Tutte's equations are recursion equations on the number of edges, for counting maps. Those equations can be solved for maps on surfaces of any topology, by a "topological recursion" on the Euler charcteristics. The general solution of the topological recursion is given by "symplectic invariants" of an algebraic curves. Symplectic invariants have many remarkable properties, in particular integrability (their sum is a Tau-function of a multi-KP hierarchy), and they commute with limits. With that method, it is immediate to find the asymptotic generating functions for large maps, and recognize the expansion of the solution of Painleve I equation familiar in quantum gravity.