Existing LLM-based theorem provers have shown impressive results on formal mathematics benchmarks, yet they remain limited to acting as autonomous agents that prove a stated proposition. This paper introduces MathCoPilot, a human-in-the-loop system embodying a new human-AI symbiotic paradigm for mathematical research, where mathematicians steer high-level mathematical direction while AI agents carry out detailed formalization and proof work under continuous human guidance.
MathCoPilot unifies three core capabilities:
- Interactive Workbench: A collaborative environment where mathematicians and AI agents work through a living proof blueprint that breaks down a proof into navigable steps for human inspection, direction, and refinement;
- Automated Proving Skill Orchestration: Integrating adaptive knowledge base search with Lean-integrated iterative verification;
- Topic-Driven Paper Retrieval: Automated formalization into a verified Lean knowledge base.
Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini 3.1 Pro, GPT-5.4, and Claude Opus 4.7, on a FormalMATH subset and two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean 4 proofs and identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.
Blogger's Review: The introduction of MathCoPilot marks a significant advancement in the collaborative landscape of mathematical research, particularly in the proof processes of complex theorems. By combining human intuition with AI computational power, this system promises to enhance the efficiency and depth of mathematical inquiry in the future. However, it is noteworthy that while current technologies perform well on basic problems, further optimization is necessary for tackling higher-level mathematical challenges.