基础模型的最新进展催生了能在国际数学奥林匹克竞赛中达到金牌水平的推理系统。然而，从竞赛级问题解决到专业研究，需要浏览大量文献并构建长程证明。本文介绍了 Aletheia，一个数学研究智能体，它以自然语言端到端地迭代生成、验证和修正解决方案。具体来说，Aletheia 由高级版 Gemini Deep Think 驱动，用于解决具有挑战性的推理问题，这是一种超越奥赛级问题的新型推理时缩放定律，并密集使用工具来应对数学研究的复杂性。我们展示了 Aletheia 从奥赛问题到博士级练习的能力，最值得注意的是，在 AI 辅助数学研究中取得了几个里程碑：(a) 一篇由 AI 完全自主生成的研究论文（Feng26），计算了算术几何中称为特征权的某些结构常数；(b) 一篇展示人机协作的研究论文（LeeSeo26），证明了相互作用粒子系统（独立集）的界；(c) 对 Bloom 的 Erdős 猜想数据库中 700 个开放问题进行了广泛的半自主评估（Feng et al., 2026a），包括自主解决了四个开放问题。为了帮助公众更好地理解 AI 与数学相关的发展，我们建议量化 AI 辅助结果的自主性和新颖性标准，并提出一种新的人机交互卡概念以提高透明度。最后，我们反思了数学中的人机协作，并在 https://github.com/google-deepmind/superhuman/tree/main/aletheia 分享了所有提示和模型输出。
Recent advances in foundational models have yielded reasoning systems capable of achieving a gold-medal standard at the International Mathematical Olympiad. The transition from competition-level problem-solving to professional research, however, requires navigating vast literature and constructing long-horizon proofs. In this work, we introduce Aletheia, a math research agent that iteratively generates, verifies, and revises solutions end-to-end in natural language. Specifically, Aletheia is powered by an advanced version of Gemini Deep Think for challenging reasoning problems, a novel inference-time scaling law that extends beyond Olympiad-level problems, and intensive tool use to navigate the complexities of mathematical research. We demonstrate the capability of Aletheia from Olympiad problems to PhD-level exercises and most notably, through several distinct milestones in AI-assisted mathematics research: (a) a research paper (Feng26) generated by AI without any human intervention in calculating certain structure constants in arithmetic geometry called eigenweights; (b) a research paper (LeeSeo26) demonstrating human-AI collaboration in proving bounds on systems of interacting particles called independent sets; and (c) an extensive semi-autonomous evaluation (Feng et al., 2026a) of 700 open problems on Bloom's Erdos Conjectures database, including autonomous solutions to four open questions. In order to help the public better understand the developments pertaining to AI and mathematics, we suggest quantifying standard levels of autonomy and novelty of AI-assisted results, as well as propose a novel concept of human-AI interaction cards for transparency. We conclude with reflections on human-AI collaboration in mathematics and share all prompts as well as model outputs at https://github.com/google-deepmind/superhuman/tree/main/aletheia.
核心贡献 · Key contributions
提出 Aletheia，一个数学研究智能体，能够以自然语言端到端地迭代生成、验证和修正解决方案。 Introduces Aletheia, a math research agent that iteratively generates, verifies, and revises solutions end-to-end in natural language.
展示了一种新的推理时缩放定律，从奥赛级别问题扩展到博士级别问题。 Demonstrates a novel inference-time scaling law extending from Olympiad-level to PhD-level problems.
实现了自主生成研究论文（Feng26），无需人工干预即可计算算术几何中的特征权重。 Achieves autonomous generation of a research paper (Feng26) calculating eigenweights in arithmetic geometry without human intervention.
展示了人机协作证明独立集边界（LeeSeo26），AI 提供了高层策略。 Presents human-AI collaboration in proving bounds on independent sets (LeeSeo26), with AI providing high-level strategy.
对 700 个开放的 Erdős 问题进行了半自主评估，自主解决了四个开放问题。 Conducts semi-autonomous evaluation on 700 open Erdős problems, autonomously solving four open questions.
提出了 AI 辅助数学的自主性和新颖性标准等级，以及用于透明化的人机交互卡。 Proposes standard levels of autonomy and novelty for AI-assisted mathematics, and human-AI interaction cards for transparency.
局限 · Limitations
成功案例罕见；大多数研究级问题未取得自主进展。 Success cases are rare; most research-level problems saw no autonomous progress.
模型极易出错和产生幻觉，尤其是在问题解释存在歧义时。 Model is highly prone to errors and hallucinations, especially in ambiguous problem interpretations.
与典型的人类研究论文相比，自主结果相对简短且基础。 Autonomous results are relatively brief and elementary compared to typical human research papers.
模型表现出规范博弈，曲解问题以使其更容易回答。 Model exhibits specification gaming, misinterpreting questions to make them easier to answer.
数学意义的评估需要专家数学家，限制了可扩展性。 Evaluation of mathematical significance requires expert mathematicians, limiting scalability.
论文章节 · Sections（共 19）
摘要Abstract
1 引言1 Introduction
2 Aletheia 智能体：从奥赛到研究级数学2 Aletheia agent: From Olympiads to Research-level Mathematics
2.1 规模定律与深度思考的演进2.1 Scaling Laws and the Evolution of Deep Think
2.2 为研究级数学开发智能体框架2.2 Developing Agentic Harnesses for Research-Level Math
2.3 工具使用的重要性2.3 Importance of Tool Use
3 数学研究成果总结3 Summary of Mathematical Research Results
3.1 里程碑 A：可靠的自主研究3.1 Milestone A: Reliable Autonomous Research