## ABSTRACT

Albert Lautman writes that “in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe”. This chapter provides an account of both this Lautmanian dialectic and of how it can be understood to govern the development of solutions to mathematical problems, and of the concept of the mathematical real that Lautman uses to frame this dialectic. It argues that it is by clarifying Lautman’s relation to the work of Plato and Heidegger that his account of the mathematical real and the dialectic operating in relation to it can best be understood. Mathematical philosophy such as Lautman conceives it does not consist “in finding a logical problem of classical metaphysics within a mathematical theory”. “An intimate link thus exists,” for Lautman, “between the transcendence of the Ideas and the immanence of the logical structure of the solution to a dialectical problem within mathematics”.