Emily Riehl Makes Infinity Categories Elementary

About this episode

Emily Riehl discusses making infinity category theory accessible to undergraduates and its implications for mathematics education.

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 (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join Links: •⁠ ⁠Emily’s profile: https://emilyriehl.github.io/ •⁠ ⁠Emily’s presentation: https://emilyriehl.github.io/files/undergraduates-TOE.pdf •⁠ ⁠A Type Theory For Synthetic ∞-Categories (paper): https://arxiv.org/pdf/1705.07442 •⁠ ⁠Could ∞-Category Theory Be Taught To Undergraduates? (paper): https://arxiv.org/pdf/2302.07855 •⁠ ⁠RZK proof assistant: https://rzk-lang.github.io/rzk/en/latest/ •⁠ ⁠Lean Zulip chat: https://leanprover.zulipchat.com/#recentnews Timestamps: 00:00 A Dream for the…

People in this episode

Host: Curt Jaimungal

Guest: Emily Riehl

Topics covered

• infinity category theory
• mathematics education
• category theory
• foundations of math
• abstraction

Keywords

• infinity categories
• category theory
• mathematics
• education
• abstraction
• Curry-Howard correspondence
• functors

Sponsors

The Economist

Mentioned in this episode

Organizations: TOE

Books & works: A Type Theory For Synthetic ∞-Categories, Could ∞-Category Theory Be Taught To Undergraduates?

More episodes of Theories of Everything with Curt Jaimungal

• We're Simulated. AI Is Conscious. And We Can't Win. · June 1, 2026 · 2h 1m
• The Genius Who Invented Reverse Mathematics · May 18, 2026 · 1h 39m
• Janna Levin: The Unreasonable Effectiveness of the Klein Bottle · May 11, 2026 · 2h 5m
• Juan Maldacena: Geometry as Entanglement, and the Emergence of Spacetime · May 4, 2026 · 1h 48m
• Slavoj Zizek: “Buddhism Can’t Explain This” · April 27, 2026 · 1h 35m
• Curt Jaimungal: Consciousness, Irreducibility, and the Local to Global · April 22, 2026 · 1h 0m