{"slug": "ineqagent-agentic-inequality-proving-in-lean-with-symbolic-computation", "title": "IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation", "summary": "IneqAgent, an agentic framework combining LLM reasoning with symbolic computation for inequality proving in Lean4, solved 175 of 186 problems (94.09%) across four benchmarks when run with the DeepSeek-V4-Flash backbone, the highest overall success rate among evaluated methods, according to the arXiv paper 2610.20681v1. The framework uses lemma-level Monte Carlo Tree Search to coordinate lemma construction, goal reformulation, and symbolic backend selection, with sum-of-squares, Bernstein, and successive difference-substitution backends producing exact certificates for local Lean proof generation. The authors also report Lean-verified strengthenings of Dittert's conjecture in dimensions four and five and a certificate for the Holens-Djokovic (4,4) inequality, implying Merris's conjecture in dimension four.", "body_md": "arXiv:2610.20681v1 Announce Type: new \nAbstract: Formal inequality proving requires mathematical reasoning and exact computation, often connected through intermediate lemmas and goal reformulations. We introduce IneqAgent, an agentic framework combining LLM reasoning with symbolic computation for inequality proving in Lean4. Lemma-level Monte Carlo Tree Search coordinates lemma construction, goal reformulation, and symbolic backend selection. Complementary sum-of-squares, Bernstein, and successive difference-substitution backends produce exact certificates for local Lean proof generation. The agent integrates these proofs with LLM-generated steps and uses Lean feedback to construct complete proofs checked against the original theorem statements. On four benchmarks, IneqAgent with DeepSeek-V4-Flash solves 175 of 186 problems (94.09%), achieving the highest overall success rate among the evaluated methods. Across four backbones, it achieves higher success rates at low LLM inference cost thresholds than Direct Agent using the same backbone, with lower mean inference costs over each method's successful runs. We also obtain Lean-verified strengthenings of Dittert's conjecture in dimensions four and five, and certify the Holens--Djokovic $(4,4)$ inequality, implying Merris's conjecture in dimension four.", "url": "https://wpnews.pro/news/ineqagent-agentic-inequality-proving-in-lean-with-symbolic-computation", "canonical_source": "https://arxiv.org/abs/2610.20681", "published_at": "2026-10-16 04:00:00+00:00", "updated_at": "2026-10-16 05:05:35.636604+00:00", "lang": "en", "topics": ["artificial-intelligence", "large-language-models", "ai-agents", "ai-research", "machine-learning"], "entities": ["IneqAgent", "Lean4", "DeepSeek-V4-Flash", "Dittert's conjecture", "Holens-Djokovic inequality", "Merris's conjecture", "Monte Carlo Tree Search", "arXiv"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/ineqagent-agentic-inequality-proving-in-lean-with-symbolic-computation", "markdown": "https://wpnews.pro/news/ineqagent-agentic-inequality-proving-in-lean-with-symbolic-computation.md", "text": "https://wpnews.pro/news/ineqagent-agentic-inequality-proving-in-lean-with-symbolic-computation.txt", "jsonld": "https://wpnews.pro/news/ineqagent-agentic-inequality-proving-in-lean-with-symbolic-computation.jsonld"}}