All episodes

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.

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.

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...

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...

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...

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.

Fixing Russell’s Paradox: The Birth of ZFC & Constructive Set Theory
How did mathematicians fix Russell’s paradox and save set theory? In this aboutlogic: premises episode, Deniz and Thorsten explore the solutions that reshaped the foundations of mathematics. From Zermelo-Fraenkel (ZFC) axioms to constructive set theories (IZF, CZF). Discover how large cardinals, the continuum hypothesis, and the iterative conception of sets became central to modern set theory and why some mathematicians still prefer type theory for its structural and computational advantages.

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Homotopy Type Theory, Narya & the Future of Proof Assistants with Michael Shulman.
How does homotopy type theory bridge the gap between abstract mathematics and computational proof systems? Mike Shulman (University of San Diego) joins Deniz and Thorsten to discuss his journey from topology to higher observational type theory, the development of the Narya proof assistant, and how these tools are reshaping the way we think about equality, equivalence, and computation in mathematics.

What Is a Set? A Beginner’s Guide to Set Theory | aboutlogic: premises #06
In this aboutlogic: premises episode, Deniz and Thorsten explore the foundations of set theory. From Cantor’s groundbreaking ideas to Frege’s logical foundations and Russell’s paradox. Discover how sets evolved from simple collections to a rigorous mathematical framework, and why the power set, well-ordering, and the continuum hypothesis remain some of the most fascinating (and controversial) ideas in math.

aboutlogic #18 | What really happened in the 1930s logic revolution? Jan von Plato (University of Helsinki, ERC Grantee) joins Deniz and Thorsten to uncover the hidden collaborations, misunderstandings, and lost manuscripts that shaped modern logic. From Gödel’s unpublished notes to Gentzen’s lost normalization proof and Bernays’ pivotal role in Hilbert’s school, this episode reveals how the history of logic is far richer—and more interconnected—than we often assume.