The association sponsors the International Congress on Mathematical Physics (ICMP), which takes place every three years, and it also supports smaller conferences and workshops.

IAMP currently awards two kinds of research prizes in mathematical physics at its triannual meetings, the Henri Poincaré Prize (created in 1997) and the Early Career Award (created in 2009).

The presidents of the IAMP since its foundation were: The Henri Poincaré Prize is sponsored by the Daniel Iagolnitzer Foundation to recognize outstanding contributions in mathematical physics, and contributions which lay the groundwork for novel developments in this broad field.

The Prize was also created to recognize and support young people of exceptional promise who have already made outstanding contributions to the field of mathematical physics.

The prize is usually awarded to three individuals every three years at the International Congress on Mathematical Physics (ICMP).