Mathematician Judy Holdener has a distinct advantage over most of her peers. She started out as an art major. "A lot of people can't understand mathematics because they see symbols but can't visualize the concepts behind the symbols," says Holdener, who studied art for two years before switching to mathematics. "When I'm designing a lesson for students, I'm always thinking about how to present the material so they can picture what's happening."

This attention to visualization often leads to the creative use of technology. In a Web-based course called "Modeling Biological Growth and Form," for example, Holdener uses computers and the Internet to simulate and quantify forms found in nature, a field known as theoretical morphology. Her creativity has been recognized by students and colleagues alike. In 2003, Holdener won two prestigious Kenyon awards, the Trustee Teaching Excellence Award and the Robert J. Tomsich Science Award.

Some of Holdener's recent research deals with number theory and perfect numbers-an interest inspired in part by her work with a student in an independent-study project. Perfect numbers-numbers equal to the sum of their proper divisors-have posed some of the most interesting and longstanding unsolved questions in mathematics. All of the known perfect numbers are even, and as mathematicians and computer scientists search for new ones, they wonder whether there could be an odd one out there waiting to be discovered.

"For two thousand years, the conjecture has been that there is no odd perfect number," says Holdener. "After my research, I'm actually thinking that there could be one."