AI News

IneqAgent is an agentic framework for formal inequality proving in Lean4, where mathematical reasoning and exact symbolic computation must be connected through lemmas and reformulated goals. Its lemma-level Monte Carlo Tree Search coordinates lemma construction, goal reformulation, and the choice of symbolic backend. Sum-of-squares, Bernstein, and successive difference-substitution methods generate exact certificates for local Lean proofs, while Lean feedback helps combine these steps with LLM-generated reasoning into complete proofs checked against the original theorem statements. On four benchmarks, the configuration using DeepSeek-V4-Flash solved 175 of 186 problems, a 94.09% success rate and the highest overall rate among the evaluated methods. Across four backbone models, IneqAgent also achieved higher success rates than a Direct Agent at low inference-cost thresholds and had lower mean inference costs among successful runs. The authors report Lean-verified strengthenings of Dittert's conjecture in dimensions four and five, as well as a certificate for the Holens--Djokovic (4,4) inequality that implies Merris's conjecture in dimension four.