分享人工智能在数学领域的进展

我们正在发布由内部前沿模型产出的一系列广泛的新数学成果。

为了改进我们与数学界分享成果的方式，我们一直在与普林斯顿高等研究院独立的数学与人工智能咨询小组⁠（在新窗口中打开）进行磋商，以制定最佳实践，并借鉴了他们的建议和公开推荐⁠（在新窗口中打开）来指导我们发布这些成果的方式。

对于本次发布，我们将成果发布在一个 GitHub 仓库中，并附有论文修订和引用的协议。我们也在继续探索其他由社区托管的替代方案，以符合委员会为本次发布制定的准则。对于未来的发布，我们承诺通过引用、数学阐述和成果呈现方式的改进，进一步提高论文质量，以便更好地理解。

作为我们 GitHub 仓库的一部分，我们正在分享许多证明在 Lean 中的形式化，Lean 是一种允许数学证明由计算机检查的编程语言。随着我们获得更多形式化，我们将更新该仓库。

为了促进科学透明度和开放性，我们还在仓库中发布了关于我们如何获得这些成果的更多细节。这些包括 10 份模型推理摘要、以 ChatGPT 中 Pro 使用量表示的计算消耗估算，以及关于尝试问题数量的统计数据。平均每个结果使用的计算量大约相当于三个小时的 ChatGPT Pro 思考。

我们希望这一进展能够推动人类知识的前沿，并促进数学的进一步进步。我们将资助一系列围绕理解人工智能产出的重大成果的研讨会、会议和特别项目——我们将在不久的将来分享更多相关信息。

我们希望直接以最先进的能力赋能科学家，并正在努力以负责任的方式发布产出这些成果的模型。这就是为什么继续在数学和其他科学领域评估我们的内部前沿模型很重要，这样我们才能加速开发推动这些领域进步的工具。我们将继续根据社区的反馈采取行动，并更新我们对未来重大科学进展披露的标准。

We’re releasing a broad range of new mathematical results produced by an internal frontier model.

As we look to improve how we share results with the math community, we’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study⁠(opens in a new window) to develop best practices, and we have drawn on their advice and public recommendations⁠(opens in a new window) to inform how we release these results.

For this release, we’re publishing the results in a GitHub repository, with protocols for paper revisions and citations. We’re continuing to explore other community-hosted alternatives for this release which meet the committee’s guidelines. For future releases, we are committed to further improving the quality of the papers via the citations, mathematical exposition, and presentation of the results for better understanding.

As part of our GitHub repository, we are sharing formalizations of many of the proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer. We will update the repository with more formalizations as we obtain them.

To promote scientific transparency and openness, we are also publishing additional details about how we obtained the results in the repository. These include 10 summaries of the model’s reasoning, estimations of compute spent in terms of Pro usage on ChatGPT, and statistics about the number of attempted problems. The average result used the equivalent compute of roughly three hours of ChatGPT Pro thinking.

We want this progress to push the frontier of human knowledge and enable further progress in mathematics. We will be funding a series of workshops, conferences, and special programs around the understanding of major results produced by AI—we will share more on this in the near future.

We want to directly empower scientists with state-of-the-art capabilities and are working to responsibly release the model that produced these results. This is why it is important to continue to evaluate our internal frontier models on mathematics and other sciences, so we can accelerate developing the tools to advance those fields. We will continue to act on feedback from the community and update our standards for future disclosures of major scientific advancements.