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For Mathematicians, 'a Once in a Century Thing'
By K.C. COLE
Mathematics has a strange gift. It is "unreasonably effective" in
places where it has no right to be. Like a hammer that turns out to be
good at scrambling eggs, or a basketball star who decides to become a
rapper. Math plays a starring role not only in fields where you might
expect it--say, physics--but also unlikely places such as Hollywood
filmmaking, ecology, medicine, traffic control.
What's a nice equation like you doing in a place like that?
This week, the superstars of mathematics are gathering at UCLA to
celebrate this strange flowering, as well as look for fertile ground to
plant new fruit. It is a gathering the likes of which has not been seen
for at least 100 years, with the equivalent of nearly a dozen Nobel
laureates. (Math has no such thing as a Nobel Prize, but other honors are
considered to confer a similar status within the field.)
"Woodstock" is the closest comparison UCLA math chair Tony Chan could
come up with. "It's a once in a century thing."
The official occasion is the hundredth anniversary of a famous lecture
given by the great mathematician David Hilbert at an international
meeting in Paris in 1900. Hilbert set out the 23 most important questions
facing mathematicians of his day--thereby setting the agenda, more or
less, for the century to come.
The meeting running this week (Aug. 6 through 12) at UCLA hopes to do
the same.
The range of subjects these rock stars of mathematics are addressing
is staggering: the mathematics of thinking and subatomic particles, of
species and ecosystems, computing and climate change, financial markets
and materials, the creation of virtual worlds and the decoding of the
human genome.
* * * How does math do it? What is it about this strange hieroglyphics of
numbers and symbols that allows it to spread its tentacles through so
many disparate fields, holding up the foundation of everything from
astronomy to human perception?
"Nobody quite knows," said Chan. "That's why they call its
effectiveness unreasonable. People have been trying to explain it [for a
long time]. They cannot."
One key is that math describes everything because it describes
nothing. It is an abstraction so extreme that in its pure form, it has
nothing to do with the real world. The glory of mathematics, as the late
Caltech physicist Richard Feynman put it, "is that we do not have to say
what we are talking about." Or as the mathematician Bertrand Russell
famously put it: "Mathematics may be defined as the subject in which we
never know what we are talking about, or whether what we are saying is
true."
Because math isn't stuck in any single context, it is endlessly
versatile--like letters of the alphabet, equally adept at writing sonnets
or advertisements. Its ability to distill the essence is what makes it
universal--like love or hate.
Curiously, however, most math doesn't start out as abstract. Often, it
grows out of something very concrete, an attempt to understand some
puzzling aspect of the physical world--say, Newton's attempt to
understand gravity, which led to calculus.
But then, something strange happens. The abstracted patterns take on a
life of their own. "At that point, it becomes mathematics," said Chan.
It can take a while for the math to settle, digest, mature. When it
does, the universality of its applications surprises almost everyone.
Like the first crude wheel that evolved into cars and trains, ball
bearings and salad spinners, roller-blades and yo-yos, navel rings and
"Wheel of Fortune"?
And that blossoming into unexpected forms is precisely what
mathematicians think is happening again today and what they intend to
celebrate--and build upon--at the conference.
The university will also be dedicating its new Institute for Pure and
Applied Mathematics, one of only three such National Science
Foundation-funded centers in the country. "This puts us on the map," said
Chan. Previously, people from the East Coast or abroad equated math on
the West Coast with UC Berkeley, he said. With the institute, UCLA
becomes a real player. Needless to say, all this is music to the
mathematicians' ears. And this week at UCLA, it's time to rock 'n roll.
* * * Information about the conference and related events can be found at:
http://www.math.ucla.edu/newsevents/news/ams2000.html
Cole can be reached at KC.Cole@latimes.com
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