The mathematical incarnation of the Alday-Gaiotto-Tachikawa proposal says that the fundamental class of the moduli space of instantons in pure four-dimensional N = 2 SU(r) supersymmetric gauge theory in Omega-background is a Whittaker vector for the W(gl_r) algebra, and the Nekrasov partition function is the squared-norm of this vector. I will explain recent works with Bouchard, Chidambaram, Creutzig and Umer where we prove that the Whittaker vector is computed by topological recursion. This has interesting consequences relating the gauge theory side to intersection theory on the moduli space of curves and to Hurwitz numbers.