Wheatley enjoying the challenge of higher math
and teaching it to elementary and
middle-school students.

It's easy to picture a Riemann surface. Think of a sphere or a donut or a pair of pants. Now imagine that the points on these surfaces correspond in a precise way to complex numbers. You get a mathematical structure that seems to have applications all over the place in mathematics.

How can such seemingly simple objects be loaded with so much deep information? Ask Stephen Wheatley (MATH '06). Every other week he met with mathematics professor I-Lok Chang to discuss Riemann surfaces. As they worked their way through a text on the subject, Chang offered guidance and answered questions. The rest was up to Wheatley.

These surfaces are very useful because they can represent multiple-valued functions intuitively and understandably.

In number theory, Riemann surfaces come up in the proof of Fermat's Last Theorem, the most famous mathematical theorem of all time. In the theory of complex functions, Riemann surfaces are the most natural spaces on which functions live. In hyperbolic and spherical geometry, dynamical systems, cryptography, and many other areas of math they also have a knack for being at the center of the action.

From his research, Wheatley hopes to learn much from Riemann surfaces because the subject encompasses a whole range of higher-level math. Understanding the topic would be a successful result.

Wheatley did research at the math department while teaching at a math camp called MathTree. MathTree helps third-to- ninth-graders with basic math up to algebra 1. After his research, he plans to lecture on Riemann surfaces at a conference in the district area and most likely at a colloquium at American U. He hopes to one day become a mathematics professor.

Reprinted by permission of Catalyst, Fall 2005.