"The point of mathematics is that we're often not answering today's questions, but rather the questions of the future."

When Peter McNamara was a teenager, he represented Ireland at the International Mathematical Olympiad in Toronto. Since joining the Bucknell faculty in 2006, he has brought the same enthusiasm that drew him into mathematics competitions to his students and the surrounding community.

"I initiated a half-credit course that teaches the techniques common in these contests, culminating in the Putnam Competition every December," says McNamara. Bucknell students have enjoyed some great success in recent years in international contests, with top-10 finishes in the prestigious Putnam Competition in 2004 and the Mathematical Contest in Modeling in 2010.

McNamara has also helped organize a Bucknell mathematics department contest for high school students: The John Steiner Gold Mathematical Competition, which attracts 150-200 students from schools as much as 100 miles away. As McNamara emphasizes, "By inviting these students to campus, we not only offer an introduction to Bucknell and a chance to tackle some very challenging problems, but we also show the participants that they have many peers who also find mathematics fun."

McNamara's early experiences in competitive mathematics have also inspired his research. He primarily studies combinatorics, an area of mathematics that appears frequently in contest problems. Combinatorics considers objects like permutations, combinations, probabilities and counting problems, and is often defined as the study of finite sets. McNamara focuses on algebraic combinatorics, explaining, "My goal is to use tools from combinatorics to answer questions from other areas of mathematics, such as algebra, topology and geometry."

Refuting the often-held perceptions that the practice of mathematical research is impractical and esoteric, McNamara draws pragmatic connections between mathematics research and real-world use. Referencing G. H. Hardy's classic essay A Mathematician's Apology (1940), McNamara says, "Hardy offers a brief discussion of the 'supreme uselessness' of the field of number theory. However, today we depend on number theory to encrypt billions of web transactions, including our Internet banking and credit card purchases. The point of mathematics is that we're often not answering today's questions, but rather the questions of the future."

Posted October 2012

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