Breakthrough in fiendishly hard puzzle has mathematicians partying

Mathematicians have made a breakthrough on an incredibly difficult problem in combinatorics, the study of combinations. It is the first significant advance in nearly a century for our understanding of Ramsey numbers, which can be used to describe the minimum size of a party where cliques of a certain size can or can’t exist.

Named after mathematician Frank Ramsey, these numbers deal with the possible relationships between nodes on a mathematical network called a graph, which are a …