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Dan Kalman Receives Prestigious Lester R. Ford Award

Photo: Heather Kinsman

Convinced that Marden's Theorem, which struck him as "the most amazing combination of ideas" while he was in college and stuck with him ever since then, deserved wider recognition, Professor Dan Kalman spent the past few years examining gaps in the theorem and developing a straight-forward, understandable proof. The resulting paper, "An Elementary Proof of Marden's Theorem," was awarded the Lester R. Ford Award by the Mathematical Association of America (MAA). Marden's Theorem is a mathematical theorem that relates the roots of a polynomial p(x) and those of its derivative p´(x) in a complex plane.

According to the MAA, "The extraordinary lucidity of Kalman's argument combines with his historical scholarship on the theorem's origins and the charm of this surprising result to make this article a model of mathematical exposition." The proof is completely elementary and yet draws on background information from several diverse parts of elementary mathematics.

A related paper, "The Most Marvelous Theorem in Mathematics," with dynamic graphics, extended historical remarks, and detailed mathematical background, is available online. The online edition uses specially-designed MAA software to turn the article into an interactive document, with hypertext that allows readers access to additional details and insights. The hypertext also provides enough supplemental background information on the paper's elementary mathematics topics that anyone with a command of first-year calculus can work through whatever details are unfamiliar or interesting.