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OpenAI 发布了一个新仓库，收录其未公开内部模型产生的 719 篇数学手稿（归为 372 个结果族），涵盖黎曼 zeta 函数零点区域、Mahler 猜想、自由群因子同构等前沿问题，其中约 42% 的结果已用 Lean 形式化验证，并附带部分推理过程摘要。
OpenAI发布了此前"解决开放数学问题"声明背后的完整论文：涵盖722份数学手稿、372项重要成果，均来自对约4000个研究问题的测试筛选，每项成果平均消耗相当于ChatGPT Pro思考3小时的算力。
作者探讨 AI 在数学证明中的角色，质疑为何 AI 不能在生成证明之外，进一步理解、解释并推广证明背后的数学思想，而非仅停留在验证层面。
OpenAI发布了700多篇由AI智能体生成的论文，声称在理论数学、计算机科学和物理领域解决了372个公开问题，其中包括关于黎曼假设的重大进展，尽管部分证明已被发现错误并撤回，专家仍称这些成果令人震惊。
Fields Medalist Hugo Duminil-Copin reacts to OpenAI's claimed resolution of 350 major mathematical problems, comparing the impact to being run over by trucks, as every research problem he used to cite in his talks and grant applications has reportedly been solved.
OpenAI's so-called 'slop drop' of hundreds of AI-generated results on open math and computer science problems has left mathematicians both impressed and skeptical, with groundbreaking proofs emerging even as questions persist about how the results were produced.
OpenAI released a repository containing 722 mathematical manuscripts (700 preprints) grouped into 372 families of proofs and counterexamples generated by an unreleased internal model, along with some Lean formalizations and abridged reasoning traces. The results span areas like the Riemann zeta function, Mahler conjectures, and free group factors, and were produced using roughly three hours of ChatGPT Pro thinking compute per result on about 4,000 posed problems.
Stephen Wolfram argues that AI-assisted headlines about solving math problems often misunderstand what pure mathematics is really about, drawing parallels to Mathematica's introduction in 1988, and contends that AI's greatest value in math lies in thematically mining and connecting human mathematical knowledge rather than replacing human researchers.
A new Google paper introduces Cogentic, a multi-agent orchestration system that enables Gemini to discover new proofs for 5 previously unsolved math problems by combining parallel idea generation, strict step-level verification, and persistent shared notes.
A research team audits OpenAI's Lean 4 formal proof of 3D Navier-Stokes blow-up, showing that while mathematically valid, the solution physically breaks down at the atomic scale (fluid vaporizing at 0.7 nm) — a case of specification gaming. They propose adding a physics-boundary layer to neuro-symbolic AI systems and open-source their verification scripts.
RePro integrates Lean-oriented neural automated theorem provers into benchmark rewriting to ensure problem validity and answer correctness for reliable evaluation of LLMs in mathematical problem solving.
This paper introduces AViD Journal, a pipeline for automated novelty verification of mathematical theorems using Lean 4, evaluating it on withdrawn arXiv papers and highlighting challenges in formal verification.
Automated theorem proving is evolving from niche tools like Lean 4 into systems aided by machine learning that can solve real mathematical problems, such as verifying a counterexample to an Erdős conjecture.
This paper proposes a self-supervised theorem-discovery algorithm that starts from axioms and inference rules alone, building a theorem library without human priors. Experiments show the discovered theorems are meaningful and improve LLM proof performance.
Google new paper proposes the LEAP framework, which decomposes math problems into goal trees, learns from Lean verifier feedback, and improves LLM accuracy on math competition problems from 10% to 70%. It solves all 12 problems of Putnam 2025 and surpasses dedicated gold-medal-level systems on IMO-style benchmarks.
Google DeepMind releases AlphaProof Nexus paper. The AI agent autonomously solved 9 Erdős problems among 353 open math problems (including two unsolved for 56 years) and proved 44 OEIS conjectures. The reasoning cost per problem is only a few hundred dollars.
Google DeepMind's AlphaProof Nexus combines LLM-driven proof generation with machine verification using Lean, solving nine out of 353 open Erdős problems, two of which had been open for 56 years, at a cost of only a few hundred dollars per problem.
This paper evaluates Claude Code in an agentic proving framework on the Clever benchmark for program verification, achieving over 98% success in specification generation and end-to-end verification, revealing that existing benchmarks may be insufficient for evaluating modern agentic provers.
This paper presents NSPI, a neuro-symbolic framework that combines LLMs and symbolic computation to prove polynomial inequalities. It uses LLM-generated sum-of-squares conjectures, refines them symbolically, and formally verifies the proofs in Lean, demonstrating scalability on polynomials with up to 10 variables.
This paper introduces Discover and Prove (DAP), an open-source agentic framework for automated theorem proving in Lean 4 that tackles 'Hard Mode' problems where the answer must be discovered independently before formal proof construction. The work releases new Hard Mode benchmark variants and achieves state-of-the-art results while revealing a significant gap between LLM answer accuracy (>80%) and formal prover success (<10%).