Mathematical Conversations

The study of the planar-circular-restricted 3-body problem led to Poincaré's "last geometric theorem", nowadays known as the Poincaré-Birkhoff theorem. It is a fixed point theorem for certain area-preserving annulus homeomorphisms. Birkhoff's proof did not allow for generalizations, and we had to wait until the 1960's when Arnold realized that the Poincaré-Birkhoff theorem (in the smoothcase) is a consequence of a certain conjecture on the number of fixed points of Hamiltonian diffeomorphisms. The conjecture was one among others of the same flavor, and they motivated the invention of Floer theory. In this talk I would like to give more details on this remarkable chain of events.