Emily Riehl Makes Infinity Categories Elementary
4/6/20262 hr 50 min
Emily Riehl, one of the world’s leading category theorists, shares her vision for making infinity category theory something undergrads can actually learn. In this talk, she breaks down how rethinking the foundations of math could change the way it’s taught and understood—and why it might redefine what math even is. I subscribe to The Economist for their science and tech coverage. As a TOE listener, get 35% off! No other podcast has this: https://economist.com/TOE Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://tinyurl.com/SpotifyTOE Become a YouTube Member...
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First 90 secondsEmily Riehl· Guest0:00
This talk was kind of a dream. I'll sort of state my dream for the future. If the foundations of mathematics had some sort of higher structure with something like homotopy type theory, then we could teach infinity category theory to undergraduates much like we teach something like abstract algebra to undergraduates today.
Curt Jaimungal· Host0:17
Today's talk is being given for the first time, so you're in for a huge treat. Professor Emily Riehl, an award-winning mathematician and professor at John Hopkins University, is a proficient explicator and one of the world's most renowned category theorists. The question explored today is, how would you teach infinity categories, so a topic that's notoriously thorny even for experts in adjacent fields of math, to undergraduates? In exploring this, we cover not only an overview of regular category theory, so don't worry, but also how homotopy type theory provides a constitutional new language that could fundamentally transform how mathematics is understood, taught, and applied. We also cover the Curry-Howard correspondence, identity types, the univalence axiom, and what the heck infinity groupoids are. My name is Curt Jaimungal, and on this channel, I investigate theories of everything, primarily from a theoretical physics background, as that's my training from the University of Toronto, but also from a mathematics and philosophy perspective. Today, I'm excited and honored that Emily Riehl has perfected this talk, revamping it from previous lectures on infinity categories for undergraduates. So you're seeing the latest version of it being delivered here for the first time on Theories of Everything.