MathCoPilot Enables Human-AI Collaboration in Mathematical Research

Current LLM-based theorem provers primarily function as autonomous agents, proving propositions independently. However, complex mathematical research often requires human intuition and guidance. MathCoPilot addresses this by proposing a new human-AI symbiotic model. This system empowers mathematicians to steer the overall direction of a proof, while AI agents manage the intricate formalization and verification steps under continuous human oversight. MathCoPilot features an interactive workbench where humans and AI collaborate through a "living proof blueprint," allowing direct inspection and refinement of proof steps. Key capabilities include orchestrating automated proving skills with adaptive knowledge base search and Lean-integrated verification, as well as topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Evaluations with state-of-the-art LLMs on various theorems show promise for undergraduate-level problems, but significant challenges remain for deep domain-specific theorems.