Andrew J. Wiles of Princeton University revealed during a meeting at the University of Cambridge that he had solved Fermat's last theorem. This problem, one of the most famous in mathematics, was posed more than 350 years ago, and its roots extend back to Pythagoras himself. Since no oxen were available, Wiles's listeners showed their appreciation by clapping their hands.
But was the proof of Fermat's last theorem the last gasp of a dying culture? Mathematics, that most tradition-bound of intellectual enterprises, is undergoing profound changes. For millennia, mathematicians have measured progress in terms of what they can demonstrate through proofs-that is, a series of logical steps leading from a set of axioms to an irrefutable conclusion. Now the doubts riddling modern human thought have finally infected mathematics. Mathematicians may at last be forced to accept what many scientists and philosophers already have admitted: their assertions are, at best, only provisionally true, true until proved false.
This uncertainty stems, in part, from the growing complexity of mathematics. Proofs are often so long and complicated that they are difficult to evaluate. Wiles's demonstration runs to 200 pages-and experts estimate it could be five times longer if he spelled out all its elements. One observer asserted that only one tenth of 1 percent of the mathematics community was qualified to evaluate the proof.Wiles's claim was accepted largely on the basis of his reputation and the reputations of those whose work he built on. Mathematicians who had not yet examined the argument in detail nonetheless commented that it "looks beautiful" and "has the ring of truth."
Absolute Certainty?