aboutlogic

Category Theory: Algebra on Steroids?

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Why Didn't Homotopy Type Theory Take Over the World?

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

Is Unique Choice Really a Choice with Giovanni Sambin

Watch our conversation with Giovanni Sambin here: https://youtu.be/81A2A2HRvrA

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/ 

Rebuilding Mathematics from the Ground Up with Giovanni Sambin

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Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/
Deniz Sarikaya: https://www.denizsarikaya.de/
Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

From Gödel to AI-Proved Math

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

Mathematics #Logic #AI #CategoryTheory #TypeTheory #SetTheory #FormalVerification #aboutlogic

Why Symbolic AI Failed — and Then Won

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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GOFAI #SymbolicAI #LLM #ArtificialIntelligence #Plato #PhilosophyOfMind #FormalVerification #aboutlogic

Category Theory Meets Agentic AI

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

AI #CategoryTheory #TypeTheory #AgenticAI #Kodamai #Containers #FormalVerification #aboutlogic

A Constructive Paradox

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Developing the Artificial Mathematical Superintelligence

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

AI #Mathematics #Harmonic #Aristotle #Lean #ProofAssistants #FutureOfMath #RiemannHypothesis #aboutlogic

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

Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

Homotopy Type Theory, Narya & the Future of Proof Assistants

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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What Is a Set? A Beginner’s Guide to Set Theory

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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The Hidden History of Logic: Jan von Plato on Gödel, Gentzen & Bernays

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This episode is also available as a video on our YouTube channel: https://www.youtube.com/@aboutlogic

Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Dependent Type Theory: A Revolution in Math & Computer Science

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 Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Wittgenstein, Turing & the Philosophy of Applied Mathematics

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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The Harry Potter Approach to Proof Assistants – Lean, Agda & AI

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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The Language of Mathematics: Frames, Narratives & AI

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Synthetic vs. Analytic Math: Inspired by Emily Riehl

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

Higher Category Theory, Homotopy & AI in Math

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Hilbert’s Hotel & Cantor’s Infinity: The Story of Set Theory

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

Dana Scott: Turing Award Winner on Logic & Computation

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Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Storytelling in Math - A Constructivist Perspective and Captain Ahab's Dilemma

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Set Theory, Pluralism & the Multiverse View

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Further Reading & Resources: Joel David Hamkins: https://jdh.hamkins.org/ Joel's substack: https://www.infinitelymore.xyz/ Joel's book Lectures on the Philosophy of Mathematics: https://mitpress.mit.edu/9780262542234/lectures-on-the-philosophy-of-mathematics/ Joel's new book, The Book of Infinity: https://mitpress.mit.edu/9780262054010/the-book-of-infinity/

Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Quantum (Physics, Computing), Topos & Homotopy Theory

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00:01:19 Introduction to Quantum Research and Technologies 00:04:34 Understanding Fermions, Bosons, and Anyons 00:10:16 The Role of Anyons in Quantum Computing 00:13:29 Understanding Topos Theory and Its Relevance 00:17:02 Mathematical Foundations: Differential Geometry and Topos Theory 00:20:55 The Intersection of Physics, Mathematics and Logic 00:32:31 Historical Context of Mathematics and Physics 00:37:26 Category Theory and Its Implications 00:41:23 Gauge Fields and Homotopy Type Theory 00:49:40 Philosophical Implications of Higher Topos Theory / Hegel

Further Reading & Resources: Urs Schreiber: https://ncatlab.org/nlab/show/Urs+Schreiber Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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Feedback, Highlights & Season 2 Preview

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Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

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ABC Conjecture, Epistemic & Linguistic Justice in non-Western maths

Further Reading & Resources:

Jordi Fairhurst: https://jordifairhurst.weebly.com/ Seunghyun Song: https://www.tilburguniversity.edu/staff/s-song_1 Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

5 Stages of Accepting Intuitionistic Math & Proofs by Contradiction

Watch this Episode on Youtube: https://youtu.be/sbQi6HjyBHM

Further Reading & Resources: Andrej Bauer: https://www.andrej.com/ Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Creative Production: Jan-Niklas Meyer: http://www.jammos.com/

Talking with Set Theorists: Insights in Mathematical Philosophy

Watch the Episode on Youtube: https://youtu.be/81CRjASvIng

Further Reading & Resources: Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/

Production: Jan-Niklas Meyer: http://www.jammos.com/

Many thanks to the Akademie der Wissenschaften in Hamburg for supporting the first season of the podcast.

Interactive Theorem Provers, Legal Reasoning, Non-Standard Logics

Further Reading & Resources: The Natural Number Game: https://adam.math.hhu.de/#/g/leanprover-community/nng4 The Xena Project: https://xenaproject.wordpress.com/ Graham Priest: https://grahampriest.net/

Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/

Production: Jan-Niklas Meyer: http://www.jammos.com/

Many thanks to the Akademie der Wissenschaften in Hamburg for supporting the first season of the podcast.

Philosophy & Sociology of Mathematics, Epistemic Injustice

Further Reading & Resources: Get the HoTT Book for free (no advertisement): https://homotopytypetheory.org/book/ Thorsten Altenkirch: http://www.cs.nott.ac.uk/~psztxa/ Deniz Sarikaya: https://www.denizsarikaya.de/ Jan-Niklas Meyer: http://www.jammos.com/

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