Michael Freedman | A Fields Medalist Panorama

The Cartesian Cafe

Michael Freedman is a mathematician who was awarded the Fields Medal in 1986 for his solution of the 4-dimensional Poincare conjecture. Mike has also received numerous other awards for his scientific contributions including a MacArthur Fellowship and the National Medal of Science. In 1997, Mike joined Microsoft Research and in 2005 became the director of Station Q, Microsoft’s quantum computing research lab. As of 2023, Mike is a Senior Research Scientist at the Center for Mathematics and Scientific Applications at Harvard University.

Patreon (bonus materials + video chat): https://www.patreon.com/timothynguyen

In this wide-ranging conversation, we give a panoramic view of Mike’s extensive body of work over the span of his career. It is divided into three parts: early, middle, and present day, which respectively include his work on the 4-dimensional Poincare conjecture, his transition to topological physics, and finally his recent work in applying ideas from mathematics and philosophy to social economics. Our conversation is a blend of both the nitty-gritty details and the anecdotal story-telling that can only be obtained from a living legend.

I. Introduction

• 00:00 : Preview
• 01:34 : Fields Medalist working in industry
• 03:24 : Academia vs industry
• 04:59 : Mathematics and art
• 06:33 : Technical overview

II. Early Mike: The Poincare Conjecture (PC)

• 08:14 : Introduction, statement, and history
• 14:30 : Three categories for PC (topological, smooth, PL)
• 17:09 : Smale and PC for d at least 5
• 17:59 : Homotopy equivalence vs homeomorphism
• 22:08 : Joke
• 23:24 : Morse flow
• 33:21 : Whitney Disk
• 41:47 : Casson handles
• 50:24 : Manifold factors and the Whitehead continuum
• 1:00:39 : Donaldson’s results in the smooth category
• 1:04:54 : (Not) writing up full details of the proof then and now
• 1:08:56 : Why Perelman succeeded

II. Mid Mike: Topological Quantum Field Theory (TQFT) and Quantum Computing (QC)

• 1:10:54: Introduction
• 1:11:42: Cliff Taubes, Raoul Bott, Ed Witten
• 1:12:40 : Computational complexity, Church-Turing, and Mike’s motivations
• 1:24:01 : Why Mike left academia, Microsoft’s offer, and Station Q
• 1:29:23 : Topological quantum field theory (according to Atiyah)
• 1:34:29 : Anyons and a theorem on Chern-Simons theories
• 1:38:57 : Relation to QC
• 1:46:08 : Universal TQFT
• 1:55:57 : Witten: Donalson theory cannot be a unitary TQFT
• 2:01:22 : Unitarity is possible in dimension 3
• 2:05:12 : Relations to a theory of everything?
• 2:07:21 : Where topological QC is now

III. Present Mike: Social Economics

• 2:11:08 : Introduction
• 2:14:02 : Lionel Penrose and voting schemes
• 2:21:01 : Radical markets (pun intended)
• 2:25:45 : Quadratic finance/funding
• 2:30:51 : Kant’s categorical imperative and a paper of Vitalik Buterin, Zoe Hitzig, Glen Weyl
• 2:36:54 : Gauge equivariance
• 2:38:32 : Bertrand Russell: philosophers and differential equations

IV: Outro

• 2:46:20 : Final thoughts on math, science, philosophy
• 2:51:22 : Career advice

Some Further Reading:
Mike’s Harvard lecture on PC4: https://www.youtube.com/watch?v=TSF0i6BO1Ig
Behrens et al. The Disc Embedding Theorem.
M. Freedman. Spinoza, Leibniz, Kant, and Weyl. arxiv:2206.14711

Twitter:
@iamtimnguyen

Webpage:
http://www.timothynguyen.org