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A reflective essay marking 100 years since Hilbert's program, tracing how Gödel's incompleteness and Turing's halting problem defeated it, and arguing that AI agents powered by proof assistants like Lean now realize Hilbert's 'proof machine' with profound consequences for mathematics and computer science.
A new Meta and NYU paper shows that h1, a simple agent loop giving models fast Lean feedback and search tools, matches or beats hand-designed theorem-proving workflows: it outperformed Goedel-Architect on PutnamBench (598 vs 597 problems) at lower cost, and with Opus 4.8 solved 83/100 hard algebra problems versus 63 for Claude Code.
Podcast interview with Lean creator Leo de Moura on how AI is making formal verification practical, the need to verify AI-generated code and autonomous agents, and the vision of a verified software stack.
This paper introduces RefactorProof, a stress test that derives 458 Lean-certified refactoring variants from VERINA tasks to measure whether LLM-generated proofs remain valid under behavior-preserving program changes. It finds substantial brittleness across reference proofs and specialized provers (DeepSeek-Prover-V2, Goedel-Prover-V2), while noting that most broken proofs can be repaired with small edits.
The paper presents EasyProver, a Lean proving system using recursive agents and asynchronous search that near-saturates PutnamBench and IMO benchmarks with an off-the-shelf frontier model, plus Aegis, a pipeline converting competitive programming into harder real-world Rust-to-Lean verification tasks for benchmarking and RL.
提出了 PACE（研究证明代理），支持在应用数学中联合进行猜想修订与证明开发，包含研究循环、独立验证器与证据追踪记忆，并发布了聚焦优化领域的 ResearchProofBench 基准，包含 51 个已知证明任务和 6 个开放问题案例。
A guest post by leading formalization researchers (Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash, Adam Topaz) reflecting on AI's rapid theorem-proving advances, cautioning against rushed large-scale formalization efforts like Math, Inc.'s sphere-packing project and Anthropic's Fermat's Last Theorem verification, and outlining a positive vision for high-quality, community-driven formalization of mathematics.
HOL Light Tutorial 提供了一套循序渐进的快速入门指南，通过分级示例帮助用户快速上手 HOL Light 定理证明器，涵盖安装、OCaml 基础、项与类型、命题逻辑、重写与战术等核心内容。
该论文评估了Lean编译成功是否等同于忠实的自然语言到Lean语句形式化，发现多个系统在编译通过与语义正确之间存在1.3至29.5个百分点的显著差距，且工具增强型代理的大部分差距源于真实的翻译错误。
A hands-on blog post comparing four theorem provers—Lean, Isabelle/HOL, HOL4, and Agda—by formalizing Euclid's proof of the infinitude of primes in each, with opinionated rankings on usability, interactivity, and enjoyment.
继其大语言模型解决二十年来最大数学突破之后，OpenAI 宣布其新内部模型已再产出 372 项成果，每项都解决或大幅推进了数学或理论计算机科学中的重大公开问题，且不再需要数百万美元的成本。
Guest post by Jeremy Avigad on Terence Tao's blog reflecting on how recent AI capabilities are disrupting mathematical research workflows, and arguing that mathematicians must adapt by pursuing harder problems and deeper understanding in the age of AI.
The paper introduces LeanPolish, a symbolic Lean 4 pipeline releasing 33k+ verified proof edits and failed attempts, showing that verified supervision can suffer from search artifacts and that iterating the symbolic compression pass beats neural hybrids on miniF2F while modestly improving whole-proof rewriting on PutnamBench.
A tutorial-style walkthrough for software engineers that formalizes a constructive proof about regular languages in the Lean theorem prover, explaining specification, implementation, induction, and the anatomy of a formal proof step by step. The piece demonstrates how Mathlib's existing theorems make formalizing textbook automata theory accessible to developers.
华为 Lagrange 数学计算研究中心提出 Sage，一个四阶段分解生成管线加双重信号语义校正循环的自动形式化框架，将答案泄漏率从70.9%降至2.7%，在 Omni-MATH NP 上达到73.3% pass@4，并在新提出的 IMO-Unformalized 基准上零样本达到87.4%验证保真度。
This paper introduces a metric for the intrinsic interestingness of mathematical theorems and trains a 27B model to predict proof difficulty, enabling the generation of more interesting and novel mathematics with reduced overlap with existing libraries.
This paper introduces a framework for LLMs to discover and prove interesting mathematical theorems by optimizing for a metric based on proof difficulty, leading to more novel and useful mathematical knowledge with reduced overlap with existing libraries.
This paper defines intrinsic interestingness for mathematical theorems using proof-to-statement length ratio and trains a 27B model to predict proof difficulty, enabling the generation of more interesting theorems and self-expanding mathematical libraries with reduced overlap with existing knowledge like Mathlib.
Mario Carneiro discovered that CIC plus LEM proves the consistency of ZF set theory, enabling a proof in axiom-free Lean with LEM, advancing type theoretic metamathematics.
The article discusses how artificial intelligence is revolutionizing the production of deep theorems in mathematics, challenging traditional measures of success, with a focus on the Nivat conjecture.