formalization

一篇技术博文，形式化地展示如何利用 Kleene 第二递归定理在无类型 lambda 演算中构造 Quine（自复制程序），并对比经典可计算性理论与函数式编程两种视角的表述。

This paper proposes a small candidate formalizer trained on offline teacher-generated lists to bridge the interface gap between open-ended LLM workloads and fast decision models, reporting up to 52.6% task success on CALVIN-D with 2.09s end-to-end latency, compared to 11.8% without the formalizer and slower baselines like Qwen3.5-27B.

Axiom Math released the first complete computer-checked proof of the Classification of Finite Simple Groups in Lean, using swarms of dozens of AI agents over 24 days to produce ~43.1 million lines of code, while also surfacing 34 deviations from the published record and a new result in group theory.

A complete formalization of the Classification of Finite Simple Groups in Lean 4, with every logical step checked by Lean's kernel, spanning 43.1M lines of Lean and following the first-generation proof. Along the way, the team discovered an issue in a published argument for the Unbalanced Group Theorem and devised an alternative route.

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.

Thomas Hales writes a guest post for Terence Tao's blog explaining what mathematicians should know about the Lean theorem prover, covering formal proof reliability, the growth of the mathlib library, and how AI-driven autoformalization has become a practical reality in 2026.

OpenAI 更新其数学仓库，新增 6 个 Lean 形式化证明、19 项修改，并撤回三项数学结果；仓库约 42% 的核心结果已完成形式化验证，且大部分成果由未发布的内部模型经大量思考计算生成。

The author introduces ARC-AGI-N, an open-source AI research tool that helps users find unsolved math and science problems and prepare prompts for agents to solve them.

This paper rethinks the linguistic notion of 'state' as a systemic morphosyntactic mechanism across synthetic languages, formalizing it as a set-valued function over grammatical templates within a Template-Based Modular Cognitive framework and offering a unified computational learning theory account.

AI systems, including ChatGPT and OpenAI's Sol, have disproved and fully formalized the Erdős Unit Distance conjecture, marking a milestone in AI-assisted mathematics. The article discusses the process and implications for the future of mathematical proof verification.

A formalization of combinatorial game theory in Lean 4, covering games, nimbers, and surreal numbers, based on Conway's work.

This paper introduces the MELD dataset for evaluating whether text embedding models capture mathematical equivalence across different terminologies, and finds that current models fail. It proposes a contrastive learning approach to align informal and formal mathematical statements, improving retrieval on both informal-formal and natural language tasks.

Terence Tao demonstrates how to use Claude Code as a red teaming tool to align Lean code style with Mathlib's official style guide, using the Riemann–Stieltjes integral formalization project as an example. The demonstration showcases the practical value of AI in code auditing and style alignment.