arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.
arXiv:2609.35790v1 Announce Type: cross Abstract: While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 f...
The paper introduces an epistemically and formally grounded ensemble (EFG) of large language model judges to evaluate autoformalization tasks in formal mathematics. It defines four criteria—logical preservation, mathematical consistency, formal quality, and formal validity—to provide a transparent, multi‑granular assessment. Experiments show that this ensemble outperforms coarse‑grained models, offering a scalable and interpretable proxy for evaluating formal mathematical reasoning.
arXiv:2607. 19374v1 Announce Type: new Abstract: Recent formal reasoning systems have reached IMO-level performance, yet they leave a fragmented landscape: algebra and number theory are handled in Lean, while geometry still relies on domain-specific languages with limited formal guarantees.
arXiv:2607. 07391v1 Announce Type: new Abstract: Mathematical reasoning benchmarks typically provide all facts needed to solve each problem, while interactive benchmarks often mix reasoning with tools, retrieval, and long-horizon dialogue.
arXiv:2606. 26525v1 Announce Type: new Abstract: Auto-formalization is critical for scalable formal verification, but existing progress largely focuses on isolated statements, while theory-scale auto-formalization, which coherently translates hundreds of interdependent definitions, lemmas, and theorems, remains open due to challenges in consistency, faithfulness, scalability, and correctness.
arXiv:2606. 15972v1 Announce Type: cross Abstract: With large language models (LLMs) increasingly applied to mathematical reasoning, formal proof assistants such as Lean can be leveraged to verify reasoning outputs with machine-checkable rigor, enabling use cases such as answer selection in test-time scaling with K sampled candidate answers.
The paper introduces TopoAlign, a framework that repurposes code repositories to train Math LLMs by decomposing code into docstrings, main functions, and dependency functions and reassembling them into structures that mirror formal mathematical statements. Using this approach, the authors train three state‑of‑the‑art models—DeepSeek‑Math, Qwen‑3, and Herald—and evaluate them on MiniF2F, Putnam, and ProofNet benchmarks. TopoAlign yields significant performance gains, notably a 17.77% improvement on BEq@10 and a 68.82% boost on typecheck@10 for DeepSeek‑Math, while also providing modest gains for Herald.
arXiv:2510. 04520v2 Announce Type: replace Abstract: Accurate auto-formalization of theorem statements is essential for advancing automated discovery and verification of research-level mathematics, yet remains a major bottleneck for LLMs due to hallucinations, semantic mismatches, and their inability to synthesize new definitions.
NL2AGBench is a benchmark that evaluates how well large language models can translate English geometry problems into the formal language required by AlphaGeometry’s theorem‑proving engine. The study tests ten state‑of‑the‑art LLMs, comparing executable translation accuracy, syntactic correctness, and error types, and finds a large gap between closed‑source and open‑source models. The authors also propose an error taxonomy and test mitigation strategies such as few‑shot prompting, fine‑tuning, and human‑guided hinting, which improve performance across model families.
arXiv:2606. 29493v1 Announce Type: new Abstract: Benchmarks for LLM-assisted theorem proving in Lean are often treated as intrinsically reliable because every solved instance comes with a machine-checked proof.
arXiv:2606. 31134v1 Announce Type: new Abstract: While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection.
arXiv:2607. 19407v1 Announce Type: new Abstract: Formal theorem proving has emerged as a frontier challenge for machine learning, yet the ecosystem is fragmented: proofs remain siloed across incompatible systems, limiting both training data for learning-based provers and the portability of verified results.