 This was proved by his Ph.D. student Karl Mahlburg in his 2005 paper "Partition Congruences and the Andrews–Garvan–Dyson Crank", linked below.This paper won the first Proceedings of the National Academy of Sciences Paper of the Year prize.A conceptual explanation for Ramanujan's observation was finally discovered in January 2011  by considering the Hausdorff dimension of the following formula_5 function in the l-adic topology