Jeffrey felt comfortable looking into Washington University because her parents, the late Sterling Schoen, Ph.D., a professor in the graduate school in the Olin School of Business, and Patricia Schoen, an adjunct professor in the Olin School and later an instructor in University College in Arts & Sciences, had spent a good portion of their careers here.

Jeffrey had visited campus many times. Still, she was a bit apprehensive when she called the Department of Mathematics in Arts & Sciences and was put in touch with Steven G. Krantz, Ph.D., professor and chair of mathematics.

"Frankly, I didn't know if the chairman of a university mathematics department would be inclined toward dealing with junior-high students," Jeffrey said. "What I had been looking for without much success was something practical and conceptual that would be held regularly and keep kids who already had a strong interest in mathematics challenged.

"I was lucky to find Dr. Krantz."

Photo by David Kilper

Steven G. Krantz, Ph.D., professor and chair of mathematics in Arts & Sciences, looks on with Adam Rosenthal (far left), a senior mathematics major from San Diego, who brought compasses and protractors for junior-high students in the Math Circles program. Wydown Middle School seventh-grader Chris Jeffrey draws a circle while his Wydown schoolmates Becca Wall and Masa Tanikawa wait their turn.

It was in this context that Krantz began to consider a program called Math Circles. Originating in the highly respected and intense intellectual tradition of Russia, Math Circles is intended to provide a perspective on math that is not always found in the classroom.

Math Circles endeavors to present mathematics as a living, breathing entity that can truly take in a student's imagination. Krantz knew of the Math Circles programs at Harvard University, instituted by well-known mathematicians Barry Mazur and Robert Kaplan, and of another at the University of California, Berkeley. Krantz gave the possibility some thought and engaged in a bit of research. As a result, this past fall he inaugurated the Washington University Math Circles program.

For approximately 10 Wednesday evenings in the fall semester, from 4:45 p.m.-5:45 p.m., approximately 10 sixth- and seventh-grade Wydown students came to Cupples I Hall Room 199 to partake in a Math Circles presentation led by a faculty member, graduate student or undergraduate math major. One of the latter was Adam Rosenthal, a senior mathematics major from San Diego who gave a presentation on compass and straight edge constructions.

"We don't give lectures," Krantz said. "We're facilitators. We try to share things, get the students involved. I had a ball giving my presentation on map-coloring problems. And I was gratified that the kids didn't want to quit; they kept talking about it. Finally, their parents had to drag them away."

Krantz's lesson dealt with what is known as the four-color problem. Simply put, the problem entails showing that any map (consisting of countries) on a sphere can be colored with just four colors. The only rule is that no two adjacent countries can be of the same color. While the problem sounds simple, it took mathematicians 150 years and ultimately 2,000 hours of supercomputer time to prove it (in 1976, by University of Illinois mathematicians Kenneth Appel and Wolfgang Haaken).

Krantz also showed them that a map on the surface of a donut can require seven colors, and that a more complicated surface, for instance, a donut with two holes, may require even more colors.

"It's a wonderful problem that you can explain to anyone," Krantz said. "Still, it is real mathematics. You can go to Princeton and study this subject for a doctorate. There's nothing flimsy about it at all.

"And it has applications. When Steve Wozniak of Apple Computer designed the 256K chip, he used graph theory ideas similar to those that we use to study the four-color problem."

Among other mathematical forays that the students were exposed to in the fall were topological constructions; the liar and truth-teller problem (imagine everyone on an island looks the same, but some are liars, some are truthful, how do you find out who's who?), which applies logic theory; and game strategy.

"Those of us who've worked with the students have found our time with them to be fun and stimulating," Krantz said. "It's a team effort, and any such group activity is rewarding. It's been great for the students. We're not trying to supersede or to replace what is being done in their classes in the Clayton schools; rather we're trying to enrich their intellectual growth."

Math Circles has reconvened for the spring semester with classes taught mainly by tenure-track faculty, meeting once a week, just as in the fall. Krantz is hoping the program will expand so that more than one class can be offered in the future.

"Dr. Krantz and his faculty and students have just done a really excellent job," Jeffrey said. "I can't say enough about the program. The kids come out of the class and they are so excited. Every week it's, 'This class was better than the last.'