HER PROJECT: Using geometry to study the relationships between numbers

WHAT LED TO THE PROJECT: Growing up, Moon Duchin heard a lot of jokes about her name. Her parents were "on the science-y fringes of the hippie classification," she says. In addition to her unusual name, her mom (an economist) and dad (who worked in the paper industry), gave her a love of numbers. "I wanted to be a mathematician since I was 7," she says. She was fascinated at the time by a book on Jackie Robinson breaking the color line in baseball, and so "I wanted to blaze a trail as a woman in math—once I decided I probably couldn't be a baseball player," she says.

Blazing such a trail required a fair amount of personal initiative. Duchin ran out of math classes to take at her Stamford, Connecticut high school her freshman year. So she forged ahead on her own (filling in the free time with debate, acting and wrestling), and the summer before her senior year, she participated in a program that let her study geometry with famed Harvard number theorist Noam Elkies.

He gave her a problem in lattice geometry (that is, the study of patterns of points regularly distributed in space) "I didn't do anything new with it," she says. "I rediscovered some things that are pretty well known to anyone who's spent time on the subject." For instance, she used existing ideas to prove that every natural number—0,1,2,3, etc.—is the sum of four perfect squares—that is, numbers that have a square root that is a whole number. Take 3: It's the sum of 0 (zero squared), 1 (one squared), 1 and 1. Or 34: It's the sum of 25 (five squared), 9 (three squared), 0 and 0.

The math may not have been new, but Duchin enjoyed the process of discovery, and she got to work collaboratively with half a dozen other math whizzes. They bounced ideas off each other. "That remains the thing that keeps me in math—the creative and communicative aspects of it," she says. She entered her paper in the 1993 Westinghouse Science Talent Search and was named a finalist.

THE EFFECT ON HER CAREER: Duchin went to Harvard to study math, but even as she pursued a fairly traditional track for a promising young mathematician, she was becoming suspicious of the traditional great "Men of Mathematics" (to quote a famous book title) concept. "Does it hinge on specific people or is it inevitable it will come out that way?" she asks. The Great Man model of a genius working alone in his garret "started to seem like it was obscuring some of the important community aspects of mathematics, and like it was controlling who would even think to enter the field," she says. Duchin stuck it out because of her 7-year-old dream and "adolescent stubbornness," but "it wasn't always easy to see my way through. Meanwhile, I'd picked up an enduring interest in cultural practices and philosophical issues in science."

So at Harvard, Duchin wound up double majoring in math and women's studies. She did a mathematics research thesis, and also one for the women's studies department looking at "Why the notion of genius is so attractive with thinking about math and how it functions, and what it does to math as a field," she says. "Lots of people think this is a non-social field—would math come out differently in a society with a different social organization?" While she's not trying to debunk the existence of genius ("there really are people you meet in math and you learn about who just synthesize things in ways that other people don't have access to with any investment of time"), the Great Man theory "definitely stilts the narrative. A real intellectual history is harder to do but it illuminates the math very differently."

Duchin later completed her PhD at the University of Chicago with a thesis called "Geodesics track random walks in Teichmüller space." That incomprehensible title is typical in Duchin’s field of geometric topology—the study of the structure of spaces. Geodesics—used famously by Buckminster Fuller—are the shortest path between two points, and Teichmüller space has to do with the surface of a structure.

While at the University of Chicago, she also followed her passion for equality, serving as an advisor for a student group that was campaigning for gender-neutral bathrooms. She told a Chicago Sun-Times reporter that they were simply trying to create more choices for more people. Conservative talk show host Rush Limbaugh wound up incorporating her quote into an on-air rant "about feminists, homosexuals, and their supposed ringleader, 'Moooon Dookin'" she says.

Fortunately, Duchin has also been able to discuss her dual interests in some more deliberative venues as well. At the University of Chicago, she taught a class on gender studies, and while doing a post-doc at the University of California, Davis she taught a class on the history of mathematics.

WHAT SHE'S DOING NOW: Duchin starts another post-doc at the University of Michigan this fall, and ultimately hopes to do cross-disciplinary teaching and research incorporating math and her interest in the humanities.

Along the way, she's been picking up fans who like her unique approach. "Most mathematicians, when handed a paper entitled 'The Sexual Politics of Genius' would feel the urge to fling it out the window," says John Stillwell, a professor of math at the University of San Francisco. "If it were written by Moon Duchin, however, they would be wrong. Moon has a keen mathematical intellect, which she brings to bear on problems of history, politics, and philosophy seldom touched by rigorous logic. Her essays and teaching breathe new life into the ancient idea that mathematics is the prerequisite for all serious thinking."