The Theory of Numbers, from Ancient Greece to the 21st Century

Australian Mathematics Society Mahler Lecturer Professor Matthew Emerton, Department of Mathematics, University of Chicago.

This lecture, aimed at members of the public interested in mathematics, will explain some of the key ideas in the theory of numbers, as developed over the last two thousand-plus years. Beginning with the theory of geometric constructions from ancient Greek geometry, and its relationship to the discovery and properties of irrational numbers, Professor Emerson will sketch in broad outlines how these ideas evolved, through the theory of equations and their symmetries as developed by Galois, culminating in a description of some of the contemporary aspects of the theory. The focus of this lecture will be on emphasising how symmetries of mathematical problems, some obvious but some not-so-obvious, play a hidden role in the nature of their solutions.

Professor Emerton’s areas of research are number theory, arithmetic geometry, and representation theory. He is known for his work on the Fontaine–Mazur conjecture, and for his construction (with Professor Toby Gee of Imperial College) of the eponymous Emerton–Gee Stacks, higher dimensional algebro-geometric objects which parameterize local Galois representations. Professor Emerton’s research is funded in part by both the National Science Foundation and the Simons Foundation.

The Mahler Lectures are a biennial activity organised by the Australian Mathematical Society and supported by the Australian Mathematical Sciences Institute. The Mahler Lectureship is awarded every two years to a distinguished mathematician working in an area of mathematics associated with the work of Professor Kurt Mahler. Professor Mahler was one of the major characters of Australian mathematics from his arrival in this country in the 1960s, until his death in 1988.