Part of a Series of Q&A Miniprofiles for Math Awareness Month
Apr 18, 2016 | Atlanta, GA
What is your research about?
I am fascinated by analogies. Much of my work involves so-called “p-adic” numbers, which are analogous to real numbers like 2 or π, but with important differences. For example, in p-adic geometry, every triangle is isosceles! This world might sound exotic and useless, but p-adic numbers play an important role in modern life, including cryptography, which is the making and breaking of secret codes.
A lot of things in mathematics appear to have no applications, but in fact, down the road, they turn out to be incredibly useful.
What has been the most exciting time so far in your research life?
In 2006, Georgia Tech postdoc Sergey Norin found a clever solution to a problem one of my undergraduate research students had been working on. Building on Norin’s solution, he and I soon proved a Riemann-Roch theorem for graphs. This theorem is another mathematical analogy, between graphs, which you can imagine as being like websites and the hyperlinks between them, and “Riemann surfaces,” which are classic geometric objects from the 19th century.
The Riemann-Roch theorem is used widely, from error-correcting codes to string theory. Norin and I were the first mathematicians to realize that it has an avatar in the world of graphs. The resulting paper is now my most cited work.
How did you find your way to mathematics research?
In middle and high school, I loved reading recreational math books by Martin Gardner. Many mathematicians of my generation got interested in the subject from his writings. A conference called Gathering for Gardner takes place every two years in Atlanta.
During my senior year in high school, my first-ever mathematics research project placed third place in the 1990 International Science and Engineering Fair. The project helped get me a full scholarship to the University of Maryland, College Park, where my professors encouraged me to pursue mathematics as a career.
Although I wanted to be a math major, for a while I considered double majoring in physics, history of science, or poetry. I decided to focus on math. It was actually difficult for me to make the transition from being a “polymath” to a “mathematician.”
What advice would you give to a college freshman who wants to be a mathematician?
Master the fundamentals. You have to be able to understand and write rigorous proofs to be a mathematician, and it takes a lot of discipline to do this. Expose yourself to different kinds of mathematics, and try to get some research experience as an undergraduate.
If you could not be a mathematician, in what line of work would you be now?
I’d be a professional magician. I’ve been interested in magic my whole life, but I never seriously considered doing it as a full-time job. I doubt I’d be good at the business end of it.
What is the most exciting thing about being at Georgia Tech?
I love the fact that the overwhelming majority of students are not only really good at math, but they appreciate its value for whatever they’re studying. Students want to be in my class to learn, rather than attending only because it’s a requirement. That’s a great position to be in as a professor. When students want to learn from me, I’m much more motivated to give them something really valuable.
What are you most surprised about in your encounters with Georgia Tech students?
I’m surprised that those who are so good at mathematics resist the temptation to major in it. Seriously, math just literally sucked me in -- I was so fascinated by its elegance and mystery.
What unusual skill, talent, or quality do you have that may not be obvious to your colleagues?
My colleagues know about the magic. They may not know that I sang in a highly regarded a cappella group in the University of Maryland, College Park; or that in 1990 I won a national poetry contest sponsored by the National Holocaust Foundation; or that in 1995 I was a contestant on Jeopardy! I came in second, but the guy who beat me went on to win the Tournament of Champions that year.
How do you like to relax?
Hmm, I’m not sure what you’re talking about.
Seriously, most of my downtime now I spend with our 6-week-old baby. That’s not always relaxing, but it’s what I want to do when I’m not working. It’s great for taking my mind off work.
What three destinations are still in your travel to-do list?
I’d like to visit southeast Asia (Vietnam, Cambodia, Thailand). I love the food, and I admire the politeness and respect for tradition in their culture. I’d also like to see Iguazu Falls, on the border between Brazil and Argentina, and Victoria Falls, on the border between Zambia and Zimbabwe. I’d explore the Amazon as well, but I hate mosquitoes. And I’m afraid of crocodiles.
If you won $10 Million in a lottery, what would you do with it?
Put it toward my kids’ college education. I’d also buy my wife some really nice jewelry, as a gesture of thanks for reviewing my responses to these questions.