It Figures

The nation’s mathematicians gathered in Anaheim last week for their annual meeting, which, like most academic confabulations, was a mixture of business and pleasure, an opportunity to hear new work and see old friends.

These are heady times for mathematics. In the last five years the pace of discovery has been phenomenal. Many important problems that had stumped the best minds for years have been solved. “When I was a student,” one mathematician was saying, “no one expected that important unsolved problems would ever be solved. Now half a dozen of them have fallen in the last few years. What is going to be left for us to do?”

No one knows why things have proceeded so quickly. Some people guess that the large increase in mathematics funding in the 1960s, and the consequent increase in the number of mathematicians, had a lot to do with it. They worry that cutbacks now will have the opposite effect in the future. A report by the National Research Council last year warned that mathematics research had suffered a “staggering” loss of financial support and that the number of Ph.D.s awarded in the field had dropped by more than 50% from 1968 to 1982.

For weeks before the meeting rumors had swept the mathematics community that Louis de Branges, who made a stunning mathematical proof last year, would announce a proof of the Riemann hypothesis, widely regarded as the richest and most important outstanding problem in mathematics today. (Suffice to say that the Riemann hypothesis, proposed by Bernhard Riemann in 1859, asserts that the non-trivial zeros of the Riemann zeta function all have the real part 1/2. The truth of this statement, we are told, has enormous consequences in number theory.)

Everyone wondered what De Branges would say. There was also animated discussion about an assertion that a Japanese mathematician, Hideya Matsumoto, has announced a proof of the Riemann hypothesis in Paris. There were daily reports of transatlantic telephone conversations with experts there. So far no one has found a flaw, but no one is prepared to say that the hypothesis is verified.

In this atmosphere hundreds of people flocked to De Branges’ invited address. De Branges described his method of attack and said he thought that it was very promising and that he hoped to have a proof within a year. This occasioned more buzz-buzz-buzzing from the crowd.

Most of the talks were fairly arcane, needless to say, but not all were inaccessible. Persi Diaconis of Stanford, the holder of one of those MacArthur Foundation genius awards, spoke on “The Search for Randomness.” He asserted, and displayed statistics to prove, that shuffling a deck of cards by hand at a friendly bridge game will probably not randomize it; there will be too many 4-3-3-3 suit distributions.

As a group the mathematicians are among the most fascinating people we know. They have a quirky turn of mind that makes them interested in mathematics and at the same time makes them interested in unusual things that you’d otherwise never hear of. Herbert Taylor of the University of Southern California, for example, gave many demonstrations of a small oddly shaped object that he had in his pocket that spins on a table in one direction, stops, then inexplicably spins in the other.

Besides being delightful, mathematics is also crucial to progress in science and technology. It is one of the most productive ways in which public money can be spent. The government is derelict and shortsighted if it does not wholeheartedly support this field.