Formula for Success
Drawn by new courses and intriguing problems, students are diving into mathematics.
PROOF POSITIVE: Math chair Eliashberg says students are attracted to rigorous thinking.
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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Data is from the past two weeks.