Apparently there has been a breakthrough in #RamseyTheory announced in talks today by Sahasrabudhe, Morris, Griffiths and Campos; the long standing upper bound of (4+𝑜(1))ⁿ of the size of a graph required to force either a clique or independent set has finally been reduced to (4−ε)ⁿ for some positive constant ε (something around 1/2000, from what I'm told). From what I understand, they have developed a new "Book algorithm" to more efficiently locate cliques and independent sets based on recursively finding companion graphs that they call "books". I don't have further details at this stage, though.