2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116315The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These equations, originating in the physics of 2-dimensional quantum gravity, have lacked mathematical justification. The goal of this paper is to provide a complete and short proof, relying on a recently established complete asymptotic expansion for the random matrix theory partition function.Submitted to the MSRI Volume related to the Workshop "Probability, Geometry and Integrable Systems", in celebration of Henry McKean's 75th birthdayMathematical Physicstext