aboutlogic

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.

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 From Gödel’s unpublished notes to Gentzen’s lost normalization proof and Bernays’ pivotal role in Hilbert’s school, this episode reveals how the history of logic is far richer—and more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.

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.

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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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.