The 42nd Ockham Lecture - Experiments in Mathematics

Professor Minhyong Kim FRSE

Former Tutor in Mathematics (2010-20), Merton College

Edmund Whittaker Professor of Mathematical Sciences, University of Edinburgh

Professor of Mathematics, Heriot-Watt University, Edinburgh

Director Emeritus, International Centre for Mathematical Sciences, Edinburgh, Fellow of King's College, Cambridge

Do mathematicians experiment? Some sophisticated thinkers tell us mathematics is just logic. Is the "Pythagorean theorem", for example, an empirical fact? Over the course of my professional life, I have continued discussions with mathematicians, physicists, and philosophers on the role of experiments in mathematics, and how they compare to experiments in physics. In this talk, I will offer some tentative conclusions by way of two examples, one a historical example from topology, and the other of great contemporary interest in number theory.