Hermes: Interleaving Informal and Formal Math Reasoning in LLMs
Researchers have unveiled Hermes, the inaugural tool-assisted agent that seamlessly integrates informal reasoning with formally verified proofs within Lean. While informal mathematics provides flexibility and efficiency for LLM reasoning, it is often plagued by logical inconsistencies and subtle mistakes that can be challenging to identify. On the other hand, formal theorem proving delivers rigorous and verifiable reasoning but lacks the freedom for exploration. Hermes reconciles these issues by conducting intermediate formal checks to avert reasoning drift and employing a memory module to maintain proof continuity throughout multi-step reasoning processes. This framework tackles a significant limitation of current LLM-based math agents, which struggle to effectively merge the advantages of both approaches. The announcement was made on arXiv with the identifier 2511.18760.
Key facts
- Hermes is the first tool-assisted agent that interleaves informal reasoning with formally verified proofs in Lean.
- Informal mathematics is flexible but prone to logical gaps and errors.
- Formal theorem proving provides rigorous, verifiable reasoning but lacks exploratory freedom.
- Hermes performs intermediate formal checking to prevent reasoning drift.
- Hermes includes a memory module for proof continuity across multi-step reasoning chains.
- The framework enables both exploration and verification in mathematical reasoning.
- Current LLM-based math agents lack a principled way to combine informal and formal reasoning.
- The work was announced on arXiv under identifier 2511.18760.
Entities
Institutions
- arXiv