Lean Theorem Proving

Lean theorem proving studies how to express mathematical claims in Lean and construct proof terms that its kernel can check. Systems combine tactic search, language models, Mathlib premise retrieval, proof decomposition, compiler feedback, and increasingly reinforcement learning or symbolic computation. Benchmarks such as miniF2F and PutnamBench show strong results on competition mathematics, while graduate-level and applied-domain problems remain harder and motivate larger, context-rich evaluations. A central challenge is that a checked proof establishes only the formal statement: ensuring that statement faithfully captures the intended mathematics, while controlling cost and generalizing beyond familiar benchmarks, remains difficult.