A P-point is a type of ultrafilter on the natural numbers with special combinatorial regularity properties, meaning every partition of the naturals into finitely many pieces has one piece that belongs to the ultrafilter. Under ZFC, the existence of P-points is independent of the standard axioms, as Shelah showed they need not exist and other models guarantee they do. The open problem is whether removing the Axiom of Choice changes this picture fundamentally, specifically whether ZF alone can decide the existence question, or whether P-points remain independent even in choiceless set theory.