AustMS2021 plenary profile – Emily Riehl

This is the fourth in a series of interviews with the plenary speakers for the upcoming 65th Annual Meeting of the AustMS.

  1. What is your earliest mathematical memory?

Not the earliest memory but an early memory is being absolutely delighted by Louis Sachar’s Sideways Arithmetic from Wayside School. Problems include EGG + EGG = PAGE, SHE+EEL = ELSE, etc.

  1. What made you decide to become a mathematician, and when?

I’ve loved math my entire life and had decided to become a mathematician by mid high school, when I started learning about proofs.

  1. Name a favourite paper by a contemporary mathematician, and why (or more than one, if you can’t decide).

John Bourke’s and Richard Garner’s “Algebraic weak factorisation systems I: accessible AWFS” is absolutely beautiful and on a topic very close to my heart. 

Though I also have to mention the delightful “Homophonic quotients of free groups” by Jean-Francois Mestre, René School, Lawrence Washington, and Don Zagier, which everyone should read immediately.

  1. What historical mathematician would you like to be able to talk maths with? What would you ask them?

I’d love to hear Emmy Noether describe the insights that lead her to modern algebra.

  1. What result would you like to see in mathematics in the next 10 years?

I’d like to see a variant of homotopy type theory which actually computes, includes higher inductive types, and has semantics in any ∞-topos. Mike Shulman has proven that traditional homotopy type theory (without higher inductive types) has semantics in any ∞-topoi, but we’re still working on understanding the semantics of the new experimental “cubical” versions of homotopy type theory which have constructive proofs of univalence.