One of the most famous questions in combinatorics is the diagonal Ramsey question. Given some n, what is the largest N for which the complete graph on N can have its edges colored red and blue so that there is no monochromatic clique of size n? The lower bound is ((\sqrt{2}+o(1))^n) and the upper bound is ((4-o(1))^n); see https://arxiv.org/abs/2005.09251 for the best known upper bound.