In 1910 the mathematician Oswald Veblen and the physicist James Jeans were discussing the reform of the mathematical curriculum at Princeton University. "We may as well cut out group theory," said Jeans. "That is a subject which will never be of any use in physics." It is not recorded whether Veblen disputed Jeans's point, or whether he argued for the retention of group theory on purely mathematical grounds. All we know is that group theory continued to be taught. And Veblen's disregard for Jeans's advice turned out to be of some importance to the history of science at Princeton. By an irony of fate group theory later grew into one of the central themes of physics, and it now dominates the thinking of all of us who are struggling to understand the fundamental particles of nature. It also happened by chance that Hermann Weyl and Eugene P. Wigner, who pioneered the group-theoretical point of view in physics from the 1920's to the present, were both Princeton professors. This little story has several morals. The first moral is that scientists ought not to make off-the-cuff pronouncements concerning matters outside their special field of competence. Jeans provides us with a clear lesson on the evil effects of the habit of pontification. Starting from this unfortunate beginning with Veblen, he later went from bad to worse, becoming a successful popular writer and radio broadcaster, accepting a knighthood and ruining his professional reputation with suave and shallow speculations on religion and philosophy. le ought not, however, to look so complacently on the decline and fall of Jeans. There, but for the grace of God, go we. After all, Jeans in 1910 was a respected physicist (although Princeton, aping the English custom in titles by Freeman J. Dyson as in pseudo-Gothic architecture, called him professor of applied mathematics). He was neither more incompetent nor more ignorant than most of his colleagues. Very few men at that time had the slightest inkling of the fruitfulness that would result from the marriage of physics and group theory. So the second and more serious moral of our story is that the future of science is unpredictable. The place of mathematics in the physical sciences is not something that can be defined once and for all. The interrelations of mathematics with science are as rich and various as the texture of science itself.
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