Four mathematicians have made a significant breakthrough in graph theory by finding an improved upper limit for the Ramsey number, a fundamental property of graphs. The Ramsey number quantifies how big a graph must be before specific patterns are guaranteed to emerge. This number has been notoriously difficult to calculate, with only the simplest instances having known values. The mathematicians’ research has led to an exponential improvement in the upper bound for the Ramsey number. The discovery has been met with great excitement and has opened up new possibilities for understanding the deep connections between combinatorics, probability, and geometry.
https://www.quantamagazine.org/after-nearly-a-century-a-new-limit-for-patterns-in-graphs-20230502/