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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.
Latest Episodes
The most recent episodes — sign up to get AI-powered summaries of each one.
- 4 days ago33 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.
- 1 weeks ago40 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.
- 2 weeks ago30 min
aboutlogic: premises #07 | Fixing Russell’s Paradox: The Birth of ZFC & Constructive Set Theory
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. 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 Or become a channel member here on Youtube. We’d love to have your support! https://www.youtube.com/@aboutlogic Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.
- 3 weeks ago1h 0m
aboutlogic #19 | Homotopy Type Theory, Narya & the Future of Proof Assistants with Mike Shulman
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.
- Aug 19, 202627 min
aboutlogic:premises #06 | What Is a Set? A Beginner’s Guide to Set Theory
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.
- Aug 13, 20261h 2m
aboutlogic #18 | The Hidden History of Logic: Jan von Plato on Gödel, Gentzen & Bernays
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.
- Aug 5, 202627 min
aboutlogic: premises #05 | Dependent Type Theory: A Revolution in Math & Computer Science
Dependent Type Theory: A Revolution in Math & Computer Science | aboutlogic: premises #05 What 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.
- Jul 29, 20261h 15m
aboutlogic #17 | José Pérez Escobar – Wittgenstein, Turing & the Philosophy of Applied Mathematics
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 conversation also dives into Turing’s structural view of math, the Dirac delta function controversy, and whether contradictions in mathematics are truly problematic.
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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