













State & Local 











Classifieds Find a home, car,
rental, job, pet,
merchandise, auction, boat,
plane or RV Place
an Ad




Print Edition Advertisements See this week's ads



OTHER EDITIONS
Print Edition, Orange County,
Valley, Ventura County,
National, Community Papers 








SHOP 'TIL YOUR LAPTOP DROPS 


















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 mumbojumbo?
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
KacMoody 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 Hillor 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 Paris100 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 thenbranching off
into some 70 specialized areas, from topology to chaos theorythat no
one was really keeping a list.
"It doesn't make sensemathematics 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 directionsand, 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, Godknowswhat, 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 domainmore 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 nonmathematician.
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 highenergy
physicist"perhaps the best hope for the longsought theory that would
tie together all the forces of nature.
"He's the new genius," said Chan. "The new Einstein."
Witten, tall and softspoken, 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 closeups. A single reporter stood asking
him questions.
Does he find it distressing that so few appreciatemuch less
understandthe 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."
Search the archives of the Los Angeles Times for similar stories about:
Mathematics,
Conventions,
University Of California At Los Angeles. You will not be charged to look for stories, only to retrieve one.
