Mandelbrot made a considerable contribution to the popularization of fractals with his books Fractals: Form, Chance, and Dimension (1977) and The Fractal Geometry of Nature (1982), which included examples such as snowflakes, mountains, and of course, coastlines. In the latter book, Mandelbrot explained how he had persevered in his search for new phenomena:
I started looking in the trash cans of science for such phenomena, because I suspected that what I was observing was not an excep- tion but perhaps very widespread. I attended lectures and looked in
ENDLESS STRUCTURE 69
This head of Romanesco broccoli reveals a very clear fractal structure in three dimen- sions. Note how each smaller level repeats the same general type of structure. (Public domain photo, www.pdphoto.org)
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Mandelbrot’s efforts may have been hampered by what some other mathematicians saw as his egotism and interest in self-promotion. Some believed that by claiming his discovery to be revolutionary he was overreaching. (This would also be said of Stephen Wolfram; see chapter 10, “A New Kind of Science.”)
In his book Chaos, science writer James Gleick suggests that Mandelbrot saw himself as an outsider in the mathematical world and perhaps insecure about his position:
Unquestionably, in his years as a professional heretic, he honed an appreciation for the tactics as well as the substance of scientific achievement. Sometimes when articles appeared using ideas from fractal geometry he would call or write the authors to complain that no reference was made to him or his book.
Gleick quotes Mandelbrot’s colleague David Mumford’s admission that “of course [Mandelbrot] is a bit of a megalomaniac, he has this terrible ego, but it’s beautiful stuff he does, so most people let him get away with it.” But another colleague provides some justification for Mandelbrot’s behavior:
He had so many difficulties with his fellow mathematicians that simply in order to survive he had to develop this strategy of boosting his own ego. If he hadn’t done that, if he hadn’t been so convinced that he had the right visions, then he would never have succeeded.
In his entry for Who’s Who, Mandelbrot provided his own justification:
Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads by choice are essential to the intellectual welfare of the settled disciplines.
unfashionable periodicals, most of them of little or no yield, but once in awhile finding some interesting things. In a way it was a naturalist’s approach, not a theoretician’s approach. But my gamble paid off.
Achievements
As people working in different fields of science began to acknowl- edge the importance of Mandelbrot’s work, he received a number of awards (including the Barnard Medal in 1985) as well as being elected to the American Academy of Arts and Sciences (1982) and the National Academy of Sciences (1987).
Mandelbrot retired from IBM in 1987, joining the mathematics faculty at Yale University. He retired from Yale in 2005 but later that year was appointed Battelle Fellow at the Pacific Northwest National Laboratory. In his later years, he received new honors, including the Wolf Prize for Physics (1993), the Japan Prize (2003), and the Einstein Lectureship of the American Mathematical Society (2006).
Through his long career, Mandelbrot has continued to seek out new ways to apply fractal analysis to phenomena, both natural and economic.
When considered as part of the larger context of chaos theory, there is much to justify Mandelbrot’s claims to have achieved a revolution- ary breakthrough in understanding the dynamic world around us.
Chronology
1924 Benoît Mandelbrot is born in Warsaw, Poland, on November 20 1936 The threat of Nazism leads the Mandelbrot family to move to
France
1940 Germany invades France; the Mandelbrot family becomes war refugees
1944 The Allies liberate France; Mandelbrot begins university studies 1947 Mandelbrot receives his bachelor’s degree in mathematics
from the Polytechnique School of Paris
1947–48 Mandelbrot studies aeronautics at the California Institute of Technology in Pasadena and earns master’s and professional degrees
1949 Mandelbrot returns to France and serves a year in the French air force
1952 Mandelbrot receives his doctorate from the University of Paris
1953–54 Mandelbrot visits the United States and is a fellow at the Institute for Advanced Study at Princeton University
1958 Mandelbrot becomes an IBM researcher and is given freedom to pursue wide-ranging mathematical interests
1960–62 Mandelbrot studies data in economics and discovers chaotic “clumping” patterns
1975 Mandelbrot coins the term fractal to describe his new kind of geometry
1979 Mandelbrot discovers the fractal that will become known as the Mandelbrot set
1980s Mandelbrot’s work becomes popular, and he wins numerous awards
1982 Mandelbrot publishes The Fractal Geometry of Nature 1987 Mandelbrot retires from IBM; he joins the mathematics fac-
ulty at Yale University
2005 Mandelbrot retires from Yale and becomes a fellow at the Pacifi c Northwest National Laboratory
Further Reading
Books
Albers, Donald J., and G. L. Alexanderson, eds. Mathematical People:
Profiles and Interviews. Chicago: Contemporary Books, 1985. Includes a chapter with background and an interview with Mandelbrot.
Gleick, James. Chaos: Making a New Science. New York: Penguin Books, 1987.
Has a chapter about Mandelbrot’s work, placing it in the larger setting of chaos theory, the branch of mathematics that finds patterns within apparently random phenomena.
Mandelbrot, Benoît. The Fractal Geometry of Nature. San Francisco, Calif.: W. H. Freeman, 1982.
The more technical and comprehensive of Mandelbrot’s two books on fractals.
———. Fractals: Form, Chance, and Dimension. San Francisco, Calif.: W. H. Freeman, 1977.
Mandel’s introduction of fractals for the general reader, including illus- trations and applications.
Article
“Benoît Mandelbrot: Mathematician.” People’s Archive. Available online. URL: http://www.peoplesarchive.com/browse/movies/2930. Accessed on July 18, 2006.
Video and transcript of an interview with Mandelbrot covering his life and work.