Ax-Prover is a multi‑agent framework that uses Large Language Models (LLMs) combined with Lean tools via the Model Context Protocol (MCP) to generate formally correct proofs in mathematics and quantum physics. It can operate autonomously or collaboratively with human experts, and its performance on public math benchmarks and new Lean benchmarks in abstract algebra and quantum theory shows it is competitive with state‑of‑the‑art provers and often outperforms them. The system also demonstrated practical assistant capabilities by helping a mathematician formalize a complex cryptography theorem.
arXiv:2607. 11307v1 Announce Type: new Abstract: Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning.
FormalFlow is a system that coordinates AI proving agents under human supervision to tackle long‑horizon formalizations, using a shared blueprint for nested planning, proving, and review loops. The team used it to produce a machine‑checked Lean 4 proof of the quantum soundness of the classical low‑individual‑degree test, a core theorem underlying MIP* = RE, in 63 days. The resulting library contains 126,367 lines of Lean code, all generated by agents, and corrects side conditions while preserving the published error bound under corrected assumptions.
arXiv:2605. 22763v2 Announce Type: replace Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.
arXiv:2606. 03303v1 Announce Type: new Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean.
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. 07779v1 Announce Type: cross Abstract: Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages.
arXiv:2603. 02668v2 Announce Type: replace Abstract: We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub.
MathAdv is a diagnostic benchmark for formal theorem proving that covers 13 undergraduate- and graduate-level mathematics domains. It includes Lean 4 proofs and up to three auxiliary tasks—multiple-choice questions, fill-in-the-blank problems, and expert-crafted transformations—to probe knowledge, informal reasoning, and robustness to problem presentation. Evaluation of current theorem provers shows formalization is a major bottleneck, performance varies by domain, natural-language guidance can help or hinder models, and equivalent reformulations reveal significant robustness gaps.
arXiv:2606. 28841v1 Announce Type: cross Abstract: Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify.
arXiv:2606. 15258v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly capable of mathematical problem solving and can even assist with research-level proofs, yet we still lack a scalable and reproducible way to measure step-level reasoning in long proofs across diverse sources.
arXiv:2604. 03789v2 Announce Type: replace-cross Abstract: Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems.
LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments.