right lens through which to examine the data. Hubbard recounted a conversation he had with Lars Ahlfors, the first recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize. "Ahlfors is a great mathematician; no one could possibly doubt his stature. In fact, he proved many of the fundamental theorems that go into the subject. He tells me," Hubbard said,

that as a young man, just when the memoirs of Fatou and Julia were being published, he was made to read them as—of course—you had to when you were a young man studying mathematics. That was what was going on. And further, in his opinion, at that moment in history and in his education they represented (to put it as he did) the pits of complex analysis. I am quoting exactly. He admits that he never understood what it was that they were trying to talk about until he saw the pictures that Mandelbrot and I were showing him around 1980. So, that is my answer to the question of the significance of the computer to mathematics. You cannot communicate the subject—even to the highest-level mathematician—without the pictures.

McMullen expressed a similar view: "The computer is a fantastic vehicle for transforming mathematical reality, for revealing something that was hitherto just suspended within the consciousness of a single person. I find it indispensable. I think many mathematicians do today."

Moreover, computer pictures of chaos and dynamical systems have succeeded—perhaps for the first time since Newton's ideas were argued in the salons of Paris—in interesting the public in mathematics. The pictures have been featured prominently in probably every major science magazine in the country and appear on tote bags, postcards, and teeshirts. Mandelbrot's 1975 book, Les objets fractals: forme, hasard et dimension (an English translation, Fractals: Form, Chance and Dimension, was published in 1977), which maintained that a great many shapes and forms in the world are self-similar, repeating their pattern at ever-diminishing scales, attracted widespread attention, and James Gleick's Chaos: Making a New Science was a surprise best-seller.

To some extent this attention is very welcome. Mathematicians have long deplored the public's unawareness that mathematics is an active field. Indeed, according to Krantz, the most likely explanation why no Nobel Prize exists for mathematics is not the well-known story that the mathematician Mittag-Leffler had an affair with Nobel's wife (Nobel had no wife) but simply that "Nobel was completely unaware that mathematicians exist or even if they exist that they do anything."

The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement