submited by

Style Pass

A year after he started his Ph.D. in mathematics at McGill University, Matt Bowen had a problem. “I took my qualifying exams and did absolutely horribly on them,” he said. Bowen was sure that his scores didn’t reflect his mathematical skills, and he resolved to prove it. Last fall he did, when he and his adviser, Marcin Sabok, posted a major advance in the field known as Ramsey theory.

For almost a century, Ramsey theorists have been gathering evidence that mathematical structure persists in hostile circumstances. They might break apart big sets of numbers like the integers or the fractions, or slice up the connections between points on a network. They then find ways to prove that certain structures are inevitable, even if you try to avoid creating them by breaking or slicing in a clever way.

When Ramsey theorists talk about splitting up a set of numbers, they often use the language of coloring. Pick several colors: red, blue and yellow, for example. Now assign a color to every number in a collection. Even if you do this in a random or chaotic way, certain patterns will inevitably emerge so long as you use only a finite number of different colors, even if that number is very large. Ramsey theorists try to find these patterns, searching for structured sets of numbers that are “monochromatic,” meaning their elements have all been assigned the same color.

Read more quantamagazi...