French philosopher Alain Badiou finds us at "the closure of an entire epoch of thought," and at this juncture he turns to a surprising adaptation: He takes set theory, an abstract branch of mathematics, as the foundation of a new philosophy. He aligns himself with Plato, Descartes, Leibniz, and Hegel, setting out to build the next great philosophical system, and to found it on mathematician Georg Cantor's pioneering theory of sets. What does it mean to transpose such a specialized, technical body of thought to a wildly ambitious philosophical project? I see in Badiou's adaptation of set theory an opportunity to read all of mathematics differently, in addition to a focal point by which to read Badiou himself more acutely.