Ramsey Theory has fascinated mathematicians ever since it was outlined by Frank P. Ramsey, who died in 1930 at age 26. Its basic thesis: "Complete disorder is impossible." Order, asserts the theory, will always emerge spontaneously within any system--natural or artificial, real or imagined--as it grows larger.

Disciples of Ramsey Theory seek to answer questions like this: If a robot blindly pokes random holes in a sheet of paper, at what number of holes will there be three that form a perfectly straight line? Or, how big must a group of people be to ensure that there are either three people who all know each or three who are mutual strangers? The answer to that one turns out to be six.

Abhi, who was born in India, began encroaching on Ramsey Theory with previous work on the Set card game. In Set, three cards are a set if they are all the same or all different--another starting point for questions like the one above, about a group of people. Now, Abhi has extended his Set research into the realm of so-called hypergraphs (graphs where data points, or nodes, are connected by three or more lines, or edges)--and proves that certain colored hypergraphs, combined with an Abelian group of numbers (they can be multiplied in any order, and the result is the same), can never have edges of a single color.

If you need to ask what that means, you probably can't afford the answer. It'll take a couple years of advanced algebra and combinatorics. But Abhi is absolutely sure that it's true. Certitude is what he likes about math. Once something has been proved, he says, you "know it to be true beyond any doubt."

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Abhi Gulati

Illinois Mathematics & Science Academy
Aurora, Ill.

Hobbies: Violin, soccer, tennis, running

Ambition: Math professor and consultant