# The art of numbers

Judy Holdener wins Trustee Teaching Excellence Award and Robrt J. Tomsich Science Award

Mathematician Judy Holdener has a distinct advantage over most of her peers. She started out as an art major.

"I'm a very visual person," explains Holdener, who was awarded tenure and promotion to the rank of associate professor of mathematics this spring. Raised by an artist, Holdener started drawing when she was only two years old, and she studied art for two years at Kent State University before switching to mathematics. "A lot of people can't understand mathematics because they see symbols but can't visualize the concepts behind the symbols. 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 creative approach to teaching and scholarship helped Holdener earn both the Kenyon College Trustee Teaching Excellence Award and the Robert J. Tomsich Science Award this year.

Holdener's recent research publications deal with number theory and perfect numbers. Some of the most interesting and longstanding unsolved mathematical questions involve perfect numbers--that is, numbers equal to the sum of their divisors.

"Some of the problems are very easy to state but extremely difficult to solve," Holdener says. "Some of the questions have been around for two millenia."

Mathematicians and computer scientists are continually searching for new perfect numbers. And since all the known perfect numbers are even, some mathematicians like Holdener are intrigued by the notion of an odd perfect number out there waiting to be discovered.

"The conjecture that's been around for two thousand years is that there is no odd perfect number," she says. "After my research, I'm actually thinking that there could be one, but there's no way to really know."

Holdener's interest in perfect numbers was sparked by her work with a Kenyon student. In the spring of 1999, Jim Riggs '99 began working with Holdener on an independent study project. Holdener encouraged Riggs, who is now a systems analyst at Kenyon's Olin Center, to try and solve a problem related to number theory presented in a mathematics journal. He took the challenge and was recognized in a later issue for coming up with the correct solution.

"When I gave him the problem, he just came alive," Holdener remembers. "He was much more of a researcher who wanted open-ended problems to tackle. When I saw him light up on this problem, I just threw away the textbook we were using."

A Kenyon faculty member since 1998, Holdener is known for her creative and interactive teaching style. She is a firm believer in using technology in the classroom. In "Modeling Biological Growth and Form," a Web-based course Holdener taught, she used computers and the Internet to simulate and quantify forms found in nature, a field known as theoretical morphology. And technology is an obvious way to help her students get the big picture in mathematics courses.

"Computer programs allow you to visualize mathematics," she says. "They help you produce the right pictures, so students can see what's going on behind the symbols."