# IneqAgent uses LLMs and symbolic math to prove inequalities in Lean4

Digest AI · Research · published 2026-10-16T04:00:00Z

Canonical: https://digestai.news/story/ineqagent-uses-llms-and-symbolic-math-to-prove-inequalities-in-lean4

## Summary

Researchers have introduced IneqAgent, a new agentic framework designed for formal inequality proving in the Lean4 theorem prover. The system combines large language model (LLM) reasoning with symbolic computation to handle mathematical tasks that require exact computation and intermediate lemmas. A key component is Lemma-level Monte Carlo Tree Search, which coordinates the construction of lemmas, reformulation of goals, and the selection of symbolic backends.

The framework utilizes complementary backends, including sum-of-squares, Bernstein, and successive difference-substitution, to generate exact certificates for local Lean proofs. These are integrated with LLM-generated steps, and the agent uses Lean feedback to construct complete proofs that are checked against original theorem statements. This approach aims to bridge the gap between heuristic LLM reasoning and rigorous formal verification.

In testing on four benchmarks, IneqAgent paired with the DeepSeek-V4-Flash model solved 175 of 186 problems, achieving a 94.09% success rate. This represents the highest overall success rate among the evaluated methods. The study also notes that IneqAgent achieves higher success rates at low LLM inference cost thresholds compared to a Direct Agent using the same backbone. Additionally, the system produced Lean-verified strengthenings of Dittert's conjecture in dimensions four and five and certified the Holens--Djokovic (4,4) inequality.

## Key points

- IneqAgent combines LLM reasoning with symbolic computation for inequality proving in Lean4.
- Using DeepSeek-V4-Flash, the agent solved 175 of 186 benchmark problems (94.09%).
- The system achieved Lean-verified strengthenings of Dittert's conjecture in dimensions four and five.

## Why it matters

This research demonstrates a viable path for integrating LLMs with symbolic solvers to achieve high-accuracy formal verification. It suggests that agentic frameworks can significantly outperform direct LLM approaches in complex mathematical reasoning tasks while managing inference costs.

## Sources

1. [IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation](https://arxiv.org/abs/2610.20681) (arXiv cs.AI, 2026-10-16, primary source)

## Cite

Digest AI, "IneqAgent uses LLMs and symbolic math to prove inequalities in Lean4", 16 October 2026, https://digestai.news/story/ineqagent-uses-llms-and-symbolic-math-to-prove-inequalities-in-lean4

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