In Proofs and Refutations, Imre Lakatos proposed to reorient the philosophy of mathematics. He suggested abandoning the search for a foundation for mathematics in favor of providing a methodology for mathematics. This essay attempts to pursue the methodological project in a different fashion. It sketches the long history of mathematics, and reflects on the kinds of benefits attained in a number of important transitions. It argues that these advances embody quite different gains. While diverging from Lakatos’s quasi-Popperian framework for mathematical progress, I conclude that his proposed reorientation of the philosophy of mathematics would be an advance that is long overdue.