Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification
This work addresses the problem of bridging informal and formal mathematical reasoning for LLMs, enabling them to produce machine-checkable proofs for mathematical problems, which is significant for researchers and practitioners in automated theorem proving and AI for mathematics.
This paper introduces Magenta, a training-free agentic pipeline that integrates Lean verification into informal mathematical reasoning. It takes a natural-language problem, generates an answer, formalizes it as a Lean 4 statement, and constructs a machine-checked proof, achieving 100% accuracy on AIME 2025, AIME 2026, and HMMT February 2026 benchmarks, and solving all six IMO 2026 problems when paired with K2-Horizon-7B.
Most of mathematical knowledge has been communicated through so-called informal use of mathematics and natural language. With large language models (LLMs) being highly adept in using natural language, they achieve strong performance, yet not perfect, in informal mathematical reasoning. Restraining LLMs to informal reasoning misses out on the opportunity to use the discrete verification abilities that machines offer through machine-checkable proofs. In this paper, we bridge the gap between informal and formal reasoning by integrating Lean signals into the informal reasoning process. We introduce Magenta, a training-free agentic pipeline that, given only a natural-language problem, produces an answer, expresses it as a Lean 4 statement, and constructs a machine-checked proof. A statement judge verifies whether the formalisation preserves the original problem, while an error-attribution judge routes failed attempts either to mathematical re-derivation or local Lean repair. Magenta achieves 100% accuracy across all evaluated olympiad benchmarks, including AIME 2025, AIME 2026, and HMMT February 2026. When paired with the open-weight K2-Horizon-7B reasoner, it solves all six IMO 2026 problems. Our analysis shows that statement adjudication is essential for preventing false certificates and that feedback-guided correction outperforms independent resampling on difficult problems.