Automated Generation and Verification of Natural-Language Math Proofs

Establish reliable automated methodologies for generating and verifying natural-language mathematical proofs produced by large language models, ensuring that their correctness and completeness can be assessed with fidelity comparable to expert human grading.

Background

The paper identifies a critical gap in current mathematical reasoning systems: most advances target problems with easily verifiable final answers, whereas proofs require nuanced assessment across multiple steps and often lack a single checkable endpoint. This makes both proof generation and verification substantially harder than final-answer tasks.

The authors motivate the need for reliable methods to handle natural-language proofs because formal verification (e.g., Lean) is detached from typical human mathematical communication, and automatic translation from informal to formal proofs remains brittle. Thus, advancing automated generation and verification of natural-language proofs is essential to accurately evaluate and improve LLM capabilities in mathematics.