Hilbert’s Sixth Problem and Topos Theory


Draft of the talk here.

Abstract: On August 8, 1900, David Hilbert presented the then community of mathematicians a list of problems in the Second International Congress in Paris. These problems shaped the mathematics of the proceeding years. One particular problem, called Hilbert's Sixth Problem, was a programmatic call for the axiomatization of physics. To date, no satisfactory axioms have been proposed. In this talk, we survey the mathematical reasons why this is the case and present a possible approach using Topos Theory.