This celebrated conjecture (https://en.wikipedia.org/wiki/Union-closed_sets_conjecture) has seen some recent breakthroughs and a (not yet peer-reviewed) proof has been claimed on arxiv on February 6 2023 (https://arxiv.org/abs/2302.03484) EDIT - retracted. Will be resolved as YES if a proof is discussed and accepted by expert mathematicians in a blog post or communicated at a major maths conference. I expect the recent arxiv proof, if incorrect, will be refuted pretty quickly and discussed by mathematicians online.