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PROOF POSITIVE: Math chair
Eliashberg says students are attracted to rigorous
thinking.
Linda Cicero |
math problems? Call 1-800-[(10x)(13i)2]-[sin(xy)/2.362x].
Seriously, folks, math is in these days. As
Elizabeth Meckes explains, “It’s a sort
of macho thing because you’re doing this very
cool stuff which is so hard to understand.”
Meckes, a third-year graduate student, spends her days
mostly thinking, trying to come up with a new proof
of an old result called the arcsine law. “I don’t
work on a computer,” she says, holding up four
hand-written pages covered with equations and occasional
prose phrases, such as “to make an exchangeable
pair.”
As she puzzles over sets and objects—and stacks
up geometrically complex piles of Coke cans in her office—Meckes
is a standard bearer for a relatively new statistic
in the world of higher mathematics: the steadily increasing
number of women, who now comprise about 25 percent of
graduate enrollment nationwide. As one of 65 grad students
in the Stanford department, she is utterly devoted to,
and dazzled by, her chosen field.
Math, she explains, goes way beyond calculus. “Calculus
is computational—here’s a problem and here’s
how to solve this type of problem. It doesn’t
involve a lot of creativity,” she says. “But
when you get to things like abstract algebra, you don’t
have problem sets anymore. You’re trying to prove
a theorem, trying to come up with an argument for why
something is true. You feel like all your tools—all
the math you’ve spent the last 12 years learning—have
been taken away from you, and you have to start all
over.”
Cool, indeed. And the department, which generally is
ranked among the top five in the nation, overfloweth
with other proselytizers. Among them is Professor Greg
Brumfiel, who directs undergraduate studies and shares
Meckes’s enthusiasm for the beauty of the abstract.
“You have to go through calculus and come out
the other side—maybe even second-year calculus,”
says Brumfiel, one of 22 tenured professors on the mathematics
faculty. “Then, maybe, you start seeing some of
the prettier structures. If there’s a simple way
to try to explain mathematics, it’s a study of
patterns. There’s a simplicity to it, and yet
it also has a mystery and a complexity, as well.”
All Stanford undergraduates must take at least one course
in a mathematical sub area, and thanks to an overhaul
of the undergraduate curriculum, the number of undergrads
actually majoring in math is on the rise, from 25 six
or seven years ago to about 100 today. As more freshmen
enter with advanced placement credit, they are opting
for the new three-quarter math 50 series, which covers
linear algebra, multivariable calculus and differential
equations. They’re also getting more personalized
instruction, in classes with 40 other students, rather
than 200 or 300.
Many undergrads combine their math majors with degrees
in other disciplines, like economics and symbolic systems,
to add mathematical tools for work in financial services,
computer science, engineering and physics. “There
used to be a kind of misunderstanding that you majored
in math only if you wanted to become a teacher,”
says department chair Yakov Eliashberg. “But now
students see it as a way of rigorous thinking, which
is important for many disciplines.” Several years
ago, he notes, the department sponsored an industry
career panel that attracted more than 300 undergraduates.
It turns out that mathematics also attracts a competitive
core of students. Last December, on the Saturday before
final exams, 71 Stanford undergraduates participated
in the 64th annual William Lowell Putnam Mathematical
Competition, a six-hour, 12-problem exam that draws
students from nearly 500 colleges in the United States
and Canada. Freshmen Robert D. Hough and Youngjun Jang
and senior Paul A. Valiant came away with honorable
mentions. “These are people who seek out extreme
challenges,” says assistant professor Ravi Vakil,
who offers preparatory Putnam seminars each fall. “If
they can get a single point, it’s a real achievement.”
As for faculty research, “When there’s an
advance in mathematics, everybody knows about it very
quickly today,” Rick Schoen, MS ’74, PhD
’77, and former department chair, says. “You
can work on a problem and it looks impossible for a
very long time, and then you see some way to go which
explains the whole thing and makes it fit together into
some larger context. It’s really that broad understanding
about connections that I find fascinating.” And
if Schoen were to come up with a significant new proof
any day soon? “I would sit for several months,”
he says. “And check. It’s very easy to make
mistakes.”
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