If you’re looking for someone who understands Fermat’s Last Theorem, Fuchsian groups, or the Teichmüller flow, you might stop by the rock wall in the Wooden Center.

Rock climbing is popular with mathematics students and professors, says graduate student Craig Citro. He compares it to working on very abstract and obscure issues in advanced mathematics. You might try a particular climb “twenty or thirty times and not be able to do it,” he says, “then you’ll shift the way your foot is positioned by 10 degrees and all of a sudden the climb is the easiest thing in the world.”

Similarly, “I spend 29 days in a row beating my head against a wall trying to understand something in Number Theory and making zero or negative progress,” he explains, “and then one day a bunch of things become clear and I make a lot of progress all at once. That one day is enough fun that I’m willing to come back and struggle again the next month.”

Citro’s research area involves the value of p-adic L-functions at certain points. While obscure to the non-mathematician, the behavior of L-functions shows up in two of the “Seven Millennium Problems” posed by The Clay Mathematics Institute—problems whose solutions will be rewarded with a $1 million prize. “It’s clear that L-functions are the right objects to be studying at the moment,” he says.

Citro’s path to L-functions hasn’t been a straight line. In high school, a calculus teacher gave him an elementary book on Number Theory. Citro “thought I wanted to do math, but I didn’t know what that meant.” He did, however, understand what video games were. As a result, he went off to Georgia Tech as a computer science major and stuck with the subject after a transfer to Indiana University.

But after a while, he decided that the topics in computer science “weren’t of great interest to me.” When he cast about for another major, “math seemed a natural candidate.” Changing majors with little more than a year to go, Citro had to rush to meet the requisites, and he arrived at UCLA feeling under-prepared. “I had to spend a lot of time catching up and filling in the gaps of my undergraduate education.”

During that period, he took a reading course with Haruzo Hida, a highly regarded mathematician in Number Theory, who calls Citro “the most multitalented student I ever had,” combining excellence as a mathematician, computer skills, and “outstanding communication and teaching ability. I expect him to become a superb teacher/researcher.”

Professor Hida became Citro’s thesis adviser. For a dissertation in mathematics, “you settle on something that you’d like to believe is true, and your goal is to come as close to proving that as you possibly can,” Citro says. The idea is to write a thesis that, with a little tweaking, becomes your first paper as a professional mathematician.

Citro’s tools in this quest basically come down to pencil and paper and perhaps some coffee. An old joke says that mathematicians are machines that turn coffee into theorems.

So if they’re not at the Wooden Center rock wall, Citro notes, mathematicians can often be found in nearby Kerckhoff Hall—at the coffee house, of course.

*Adapted from a story in the Fall 2007 issue of the Graduate Quarterly*

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