Formal Reasoning Meets LLMs: Toward AI for Mathematics and Verification

Overview

Explore AI for formal mathematical reasoning, focusing on theorem proving and autoformalization. Learn about challenges through projects on inequality problems and Euclidean geometry formalization.

Syllabus

• Introduction to Formal Reasoning and Large Language Models (LLMs)
Overview of formal reasoning in AI
Introduction to Large Language Models (LLMs)
Applications of AI in mathematics and verification
• Theorem Proving
Basics of formal logic and theorem proving
Overview of automated theorem proving systems
Hands-on exercises with theorem provers
• Autoformalization
Understanding autoformalization and its challenges
Techniques for autoformalization
Case studies on successful formalizations
• AI for Inequality Problems
Analysis of inequality problem domains
Implementation of AI solutions for inequality problems
Project: Developing an AI-based system for solving inequality problems
• Formalization of Euclidean Geometry
Introduction to Euclidean geometry concepts
Challenges in formalizing geometry using AI
Project: Formalizing Euclidean geometry theorems with AI systems
• Integrating LLMs in Formal Reasoning
Role of LLMs in enhancing formal reasoning capabilities
Techniques for integrating LLMs with theorem provers
Examples of LLM-enhanced formal reasoning systems
• Research and Challenges in AI for Mathematics
Current research in AI-driven mathematics
Key challenges and open problems
Future directions for AI in formal mathematics and verification
• Project Presentations and Feedback
Final project presentations
Peer review and feedback sessions
Course reflections and concluding discussions

Subjects

Computer Science