Advice to freshmen math majors: Practice proofs and computations
Apr 5, 2017 | Atlanta
Stavros Garoufalidis started his mathematics education in Greece. As a high-school student, he participated in an International Mathematical Olympiad. He received a B.S. in Mathematics from the University of Athens, Greece. He completed M.S. and Ph.D. degrees in mathematics at the University of Chicago. He joined Georgia Tech in 1999. Fluent in four languages—Greek, English, French, and German—he is also an associate editor at the Journal of Knot Theory and Its Ramifications, as well as an avid beekeeper.
What is your research about?
My main area of research is quantum topology, which is a combination of studying all three-dimensional shapes, building physical theories about them, and thinking of each shape as a possible universe. 3-D shapes can be described by drilling tubes through a solid (for example, cheese) and then filling them in after possibly twisting. The holes are known as knots in three-dimensional space, that is circles that are allowed to move as long as they do not meet themselves.
What has been the most exciting time so far in your research life?
I have enjoyed collaborating with more than 54 researchers over the years on several projects, discovering new connections and predicting outcomes of difficult computations.
One of those predictions involves the number 697, which we found in some numerical computations with Don Zagier, the American mathematician who is now the director of the Max Planck Institute for Mathematics. The number appeared in totally unrelated mathematical physics computations in a different context. The presence of that number gave us confidence that our results are not coincidental, and in fact, they formed the foundation of deep conjectures and theorems in number theory, quantum topology, and mathematical physics.
How did you find your way to mathematics research?
When I was a high school senior in Greece, I participated in the high school math competitions and took part in the 24th International Mathematical Olympiad, in 1983 in Paris. I got a bronze medal and a distinction for a solution to a number theory problem that was originally rejected, but eventually accepted as very original by the committee.
I was equally interested in physics and mathematics at that time, but I chose to study mathematics as an undergraduate. Mathematics was clear and conceptual for me. This path brought me to do a Ph.D. in the University of Chicago—my first ever time in the U.S.—where I realized what first-rate research is all about. I continued to be exposed to world-class research at MSRI, MIT and Harvard.
What advice would you give to a college freshman who wants to be a mathematician?
There are a lot of misconceptions about mathematics taught at U.S. high schools. I would advise a freshman to learn the concepts of math, not be afraid of real mathematical thought, and to practice proofs and computations.
If you could not be a mathematician, in what line of work would you be now?
In the past eight years, I have been involved with beekeeping, as a way to stay in tune with nature, seasons and geography, as well as an entrance to an alien world of insects working together as a superorganism. Beekeeping could become a profession if math was not available.
What three destinations are still in your travel to-do list?
I love traveling and have been to 30 countries so far, but I have always been thinking of visiting Africa, India, and Antarctica. Since my teenage years, and while learning history of the Middle East, I've been fascinated about the idea of traveling through Turkey, Iraq, Iran, Afganistan, Pakistan, and eventually reach India. Such a trip would be rich in experience, history, and culture. Unfortunately, the times that we live in make this idea impractical.
If you could have dinner with any person in history, whom would you invite?
I wish I could have dinner with Archimedes and Gauss—the two best mathematicians of all times.