Number Theory Seminar
Speaker: Joël Ouaknine (MPI Saarbrücken)
Title: Fragments of Hilbert’s Program
Abstract: Hilbert’s dream of mechanising all of mathematics was dealt fatal blows by Gödel, Church, and Turing in the 1930s, almost a hundred years ago. Paradoxically, assisted and automated theorem proving have never been as popular as they are today! Motivated by algorithmic problems in discrete dynamics, nonlinear arithmetic, and program analysis, we examine the decidability of various logical theories over the natural numbers, and discuss a range of open questions at the intersection of logic, automata theory, and number theory.
Abstract: Hilbert’s dream of mechanising all of mathematics was dealt fatal blows by Gödel, Church, and Turing in the 1930s, almost a hundred years ago. Paradoxically, assisted and automated theorem proving have never been as popular as they are today! Motivated by algorithmic problems in discrete dynamics, nonlinear arithmetic, and program analysis, we examine the decidability of various logical theories over the natural numbers, and discuss a range of open questions at the intersection of logic, automata theory, and number theory.