In mathematics, the institute develops research in the following areas:

Research in calculus of variations and differential equations is based on problems from geometry, physics or engineering sciences that are, in general, impossible to solve explicitly. They concern the existence, uniqueness, regularity and symmetries of solutions of these problems.

In algebra, research is mainly concerned with group theory.

Research in category theory, an abstract field of mathematics, has many interactions with algebra, logic, algebraic topology, algebraic geometry and theoretical computer science. At IRMP, research in category theory concerns both algebraic and geometric aspects of the theory.

Algebraic topology is the study of structures and properties of spaces that are invariant by continuous deformation. The research focuses on the development and geometric applications of rational homotopy, which is one of the best algebraic modelling of spaces. The emphasis is on applications to differential topology.

Members of the institute also pursue research in didactics and epistemology of mathematics and in the history of sciences.