccoli, clouds, lightning bolts, and snowflakes, as well as in coastlines, mountain ranges, and animal patterns.
Mandelbrot was born in Poland in 1924, but moved to France as a young child (in 1936, before the Nazi regime). He spent most of his professional life working at IBM’s Thomas J. Watson Research Center, but later became Sterling Professor of Mathematical Sciences at Yale University.
He leaves behind his wife, Aliette, two sons, and three grandchildren.
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