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by Deniz Sarikaya, Thorsten Altenkirch
aboutlogic is a podcast on logic, foundations of mathematics, philosophy, and theoretical computer science. aboutlogic features in-depth conversations with people working in and around the foundations of these subjects. We talk about topics ranging from the foundations of computer science and set theory to critical thinking, puzzles, and what academic life is really like—its motivations, frustrations, and surprises.
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- Today58 min
aboutlogic #24 | Why Didn't Homotopy Type Theory Take Over the World? | Ulrik Buchholtz
Why Didn't Homotopy Type Theory Take Over the World? | aboutlogic #25 From ordinal analysis to homotopy type theory: Ulrik Buchholtz (University of Nottingham) talks with Deniz and Thorsten about his journey from algebraic topology to Sol Feferman's unfolding program and from there into univalent foundations. Why do ordinals measure the strength of mathematical theories? What makes a definition predicative? And what is the one open problem that keeps homotopy type theory from taking over mathematics?
- 1 weeks ago32 min
aboutlogic premises #10 | Is Unique Choice Really a Choice? (Follow-up to Giovanni Sambin)
Is Unique Choice Really a Choice? (Follow-up to Giovanni Sambin) | aboutlogic premises #10 If there is only one possible choice, are you making a choice at all? In this Premises, Thorsten and Deniz pick up the debate from our conversation with Giovanni Sambin: why does his minimalist foundation reject the Axiom of Unique Choice, while homotopy type theory proves it, and why does Lean make it so hard to use constructively? Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.
- 2 weeks ago57 min
aboutlogic #23 | Rebuilding Mathematics from the Ground Up | Giovanni Sambin
What does set theory have to do with reality? Giovanni Sambin, Professor at the University of Padua and a leading figure in constructive mathematics, couldn't accept the standard axiomatic foundations of mathematics. So he spent nearly 50 years building an alternative from the ground up. He joins Deniz and Thorsten to discuss his new book Positive Topology, the culmination of decades of work connecting Per Martin-Löf's type theory, point-free topology, and his own "minimalist foundation" for mathematics.
- 4 weeks ago27 min
Season 2 Recap: From Gödel to AI-Proved Math | aboutlogic #22
Season 2 Recap: From Gödel to AI-Proved Math | aboutlogic #22 Nine guests, four emerging themes, and one big question running through all of it: what happens to mathematics when symbolic reasoning and statistical AI finally meet? In this Season 2 recap, Thorsten Altenkirch and Deniz Sarikaya look back at conversations with Urs Schreiber, Joel David Hamkins, Dana Scott, Emily Riehl, Bernhard Fisseni, Bernhard Schröder, José Pérez Escobar, Jan von Plato, Mike Shulman, Tudor Achim, and Neil Ghani — and preview where Season 3 is headed.
- Sep 30, 202631 min
aboutlogic Premises #09 | Why Symbolic AI Failed — and Then Won
Why Symbolic AI Failed — and Then Won | aboutlogic Premises #09 Symbolic AI — "GOFAI" — was meant to be the foundation of machine intelligence, and it failed spectacularly in the 1980s. In this premises episode, Thorsten and Deniz explore why, and how statistical AI, the technology that replaced it, may now be quietly bringing symbolic reasoning back — including a Platonic twist: if Plato thought the world of ideas came first, modern AI suggests structure and reasoning actually emerge only after fuzzy, statistical pattern recognition. They land on what Thorsten calls a "paradoxical synthesis": statistical AI winning the race is exactly what now makes rigorous, formally verified symbolic AI possible.
- Sep 23, 202654 min
aboutlogic #21 | Category Theory Meets Agentic AI | Neil Ghani (Kodamai)
Category Theory Meets Agentic AI | Neil Ghani (Kodamai) Why does almost all agentic AI today run completely untyped — even though 40 years of type theory and category theory research says that's a mistake? Neil Ghani, Co-Founder of Kodamai, Professor of Computer Science at the University of Strathclyde and a world-leading authority in Applied Category Theory, joins Deniz and Thorsten to explain how the same mathematical structures used to reason about data types can bring trustworthiness, scalability, and adaptability to AI agents. The conversation ranges from the origins of container theory to why LLMs are fundamentally untyped, whether category theory is "abstract nonsense," the GOFAI failures of the 1980s, and how formal verification tools like Lean might be the unlikely savior of both mathematics and AI.
- Sep 16, 202633 min
aboutlogic: premises #08 | Choice vs. Excluded Middle: A Constructive Paradox
Choice vs. Excluded Middle: A Constructive Paradox | aboutlogic: premises #08 Constructive mathematics is all about building things explicitly — so why does it reject the Axiom of Choice, which sounds trivial in a constructive context. In this Premises episode, Thorsten walks Deniz through Diaconescu's theorem: the surprising proof that the Axiom of Choice implies the Law of Excluded Middle, turning a seemingly innocent principle into full-blown classical logic. Using an intuitive type-theoretic explanation (starting with a very relatable glove-matching example), Thorsten builds up to Diaconescu's classic argument, touching on propositional extensionality, the difference between intensional and extensional predicates, and why the Axiom of Choice turns out to be a stronger form of "magic" than Excluded Middle itself.
- Sep 9, 202640 min
aboutlogic #20 | Can AI Prove the Riemann Hypothesis? | Tudor Achim (Harmonic)
Can AI prove the Riemann Hypothesis? Tudor Achim, CEO of Harmonic and creator of Aristotle — the first AI to win IMO gold and solve Erdős problems using the Lean theorem prover — joins Deniz and Thorsten to discuss how mathematical superintelligence is transforming research, education, and the very nature of proof.
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About aboutlogic
aboutlogic is a podcast on logic, foundations of mathematics, philosophy, and theoretical computer science. aboutlogic features in-depth conversations with people working in and around the foundations of these subjects. We talk about topics ranging from the foundations of computer science and set theory to critical thinking, puzzles, and what academic life is really like—its motivations, frustrations, and surprises.
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