May 14, 2014

# Aaron Levin: Spilling the beans about math

May 14, 2014

Aaron Levin is an assistant professor of mathematics whose research focuses on number theory. He recently received one of the National Science Foundation's most prestigious and competitive awards for junior researchers—a Faculty Early Career Development grant.

“How many jelly beans are in the jar?”

Thus began one of the earliest memories I have of the power and efficiency of mathematics. I was in fourth grade, and the teacher had asked the class to estimate, by any means, the number of jellybeans sitting in a clear jar on a plain desk in the front of the room. We were allowed to make any measurements we wanted and kids could be seen twirling the jar in all directions trying to gain some extra advantage.

Earlier in the week, while riding in the car, I remember having coincidentally asked my mother how to calculate the area of a circle. I quickly put the knowledge to work, using a ruler to make some measurements, and estimated the volume of the cylindrical jar and the volume of a jellybean. Dividing the volume of the jar by the volume of a jelly bean, and then subtracting a bit to allow for some space between the jelly beans, I wrote down my estimate on a torn piece of paper and gave it to the teacher.

I was genuinely surprised when I ended up coming the closest to the actual number of jellybeans in the jar. I never forgot that simple illustration of the strength of mathematics. Or it could have been the fact that I got to eat the jellybeans.

By the time I was in high school my interests had expanded from jellybeans to include number theory, the subject in mathematics that would eventually become my primary focus. In particular, I became enamored with Diophantine equations. These equations, named after the third-century mathematician Diophantus of Alexandria, are polynomial equations where one is interested in solutions in which the variables have integer values. Diophantine equations are notoriously difficult to solve, and I enjoyed trying my hand at some of the famous open problems.

While this may seem far from the practical world of counting jellybeans, pure mathematics has often had surprising and unexpected practical applications. Number theory has turned out to be indispensable in the modern world. It is an essential tool in modern cryptography and is used, for example, every day to securely send credit card information for purchases made over the internet.

My current research is still focused on Diophantine equations and its many related topics in number theory. In support of my research program, I have recently received an NSF CAREER award. This five-year grant will support my research and related activities at MSU, including a funded education component concentrated on undergraduate research projects.

I have a strong personal connection with undergraduate research that goes back to my freshman year in college, when a research project slowly grew out of my attempts to understand a remark that I had seen in an exercise in the first-year calculus text. This undergraduate project eventually led to my first two published papers.  I am excited that my current NSF CAREER grant will further my opportunity to help cultivate the potential that lies in our talented undergraduates at MSU.

Photo by G.L. Kohuth