LLMs Discover New Theorems via In-Context Proof Learning in Lean
The Conjecturing-Proving Loop (CPL) is a newly developed pipeline that allows large language models to create innovative mathematical conjectures and generate verified proofs using Lean 4. Each cycle utilizes previously established theorems and their formal proofs to enhance proof strategies via in-context learning, all without altering parameters. Both theoretical and experimental findings indicate that CPL significantly boosts the rate of discovering challenging theorems when compared to simultaneous generation. By leveraging the LLM's own formally verified outputs as context, subsequent proof success rates are consistently improved, showcasing a self-improvement mechanism. This research is thoroughly outlined in arXiv:2509.14274v2.
Key facts
- CPL iteratively generates conjectures and attempts proofs in Lean 4.
- Each iteration conditions the LLM on prior theorems and proofs.
- In-context learning enables parameter-free improvement of proof strategies.
- CPL increases discovery rate of hard-to-prove theorems.
- Reusing LLM's own verified outputs improves proof success.
- Study published on arXiv as 2509.14274v2.
- Pipeline uses large language models for formal theorem proving.
- Experiments show self-improvement through in-context learning.
Entities
Institutions
- arXiv