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PODCAST

aboutlogic

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.

science mathematics

All Episodes

31:10

aboutlogic Premises #09 | Why Symbolic AI Failed —...

aboutlogic ·

2026/09/30

Why Symbolic AI Failed — and Then Won | aboutlogic Premises #09Symbolic 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

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54:42

aboutlogic #21 | Category Theory Meets Agentic AI |...

aboutlogic ·

2026/09/23

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,

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33:25

aboutlogic: premises #08 | Choice vs. Excluded...

aboutlogic ·

2026/09/16

Choice vs. Excluded Middle: A Constructive Paradox | aboutlogic: premises #08Constructive 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

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40:36

aboutlogic #20 | Can AI Prove the Riemann Hypothesis?...

aboutlogic ·

2026/09/09

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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30:22

aboutlogic: premises #07 | Fixing Russell’s Paradox:...

aboutlogic ·

2026/09/02

Fixing Russell’s Paradox: The Birth of ZFC & Constructive Set TheoryHow 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

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60:44

aboutlogic #19 | Homotopy Type Theory, Narya & the...

aboutlogic ·

2026/08/26

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.

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27:17

aboutlogic:premises #06 | What Is a Set? A Beginner’s...

aboutlogic ·

2026/08/19

What Is a Set? A Beginner’s Guide to Set Theory | aboutlogic: premises #06In 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.

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62:52

aboutlogic #18 | The Hidden History of Logic: Jan von...

aboutlogic ·

2026/08/13

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.

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27:49

aboutlogic: premises #05 | Dependent Type Theory: A...

aboutlogic ·

2026/08/05

Dependent Type Theory: A Revolution in Math & Computer Science | aboutlogic: premises #05What makes dependent type theory so powerful? In this aboutlogic: premises episode, Deniz and Thorsten explore the evolution of type theory. From simple types to Pierre Martin-Löf’s groundbreaking dependent types. Discover how this innovation transformed mathematics and computer science by allowing types to depend on values, enabling more expressive and precise reasoning.

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75:39

aboutlogic #17 | José Pérez Escobar – Wittgenstein,...

aboutlogic ·

2026/07/29

aboutlogic #17 | Why is mathematics so effective in science? José Pérez Escobar (UNED, Madrid) joins Deniz and Thorsten to explore Wittgenstein’s philosophy of applied mathematics, the role of rules vs. structures in math, and how models shape our understanding of reality.From neuroscience to physics, José explains why mathematical models often act as rules of description rather than mere representations of reality and how this perspective resolves Wittgenstein’s "rule-following paradox." The

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28:18

aboutlogic: premises #04 | The Harry Potter Approach...

aboutlogic ·

2026/07/22

Your support helps us keep these conversations going! If you’d like to contribute, you can buy us a coffee here: https://buymeacoffee.com/aboutlogic How do interactive theorem provers like Lean and Agda change the way we teach and do mathematics? In this aboutlogic: premises episode, Deniz and Thorsten discuss the role of proof assistants in education, the differences between Lean and Agda, and how AI is transforming formal verification.

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50:02

aboutlogic #16 | Schröder & Fisseni – The Language of...

aboutlogic ·

2026/07/15

aboutlogic #16 | How is mathematical language structured, and what can linguistics teach us about proofs, ambiguity, and storytelling in math? In this episode, Bernhard Fisseni and Bernhard Schröder (University of Duisburg-Essen) join Deniz and Thorsten to explore the frames, narratives, and pragmatic structures behind mathematical texts.

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38:14

aboutlogic: premises #03 | Synthetic vs. Analytic...

aboutlogic ·

2026/07/08

Inspired by our conversation with Emily Riehl on higher category theory, this aboutlogic: premises episode dives into the synthetic vs. analytic approach in mathematics. Deniz and Thorsten explore how Euclid’s geometry, category theory, and higher categories embody the synthetic approach. Focusing on abstract structures and relationships rather than concrete coordinates or definitions.

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58:33

aboutlogic #15 | Emily Riehl – Higher Category...

aboutlogic ·

2026/07/01

aboutlogic #15 | Emily Riehl (Johns Hopkins University) joins us to explore higher category theory, homotopy, and the role of AI in modern mathematics. From the foundations of category theory to the challenges of formalizing math with proof assistants like Lean, Emily shares her insights on synthetic vs. analytic approaches, the beauty of abstraction, and how AI is changing mathematical research.

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26:57

aboutlogic: premises #02 | Hilbert’s Hotel & Cantor’s...

aboutlogic ·

2026/06/24

Your support helps us keep these conversations going! If you’d like to contribute, you can buy us a coffee here: https://buymeacoffee.com/aboutlogic What is set theory—a foundation of math or a science of infinity? In this aboutlogic: premises episode, Deniz and Thorsten explore the history, paradoxes, and philosophical debates behind set theory. From Cantor’s diagonal argument to Hilbert’s Hotel and the role of ZFC, they discuss why set theory became the language of mathematics—and where its

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33:00

#14 aboutlogic | Dana Scott – Lambda Calculus,...

aboutlogic ·

2026/06/17

aboutlogic #14 | Turing Award winner Dana Scott joins us to discuss his groundbreaking work on lambda calculus, forcing, and Boolean-valued models and how these ideas revolutionized set theory and computability. From his collaborations with Kleene and Solovay to his thoughts on constructive mathematics, Scott shares insights into the history and future of logical foundations. Hear anecdotes about Gödel’s unpublished ideas, Einstein’s influence, and the telephone conversations that shaped modern

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26:01

aboutlogic: premises #01 | Is Math a Story? A...

aboutlogic ·

2026/06/10

Our weekly Premises: Behind-the-scenes thoughts, deep dives, and the ideas that didn’t fit into the main episodes.Is mathematics a discovery or a story we tell ourselves? In this first aboutlogic: premises episode, Deniz and Thorsten explore why math might be more like fiction than absolute truth and what that means for logic, proof, and the future of the field.

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84:46

aboutlogic #13 | Joel David Hamkins – Set Theory,...

aboutlogic ·

2026/06/03

aboutlogic #13 | In this episode of aboutlogic, we’re joined by Joel David Hamkins, professor at the University of Notre Dame and a leading figure in set theory, mathematical logic, and the philosophy of mathematics. Joel shares his insights into the multiverse view of set theory, a perspective that challenges the traditional "universe view" by embracing a pluralistic approach to mathematical truth. We explore how this view connects to constructivism, potentialism, and the foundations of

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59:33

aboutlogic #12 | Urs Schreiber – Quantum (Physics,...

aboutlogic ·

2026/05/20

aboutlogic #12 | In this episode of aboutlogic, we’re joined by UrsSchreiber, a senior scientist at New York University Abu Dhabi. Urs shares insights into his work at the intersection of quantum physics, topos theory, and homotopy type theory. We explore how these advanced mathematical frameworks help address fundamental questions in physics, from understanding gauge fields to the role of higher category theory in describing the universe. Urs also discusses the historical and philosophical

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63:32

aboutlogic #11 | Season 1 Recap: Feedback, Highlights...

aboutlogic ·

2026/05/06

aboutlogic #11 | In this special Season 1 Recap of aboutlogic, Deniz and Thorsten reflect on your comments and feedback, revisit some of the most intriguing topics, and look back at all the incredible guests from the first season. What were the highlights? What did we learn? And what’s in store for Season 2? Join us for a wrap-up filled with insights, gratitude, and a sneak peek at what’s next.

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31 results

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