Leaving mathematics for philosophy

Abstract

This lecture is an overview of the author's own work from homotopy theory and homological algebra to the recent books Esquisse d'une Sémiophysique and Apologie du Logos, with emphasis on the rôle played by different ideas from biology in catastrophe theory.

The attitude adopted is critical towards experimentation with no underlying theory and towards an improper use of statistics as a justification of analogical thinking in science.

Fields Medal 1958 for inventing and developing the theory of cobordism in algebraic topology. This classification of manifolds used homotopy theory in a fundamental way and became a prime example of a general cohomology theory.

Prepared from the author's text and the videotape of the talk, by Àngel Calsina.