Bridging Informal and Formal Mathematical Reasoning with Neural Language Models

Explore the intersection of mathematics and machine learning in this hour-long lecture on bridging informal and formal mathematical reasoning using neural language models. Delve into the development of NaturalProver, a language model capable of generating proofs in natural mathematical language by grounding them in reference documents. Learn how this model can prove theorems and provide next-step suggestions that university-level mathematics students find correct and useful. Discover the innovative Draft, Sketch, and Prove approach, which translates informal proofs into formal proof sketches to guide automated provers. Examine how large language models can produce well-structured formal sketches that follow the same reasoning steps as informal proofs. Understand how this method surpasses the state of the art on a benchmark of mathematical competition problems, offering stronger logical grounding. Join Sean Welleck from the University of Washington and AI2 as he discusses the challenges and advancements in teaching machines complex mathematical reasoning.