OpenAI 再公布一批数学突破成果

OpenAI 已公布解法，涉及若干长期数学难题。这些解法由一款尚未发布的前沿模型产出，并被整理为722 篇手稿、372 个结果系列，每个结果系列汇集了相互关联的论文。这延续了近期一系列数学突破：它们既令部分数学界人士印象深刻，也令其感到不安，同时引发了有关研究伦理和学术行为的问题。根据 AGMAI——这个新成立、由顶尖数学家组成的独立咨询小组，负责推动以负责任的方式沟通这些成果——此次发布包含对“数百个”开放问题的解答。

这些结果数周前便已受到预期，但在此之前，OpenAI 并未说明模型究竟解决了哪些问题，也未明确其发布时间。今年 9 月，该公司表示，其模型已“解决了横跨大多数数学领域的 100 多个长期开放问题”。已发布的论文和其他资料还包括对模型推理过程的一些总结、所用计算量的估计，以及尝试解决问题数量的统计数据。OpenAI 称，“平均每项成果”使用了相当于 ChatGPT Pro 思考三小时的计算量。

AGMAI，即数学与人工智能咨询小组（Advisory Group on Mathematics and Artificial Intelligence），于 9 月下旬发布了首份建议，敦促 AI 实验室及时发布数学成果，并尽可能通过既有学术渠道发布；同时披露所用模型名称、提示词和计算成本等细节。该小组还恳请 AI 公司“不要将数学成果的发布视为推广其模型的营销工具”，称这种做法会对数学界造成重大伤害。

以下是 OpenAI 对此次发布流程的说明：

对于此次发布，我们将在 GitHub 仓库中公布结果，并提供论文修订与引用规范。我们将继续探索其他由社区托管、且符合委员会指南的发布替代方案。对于未来的发布，我们承诺通过完善引用、数学阐述和结果呈现方式，进一步提高论文质量，以便更好地理解相关成果。

数学家需要对这些成果进行评估和消化，其完整影响可能还要一段时间才能显现。它们进一步扩充了来自 OpenAI 及 Anthropic 等竞争实验室、且仍在被该领域消化处理的快速增长的数学研究成果；其中还包括与千禧年大奖难题相关的结果，该类问题是这一领域最著名的开放问题之一。今年，AI 实验室迅速进入这一学科——尤其是其处理公告的方式——已就研究实践、伦理，以及公司应如何认可其系统所依赖、并可能用于产生成果的人类数学家的工作，引发了激烈争论。

OpenAI has revealed solutions to a number of long-standing mathematics problems produced by an unreleased frontier model in a batch of 722 manuscripts, covering 372 result families that group related papers. It extends a run of breakthroughs that have both impressed and unsettled parts of the mathematical community while raising questions about research ethics and academic conduct. According to AGMAI, the newly formed independent advisory group of elite mathematicians put together to work on communicating the results responsibly, the release includes solutions to “hundreds” of open questions.

The results have been expected for weeks, although until now OpenAI had not provided details about which problems the model had solved or exactly when they would be published. In September, the company said its model had “resolved more than 100 long-standing open problems across most areas of mathematics.” The released papers and other details also include some summaries of the model’s reasoning, estimates of the compute used, and stats about the number of problems attempted. OpenAI claims the “average result” used the equivalent of three hours of ChatGPT Pro thinking.

AGMAI, or the Advisory Group on Mathematics and Artificial Intelligence, published its first recommendations in late September, urging AI labs to release mathematical results promptly and through established academic channels where possible, while disclosing details such as the name of the model used, prompts, and compute costs. The group also implored AI companies to “refrain from treating the release of mathematical results as marketing vehicles to promote their models,” a practice they said inflicts significant harm on the mathematical community.

Here’s how OpenAI described its process for this release:

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

The full impact of the results will likely take some time to be felt as mathematicians assess and digest them. They add to a rapidly growing body of mathematical results from OpenAI and rival labs like Anthropic that the field is still processing, including results concerning a Millennium Prize problem, among the most famous open questions in the field. The speed at which AI labs have barreled into the discipline this year — particularly their handling of announcements — has provoked fierce debate over research practices, ethics, and how companies credit the human mathematicians whose work their systems build upon and potentially use to produce results.