The 2025 Tarski Lecture
The 2025 Tarski Lecture will be given by Jeremy Avigad, Carnegie Mellon University
How Mathematics Works
Because logic offers a rigorous framework for studying mathematical language and inference, it provides a powerful means of understanding how mathematics works. So does the history of mathematics; seeing how ideas and methods have evolved over the centuries can help us understand the goals of mathematics and the forces that shape its development. Contemporary proof assistants, which support writing mathematical definitions, theorems, and proofs so that they can be processed and checked by computer, provide yet another perspective.
We will consider three important mathematical developments from these perspectives to see what we can learn from them. The lectures are independent of one another and are meant to be accessible to anyone interested in mathematics and mathematical reasoning.
- Lecture 1: Euclid's Elements and Diagrammatic Reasoning in Geometry
- Lecture 2: Dirichlet's Theorem on Primes in an Arithmetic Progression and the Treatment of Functions as Objects
- Lecture 3: Dedekind's Theory of Ideals and Modern Algebraic Abstraction
Jeremy Avigad is a professor in the Department of Philosophy and the Department of Mathematical Sciences at Carnegie Mellon University. His research interests include formal methods and AI for mathematics, mathematical logic, and the history and philosophy of mathematics. He is the Director of the Hoskinson Center for Formal Mathematics and he serves on the Board of Directors for the Lean Focused Research Organization.