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# Chalk talk

An afternoon of pure math with the BC-MIT Number Theory Seminar

On March 17, I downed a generous shot of my own ignorance, and the effect was pleasantly disorienting. It started with a hike up to the second-floor conference room of McElroy Commons, following the pink flyers announcing a meeting of the joint BC-MIT Number Theory Seminar.

Number theory is not a subject I’m familiar with, even remotely. So I asked Sol Friedberg, chair of Boston College’s mathematics department and an organizer of the six-part series of seminars, for an explanation. He replied, “Number theory is quite simply the study of numbers, especially the integers.” The standard number crunching that most people call math, he said, is part of higher—or “pure”—math. “For example, we learn in grade school about prime numbers [numbers divisible only by one and themselves], but they are also of great concern to number theorists.” Turns out, that there is still much to learn about prime numbers, and to demonstrate this Friedberg posed the question, “If you choose a whole number at random, what is the chance that it is a prime number?” The answers, he said (and they are plural), are interesting to number theorists.

That sounded to me like a small group, and I asked Friedberg if it was an isolated world. On the contrary, he said, “there are lots of people all over the world with whom I share the passion for number theory.”

Friedberg and his colleagues at Boston College and MIT created the number theory seminar series to provide a local forum for the review and discussion of important issues in number theory. The colloquia, which spanned nine months and alternated between the two schools, brought together leading mathematicians from universities throughout the United States and Canada.

In McElroy, I took my seat among a coterie of twenty or so slouching, chin-gripping guys—at this session, the fifth in the series, they were all guys. The seminar commenced with Columbia University mathematics professor Dorian Goldfeld half-jokingly asking Friedberg, “What’s my topic?” I almost raised my hand. I had read that Goldfeld, a compact mathematician in a blue sweater vest, would talk about “Symmetry types of higher rank Rankin-Selberg L-functions.” It was the last answer I would have all afternoon.

At that we entered the culture of chalk, the atmosphere of equation. Goldfeld worked the blackboard with dizzying speed—numbers, letters, and symbols spilling across the surface only to disappear in a few rapid swipes of an eraser, to be replaced by a new set. He led off with a discussion of L functions—”a collection of mathematical objects in number theory,” as Friedberg described it to me—and how they’re sometimes clustered in families. Stanford University’s Brian Conrad, a young, bomber-jacketed professor, followed with a second presentation. He was the more colloquial of the two, and I felt grateful when he said colorful things like, “Kill off the unipotent radical,” or referred to an element in his equation as a “guy,” as in: “Kill off that guy, okay?”

The audience, students and professors from the math departments of Boston College and other schools in the area, followed the presentations intently. Occasionally someone in the audience offered a minor correction or a suggestion, and both speakers met these with modest equanimity. At one point when a listener raised a detailed query, Conrad replied graciously, “Ask me in a week. I don’t know.” When Goldfeld made a minor error, the gallery politely called attention to the problem. “Sorry, ” he said, making the change on the blackboard. Heads nodded in agreement.

After Conrad concluded his presentation, I struck up a conversation with George McNinch, an associate professor of mathematics from Tufts. We chatted about the seminar, and number theory, and issues about teaching math in 2009. “Math has a PR problem,” McNinch said. As I began to chuckle, two grad students nabbed the few remaining cookies at the back of the room.

Ken Gordon is a writer in the Boston area.

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