The original version of this story appeared in Quanta Magazine. So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating mathematical patterns.

Add Yahoo as a preferred source to see more of our stories on Google. The number zero was a relatively recent and crucial addition − it allows numbers to extend in both directions forever.

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So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating mathematical patterns. The first result put a new cap on how big a set of integers can ...