On May 19, Ashwin Sah posted the best result ever on one of the most important questions in combinatorics. It was a moment that might have called for a celebratory drink, only Sah wasn’t old enough to order one...
...Sah’s proof, in contrast, improved the upper bound for two-color Ramsey numbers. He achieved it by optimizing a method that originated with Erdős and Szekeres, and which a small number of mathematicians have managed to improve since. Sah’s result proves that once a graph reaches a certain size, it inevitably contains a clique of some corresponding size. Many in the field see Sah’s proof as the best result that can be achieved using the existing line of research...
Read more about the research from Quanta Magazine: Undergraduate Math Student Pushes Frontier of Graph Theory