Saturday, August 12, 2000 | Print this story

Math Convention Problems Just Keep On Multiplying
Academia: The top minds in the field gather to ponder the myriad puzzles they face in 21st century.

By DAVID FERRELL, Times Staff Writer

     You want real convention issues? All but unsolvable problems? Speeches that ramble on like so much mumbo-jumbo?
     Forget the Democrats. Check out the mathematicians.
     They held their own national convention this week at UCLA, exploring such puzzles as "Quasiconformal Mappings in Loewner Space" and "Affine Kac-Moody Superalgebras: Involutive Automorphisms and Iwasawa Decompositions."
     It was death for sound bites, but for sheer brain power it was a summit seldom seen on Capitol Hill--or anywhere else on the planet. Eight of the 30 speakers were winners of the Fields Medal, the mathematics equivalent of the Nobel Prize. At least one, Princeton University's Edward Witten, whose advancements of "string theory" suggest some of the most bizarre notions of the universe ever concocted, draws comparisons with Albert Einstein.
     The last such conference of eminent mathematicians for a similar purpose was believed to have been in Paris--100 years ago.
     The goal this time sounded simple: Lay out the fundamental challenges facing mathematics in the century ahead. In a few cases, they turned out to be the same old intractable problems left over from Paris.
     No matter. Math has so radically evolved since then--branching off into some 70 specialized areas, from topology to chaos theory--that no one was really keeping a list.
     "It doesn't make sense--mathematics is too broad now," said Felix Browder of Rutgers University, who spent five years organizing the special convention of the American Mathematical Society. A more modest aim was to set general directions--and, as much as possible, to emphasize the connection between math and related sciences in a world undergoing extraordinary change.
     Math, admittedly, has an image problem. Murky, abstract, lost in its own eccentricities and eccentrics, it drifted down its own dark hallways of isolation for much of the 20th century.
     But evolving technologies have created an insatiable need for sophisticated new applications of mathematics in everything from artificial intelligence to data encryption. Unlocking the secrets of the human genome has, by itself, set loose an avalanche of chemical sequences and undeciphered patterns.
     "There are tidal waves of data bearing down on us . . . numbers, shapes, God-knows-what, data of all kinds," Browder said.
     Math has not kept up. Take fluid dynamics, for example, a science essential to space flight, aircraft design and cardiology. As yet no formula can accurately predict the onset of turbulence.
     Mathematics is a tormented domain--more alive, more dynamic than at any time in memory, but also under stress. Some scholars, such as UCLA's Tony Chan, head of the university's new Institute for Pure and Applied Mathematics, talk with great zeal about the "Holy Grails" that await discovery: mathematical models of a living human cell, a living brain.
     Others agonize. The work is excruciatingly difficult. One MIT graduate spoke privately of the "intense suffering," years of fruitless toil over problems that no genius has ever solved.
     "Extremely frustrating" is how another scholar, Peter Sarnak, described his chosen field. "Your steady state is to be stuck," he said. "You work a long time. Maybe you solve a problem every few years, and you feel good. It doesn't last long."
     Sarnak, a Princeton luminary who delivered an address on number theory and analysis, bangs his head against an old wall: one of those enigmas put forth by the great mathematician David Hilbert 100 years ago in Paris. Hilbert cited 23 problems at that famous meeting.
     Sarnak's focus is on Hilbert problem No. 8, a challenge to prove the Riemann Hypothesis. The problem involves a clever mathematical function that generally describes the distribution of prime numbers. It is so complicated he can scarcely even state the riddle to a non-mathematician.
     However, he dreams of its implications.
     "It captures the deepest things we know about primes and whole numbers," he said. "Once we prove this, we'll have a machine gun. Right now . . . we go around trying to fix things with a screwdriver. But once we prove this we'll have a machine gun. It'll just blow away problems."
     How soon will it happen? This century, he thinks. Maybe.
     The convention, which ends today, was all about uncertainty. But the 1,000 or so people who wandered in and out of UCLA's Royce Hall, without the interference of protesters or satellite trucks, heard some highfalutin' ideas.
     Michael Freedman, a Fields winner now working for Microsoft, talked about using topological shapes to ensure the reliability of as yet uninvented quantum computers. David Mumford, a Fields winner from Brown University, discussed the inference algorithms needed to model human perception.
     A packed crowd heard Witten, the Princeton physicist whose abstruse insights into string theory portray a universe cast in 11 dimensions and made of invisible vibrating strings and vibrating sheets he calls membranes. In one popular book, "Hyperspace," by physicist Michio Kaku, Witten is described as today's "most brilliant high-energy physicist"--perhaps the best hope for the long-sought theory that would tie together all the forces of nature.
     "He's the new genius," said Chan. "The new Einstein."
     Witten, tall and soft-spoken, ambled slowly outside after his lecture, speculating on all the math work yet to be done. It will go on forever, he predicted.
     No TV crews zoomed in for close-ups. A single reporter stood asking him questions.
     Does he find it distressing that so few appreciate--much less understand--the radical concepts that govern his life, that may change our whole understanding of reality?
     He thought a moment.
     "It bothers me more," he said, "that I don't understand the math."

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