Rôle of integrable models in the development of mathematics

Abstract

The history of mathematics and theoretical physics shows that the starting ideas of the best mathematical methods were discovered in the process of solving integrable models.

Mathematical discoveries of the last twenty years will be especially discussed as by-products of the famous integrable systems of the soliton and quantum theories.

Fields Medal 1970 for his important advances in topology, the best known being his proof of the topological invariance of the Pontrijagin classes of a differentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces.

Prepared from the author's text and the videotape of the talk, by Regina Martínez.