American Go E-Journal

A striking advance in mathematical game theory earned top honors for the team of James Pinkerton 1d (l), and Rafael Setra (r) in the recent Region Five Finals of the 2010-11 Siemens Competition in Math, Science & Technology, a premier science research competition for high school students. Pinkerton, an avid go player, and Setra are seniors at Montgomery Blair High School in Silver Spring, Maryland.  Their win in the team category has scored them a $6,000 scholarship for their mathematics project, The Duplicator-Spoiler Game for an Ordinal Number of Turns.  Their math research might be analogized to mirror go–the players, a spoiler and a duplicator alternate turns, choosing elements from two sets until the duplicator is unable to mirror the spoiler’s move.

In the math, the number of turns for the spoiler to win tells you about the complexity of statements in mathematical logic needed to differentiate the sets.  Traditionally the games have a finite number of turns and their research extended the games to arbitrary lengths over various infinite structures. “This team has made a striking extension of a game-theoretic interpretation of descriptive logic that dates back to the 1960s. Using it, they can distinguish between mathematical structures not separable by simple queries,” said competition judge Haynes Miller, Professor of Mathematics at MIT. “Their work has potential applications to resource allocation in designing search algorithms. What impressed me about these students was their clarity of thought. It’s a very confusing subject to work in and they found their way through it to a new frontier.”

Pinkerton is president of the Chess Club and a member of the National Honors Society and French Honors Society. Fluent in French, he single sculls on the Potomac and plays chess and go competitively. Pinkerton teaches chess as a volunteer in several programs in his county and in inner-city Washington, DC. He also teaches mathematics to underclassmen. He credits his father (E-J staff photographer John Pinkerton) who taught him “fun mathematics, not the dreary algebra of secondary school,” with nurturing his love for the subject.  Pinkerton would like to study mathematics in college and to become a university professor. Setra was born in Sao Paulo, Brazil, and moved to the US when he was eight years old. He speaks Portuguese and Spanish and is part of Operation Fly, National Honors Society and the Martial Arts Club. A volunteer at Viers Mill Elementary School, Setra plays Starcraft 2, non-competitive football and has just learned how to play go from Pinkerton. He would like to study mathematics, engineering and computer science and to become a college professor.