Hausdorff Center for Mathematics Courses

Indexing and Retrieval in a Heterogeneous Formal Library

Explore advanced techniques for indexing and retrieving information in diverse formal libraries, enhancing research efficiency and knowledge management in mathematics.

• YouTube
• 46 minutes
• On-Demand
• Free Video

First-Order Logic from a Naproche Perspective

Explore first-order logic through the lens of Naproche, a natural language proof checker, in this insightful talk by Peter Koepke at the School on Formal Mathematics.

• YouTube
• 24 minutes
• On-Demand
• Free Video

The Proofgold Blockchain: Integrating Formal Proofs with Cryptocurrency

Explore the innovative Proofgold blockchain system, its applications in mathematics and formal verification, and its potential impact on decentralized proof-checking and cryptocurrency.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Impromptu Chat About Hahn-Banach Theorem in Lean

Explore the intricacies of HB implementation in Lean with Mario Carneiro in this impromptu discussion, gaining insights into advanced mathematical formalization techniques.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Aspects of Mathematical Knowledge - The Tetrapod Model

Explore the Tetrapod Model's innovative approach to understanding mathematical knowledge, offering insights into its structure, representation, and practical applications in research and education.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Condensed Type Theory - Axioms and Applications

Explore condensed sets' topos and internal type theory, examining axioms, predicates, and their interactions. Learn about compact Hausdorff and overt discrete types, with applications in category theory.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Automating Reasoning in Cubical Type Theory

Explore automated reasoning techniques in Cubical Type Theory, focusing on computational aspects and applications in formal verification and mathematics.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Calculating Ordinal Invariants - Can You Do Better Than a Human?

Explore ordinal invariants calculation techniques, comparing human and computational approaches in this advanced mathematics lecture by Mirna Džamonja.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Dialectica Categories for All

Explore dialectica categories and their applications in logic, mathematics, and computer science with expert Valeria de Paiva in this insightful talk.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Capturing Mathematical Equality - Constructivism and Canonical Isomorphisms

Explore the impact of rejecting constructivism in mathematics, examining the confusion between theorems and definitions and the overuse of "canonical isomorphism" in number theory.

• YouTube
• 35 minutes
• On-Demand
• Free Video

An Alternative Approach to Formal Mathematics - Prioritizing Communication over Certification

Exploring a communication-oriented approach to formal mathematics, emphasizing accessibility and practicality for a wider range of practitioners without sacrificing rigor.

• YouTube
• 34 minutes
• On-Demand
• Free Video

Peculiarities of the Minimalist Foundation for Formal Mathematics

Explore the unique aspects of the Minimalist Foundation in formal mathematics, examining its peculiarities and implications for mathematical reasoning and proof construction.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Informath: Informalization of Formal Mathematics

Exploring methods to bridge formal mathematics and everyday mathematical language, aiming to make advanced concepts more accessible and enhance AI's ability to construct formal proofs.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Injecting Formal Mathematics into LaTeX

Explore techniques for integrating formal mathematical proofs into LaTeX documents, enhancing precision and verifiability in academic writing and research publications.

• YouTube
• 24 minutes
• On-Demand
• Free Video

A Natural Language Formalization of Perfectoid Rings in Naproche

Explore the formalization of perfectoid rings using natural language in Naproche, bridging advanced mathematics with computational logic.

• YouTube
• 40 minutes
• On-Demand
• Free Video