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. The first result put a new cap on ...

Then last fall, Milman came up for sabbatical and decided to visit Neeman so the pair could make a concentrated push on the bubble problem. “During sabbatical it’s a good time to try high-risk, high-gain types of things,” Milman said. ...