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  • aboutlogic: premises #07 | Fixing Russell’s Paradox: The Birth of ZFC & Constructive Set Theory

    aboutlogic: premises #07 | Fixing Russell’s Paradox: The Birth of ZFC & Constructive Set Theory
    2026/09/02
    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.
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    30 分
  • aboutlogic #19 | Homotopy Type Theory, Narya & the Future of Proof Assistants with Mike Shulman

    aboutlogic #19 | Homotopy Type Theory, Narya & the Future of Proof Assistants with Mike Shulman
    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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    1 時間 1 分
  • aboutlogic:premises #06 | What Is a Set? A Beginner’s Guide to Set Theory

    aboutlogic:premises #06 | What Is a Set? A Beginner’s Guide to Set Theory
    2026/08/19
    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.
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    27 分
  • aboutlogic #18 | The Hidden History of Logic: Jan von Plato on Gödel, Gentzen & Bernays

    aboutlogic #18 | The Hidden History of Logic: Jan von Plato on Gödel, Gentzen & Bernays
    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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    1 時間 3 分
  • aboutlogic: premises #05 | Dependent Type Theory: A Revolution in Math & Computer Science

    aboutlogic: premises #05 | Dependent Type Theory: A Revolution in Math & Computer Science
    2026/08/05
    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.
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    28 分
  • aboutlogic #17 | José Pérez Escobar – Wittgenstein, Turing & the Philosophy of Applied Mathematics

    aboutlogic #17 | José Pérez Escobar – Wittgenstein, Turing & the Philosophy of Applied Mathematics
    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 conversation also dives into Turing’s structural view of math, the Dirac delta function controversy, and whether contradictions in mathematics are truly problematic.
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    1 時間 16 分
  • aboutlogic: premises #04 | The Harry Potter Approach to Proof Assistants – Lean, Agda & AI

    aboutlogic: premises #04 | The Harry Potter Approach to Proof Assistants – Lean, Agda & AI
    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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    28 分
  • aboutlogic #16 | Schröder & Fisseni – The Language of Mathematics: Frames, Narratives & AI

    aboutlogic #16 | Schröder & Fisseni – The Language of Mathematics: Frames, Narratives & AI
    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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    50 分