aboutlogic

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 race is exactly what now makes rigorous, formally verified symbolic AI possible.

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.

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.

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.