Millennium Prize Problems Lecture

Date: September 17, 2025

Location: Harvard Science Center Hall D & via Zoom Webinar

Time: 5:00–6:00 pm

Speaker: Michael Freedman, Harvard CMSA and Logical Intelligence 

Title: The Poincaré Conjecture and Mathematical Discovery  

Abstract: The AI age requires us to re-examine what mathematics is about. The Seven Millenium Problems provide an ideal lens for doing so. Five of the seven are core mathematical questions, two are meta-mathematical – asking about the scope of mathematics. The Poincare conjecture represents one of the core subjects, manifold topology. I’ll explain what it is about, its broader context, and why people cared so much about finding a solution, which ultimately arrived through the work of R. Hamilton and G. Perelman. Although stated in manifold topology, the proof requires vast developments in the theory of parabolic partial differential equations, some of which I will sketch. Like most powerful techniques, the methods survive their original objectives and are now deployed widely in both three- and four-dimensional manifold topology. 

Read more about the Poincaré Conjecture at the Clay Math website.

Organizers: Martin Bridson, Clay Mathematics Institute | Dan Freed, Harvard University and CMSA | Mike Hopkins, Harvard University

Millennium Prize Problems Lecture Series