aboutlogic

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?

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?

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