Benoit B. Mandelbrot, a pioneer in the field of fractals, has died of pancreatic cancer at the age of 85. <\/p>\n
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. <\/p>\n
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.”<\/p>\n
Mandelbrot first published his ideas in his 1982 book, The Fractal Geometry of Nature<\/i>. Among the examples he cited were clouds and coastlines. In subsequent works he extended his analysis to geology, medicine, cosmology and engineering.<\/p>\n
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] doesn\u2019t 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.”<\/p>\n
Additional details are available at [Hoffman2010], from which some of the above material was excerpted.<\/p>\n
References<\/p>\n
Benoit B. Mandelbrot, a pioneer in the field of fractals, has died of pancreatic cancer at the age of 85. <\/p>\n
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. <\/p>\n
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 <\/p>\n