Dartmouth professors honored for cracking 30-year-old math problem: Can one hear the shape of a drum?

Posted 01/12/01

Two Dartmouth mathematicians, Carolyn S. Gordon and David L. Webb, received the prestigious Chauvenet Prize this week from the Mathematical Association of America (MAA). The prize, first awarded in 1925, recognizes an outstanding expository article on a mathematical topic by a member of the association.

Gordon, the Benjamin Cheney Professor of Mathematics, and Webb, Professor of Mathematics, received the award for their article "You Can't Hear the Shape of a Drum," published in the journal American Scientist in January 1996. The article describes work they carried out with colleague Scott Wolpert in response to a question first raised in a 1966 article titled "Can One Hear the Shape of a Drum?" by Mark Kac.

"I was surprised and deeply honored to learn that our article was chosen for the Chauvenet Prize. It is especially gratifying that the Association chose an article that was written not specifically for mathematicians but rather for a general scientifically literate audience," said Gordon.

In the article, Gordon, Webb and Wolpert suggested that two drumheads of different shapes could have the same vibration frequencies, thus answering Kac's question in the negative.

The MAA cited the article as being "exciting, its mathematical content understandable by anyone with a minimal knowledge of differential equations, group theory, and linear algebra; and it contains a great deal of historical information concerning what can be inferred about vibrating systems from their frequencies."