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By Caitlin Jennings, Communications Coordinator, Society for Science & the Public

Jacob Fox won second place at Intel STS 2002 for his project in an area of discrete mathematics known as Ramsey Theory; his findings, “Rainbow Arithmetic Progressions and Anti-Ramsey Results,” were published in 2003 in *Combinatorics, Probability, and Computing*.

Perhaps it is not surprising then that, eight years later, he won the Konig Prize, named after Denes Konig, a pioneer in discrete math, for new findings in Ramsey Theory. “[STS] was really a starting point for me,” Jacob says . “I’m still in the field, and it’s not far from what I do now.” He won the prize, which is funded by Google and given by the Society for Industrial and Applied Mathematics, based on his work making progress on questions that mathematicians have been pondering for decades. “These are really old, classical questions,” he says.

Ramsey Theory originates from the mathematical work of Frank P. Ramsey, a brilliant theorist whose life was cut short at 26 years, in 1930; the same year he published the paper *On a problem of formal logic* that contained the theory that would be named after him. Ironically, the theory was used as a minor lemma, or proven proposition to support a larger statement, in the paper, but mathematicians have been studying it ever since.It concerns conditions where there must be order, even in seemingly disordered systems.

For example, according to Ramsey's theorem, at a party of six people there must be three of them that are mutual strangers (no two of them met before the party) or are mutual acquaintances (each pair of them have met before). No matter what the combination of pairs of strangers and acquaintances, this theorem holds true. However, this theorem does not remain true for any party of less than six people. This fact is written like this: R(3,3) = 6.

In this case, R(3,3) is called a Ramsey number and, while the above example has a clear answer, Ramsey numbers are tricky to determine. It is theorized that we will never know the exact value of certain Ramsey numbers unless there is a theoretical breakthrough. The mathematician Joel Spencer summed up mathematician Paul Erdős’ thoughts on this in Ten Lectures on the Probabilistic Method. “Erdős asks us to imagine an alien force, vastly more powerful than us, landing on Earth and demanding the value of R(5, 5) or they will destroy our planet. In that case, he claims, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they ask for R(6, 6). In that case, he believes, we should attempt to destroy the aliens.”

This is why Jacob’s award-winning work is so important: he made progress on estimating Ramsey numbers. Although there is still a lot of work to do, the progress he has made with his collaborators Benny Sudakov and David Conlon on these decades-old questions has people excited.

Jacob was always excited by math and discrete math and went to several study programs, conducting his Intel STS project research at the Research Science Institute at MIT. “STS was an amazingly inspiring experience for me,” he says, “It was a really pivotal point looking back, to what I am doing now…If other people show that they are interested in what you are doing, it gets you pushing farther in the same direction,” he says. He pushed farther by going on to MIT, where he studied theoretical mathematics, and then Princeton, where he recently completed his Ph.D.

He also notes that, along the way, he has run into a lot of other people who share his connection to STS and ISEF. “It’s really a small world,” he says. For example, this fall he will be joining Jonathan Kelner (STS 1998, ISEF 1998) as an assistant professor in the MIT math department. Perhaps, in this way, the Intel STS and Intel ISEF have helped Jacob turn more strangers into acquaintances and friends.

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