aboutlogic

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.

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.

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.

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 limits lie. Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

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 Hear anecdotes about Gödel’s unpublished ideas, Einstein’s influence, and the telephone conversations that shaped modern logic.

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.

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 mathematics, and discuss its implications for understanding concepts like the Continuum Hypothesis (CH) and the nature of mathematical reality. Joel also reflects on the historical contingency of mathematical axioms, the role of categoricity in mathematics, and how different philosophical perspectives, such as Platonism, formalism, and fictionalism, shape the way mathematicians approach their work. Whether you're a mathematician, philosopher, or simply curious about the foundations of logic, this conversation offers a deep dive into the diverse and evolving landscape of mathematical thought.

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 connections between physics and logic, and how modern mathematics is shaping our understanding of reality.

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.

aboutlogic #10 | In this episode, we talk with Seunghyun Song and Jordi Fairhurst about the ABC conjecture, the importance of epistemic justice, and the role of linguistic justice in non-Western mathematical traditions. How do diverse perspectives reshape our understanding of mathematics? Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

aboutlogic #09 | In this episode, we talk with Andrej Bauer about the five stages of accepting intuitionistic mathematics and the challenges surrounding proofs by contradiction. Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

aboutlogic #08 | In this episode, Deborah Kant presents findings from her interview study with set theorists, exploring the relationship between philosophy and empirical methods in mathematics. Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

aboutlogic #07 | We’re joined by Alexander Steen, who works on logics to be used in legal contexts. In this episode, we talk about the relationship between ethics and law, how good old-fashioned artificial intelligence can help legal practitioners, and how to use theorem proving practices for this. Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

aboutlogic #06 | We’re joined by Colin Rittberg to discuss the philosophy and sociology of mathematics and the concept of epistemic injustice within mathematical communities.

We’re joined by Steve Awodey, one of the founders of Homotopy Type Theory. In this episode, we talk about the relationship between philosophy and mathematics, the main ideas behind geometric thinking and logic, and how all of this connects to computer science. Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

Today we’re joined by Graham Priest from New York, a philosopher who also studied mathematics and is well known for many things. In particular, we will talk about contradictory logics – logics where we can work with a contradiction without being able to prove everything. We’ll also discuss non-standard topics, including non-standard arithmetic and non-standard set theory, and how all of this is philosophically motivated. Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

This weeks interview with Deniz Sarikaya touches on topics like: Philosophy of Mathematical Practice, Sociology of Mathematics, Set Theory and the Universe vs. Multiverse-Debate

This weeks interview with Thorsten Altenkirch touches on topics like: Theorem proving software in education, constructive mathematics, type theory and many more.

This weeks interview with Kevin Buzzard touches on topics like: Theorem Proving Software, LEAN, Fermat's Last Theorem and Foundations of Mathematics.

Welcome to aboutlogic, a dedicated space where the realms of logic, mathematics, philosophy, and computer science converge. Every two weeks, we feature in-depth conversations with some of the most brilliant minds in these fields, who were somehow stupid enough to speak with us.