Benoit B. Mandelbrot, a pioneer in the field of fractals, has died of pancreatic cancer at the age of 85.

Mandelbrot coined the term “fractal” for figures that exhibit self-similar irregularities across a wide range of spatial dimensions. The field has numerous applications in physics, biology, and even mathematical finance. Many of these applications were first identified and analyzed by Mandelbrot himself.

David Mumford of Brown University explains as follows: “Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found. … [Mandelbrot] was one of the primary people who realized these were legitimate objects of study.”

Mandelbrot first published his ideas in his 1982 book, *The Fractal Geometry of Nature*. Among the examples he cited were clouds and coastlines. In subsequent works he extended his analysis to geology, medicine, cosmology and engineering.

In a very real sense, Mandelbrot was a practicing experimental mathematician, before the term “experimental mathematician” even existed. What’s more, he worked at IBM, largely outside the “orthodox” community of academic mathematicians. As Heinz-Otto Peitgen of the University of Bremen explained, “[Mandelbrot] doesnâ€™t spend months or years proving what he has observed,” for which he “has received quite a bit of criticism. … But if we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last 50 years.”

Additional details are available at [Hoffman2010], from which some of the above material was excerpted.

References

- Jascha Hoffman, “Benoit Mandelbrot, Mathematician, Dies at 85,”
*New York Times*, 16 Oct 2010, available at Online article.