Mathematicians warn of AI threats to profession as industry encroaches
Mathematicians warn of AI threats to profession as industry encroaches
数学家警告：随着科技行业入侵，人工智能对数学专业构成威胁
Mathematicians warned against rising tech industry influence in a declaration describing the many challenges that AI poses to mathematics research. The timing of the declaration comes two weeks after OpenAI publicized one of its AI models as having disproved an 80-year-old mathematical conjecture in geometry. 在一份描述人工智能对数学研究构成诸多挑战的声明中，数学家们对科技行业日益增长的影响力发出了警告。该声明发布的时间点，距离 OpenAI 宣布其人工智能模型推翻了一个 80 年历史的几何学猜想仅过去两周。
The declaration was developed by a working group of 16 researchers over eight months following a conference held at Leiden University in the Netherlands in September 2025. Published on June 2, 2026, the resulting Leiden Declaration on Artificial Intelligence and Mathematics has been endorsed by the International Mathematical Union—the international non-governmental organization that hosts conferences and oversees the most prestigious prizes in mathematics such as the Fields Medal. 这份声明由一个由 16 名研究人员组成的工作组历时八个月编写而成，此前他们于 2025 年 9 月在荷兰莱顿大学举行了一次会议。这份名为《关于人工智能与数学的莱顿宣言》（Leiden Declaration on Artificial Intelligence and Mathematics）于 2026 年 6 月 2 日发布，并得到了国际数学联盟（IMU）的支持——该组织是一个国际非政府组织，负责举办各类会议并管理菲尔兹奖等数学界最负盛名的奖项。
“Mathematicians should find it quite striking that tech companies are suddenly interested in their work,” said Kevin Buzzard, a mathematician at Imperial College London, in a statement. “The Leiden Declaration is a well-thought-through response to what is currently happening, as AI continues to disrupt this space.” “科技公司突然对数学家的工作产生兴趣，这应该会让数学家们感到非常震惊，”伦敦帝国理工学院的数学家凯文·巴扎德（Kevin Buzzard）在一份声明中表示。“《莱顿宣言》是对当前正在发生的事情经过深思熟虑后的回应，因为人工智能正在持续扰乱这一领域。”
The Leiden Declaration, which has already drawn hundreds of signatories, warns that recent AI developments are threatening “characteristic values” of mathematical research, “often in ways that disproportionately affect students and early-career mathematicians, and hence the long term future of the discipline.” 《莱顿宣言》已经吸引了数百名签署者，它警告称，近期人工智能的发展正在威胁数学研究的“核心价值”，“其影响方式往往对学生和职业生涯早期的数学家造成不成比例的伤害，从而影响该学科的长期未来。”
First, it points out how AI models can “produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs.” Such developments put reviewers under increasing pressure and are “jeopardizing our ability to implement traditional standards for the correctness, transparency, and independent verifiability of proof,” the declaration warns. 首先，宣言指出人工智能模型如何能够“产生看似合理但不可靠（甚至错误）的论证，而这些论证很难与正确的数学证明区分开来。”宣言警告称，此类发展使审稿人承受着越来越大的压力，并“危及我们执行关于证明的正确性、透明度和独立可验证性等传统标准的能力。”
“Inaccurate AI-generated drafts are cheap to produce, and there is a risk of cluttering the literature with claimed results that are simply wrong,” said Leslie Ann Goldberg, head of computer science at the University of Oxford, in a statement. “Once that happens, the errors are likely to propagate as new results are built on faulty foundations.” “生成不准确的人工智能草稿成本低廉，这存在一种风险，即文献中会充斥着完全错误的所谓研究成果，”牛津大学计算机科学系主任莱斯利·安·戈德堡（Leslie Ann Goldberg）在一份声明中表示。“一旦这种情况发生，随着新的研究成果建立在错误的基石之上，这些错误很可能会进一步扩散。”
Second, the declaration highlights how “models trained on published works frequently return outputs that do not properly cite the human works they synthesize,” while also pointing out that many current AI models were trained on data obtained through “exploiting licenses and access arrangements” or “simply violating copyright protections.” 其次，宣言强调了“基于已发表作品训练的模型，在输出结果时往往无法正确引用其所综合的人类作品”，同时指出许多当前的人工智能模型是在通过“利用许可和访问协议”或“直接违反版权保护”所获取的数据上进行训练的。
Third, the declaration describes how the use of AI “may become incentivized for its own sake, disrupting our mechanisms for hiring, funding and recognition” while leaving out researchers who lack access or are “unwilling to use technologies controlled by organizations whose values they do not share.” 第三，宣言描述了人工智能的使用“可能会为了使用而使用，从而扰乱我们的招聘、资助和认可机制”，同时将那些缺乏使用权限或“不愿使用由价值观不一致的组织所控制的技术”的研究人员排除在外。
Fourth, the declaration warns against mathematics research “communicated through informal channels such as press releases or blog posts, often without any research paper or other disclosure of information necessary for scientific evaluation.” Such communication strategies can lead to “oversimplification” in media reporting that overemphasizes AI tools’ significance at the expense of prior human contributions, and “misleadingly uses specific mathematical tasks as metrics for the general reasoning capacities of commercial products.” 第四，宣言警告不要通过“新闻稿或博客文章等非正式渠道传播数学研究，这些渠道往往缺乏科学评估所必需的研究论文或其他信息披露。”这种传播策略可能导致媒体报道中的“过度简化”，在牺牲人类既往贡献的情况下过分强调人工智能工具的重要性，并“误导性地将特定的数学任务用作衡量商业产品通用推理能力的指标。”
Fifth, the declaration describes “increasing involvement of technology companies in mathematical research” as threatening the “autonomy of mathematics,” especially as university budgets are under pressure and researchers may feel greater professional incentive to collaborate with technology companies on “asymmetric terms.” This also raises the risk that mathematics research questions amenable to AI-driven techniques may be prioritized. 第五，宣言将“科技公司对数学研究的日益介入”描述为对“数学自主性”的威胁，特别是在大学预算面临压力、研究人员可能感到更大的职业动力去以“不对等条款”与科技公司合作的情况下。这也增加了那些适合人工智能驱动技术的研究课题被优先考虑的风险。
The OpenAI example
OpenAI 的案例
Many of the Leiden Declaration’s warnings seem especially relevant to how OpenAI announced its model’s mathematical achievement on the same day that news publications reported the company was preparing to offer stock shares to the general public. The declaration pointedly described corporate press releases highlighting AI mathematical achievements as operating on “market timelines before the accepted processes of community evaluation in mathematics can take place.” 《莱顿宣言》中的许多警告似乎与 OpenAI 宣布其模型数学成就的方式特别相关——就在同一天，新闻媒体报道称该公司正准备向公众发行股票。宣言尖锐地指出，那些强调人工智能数学成就的企业新闻稿是在“市场时间表”下运作的，而“数学界公认的评估流程尚未完成”。
“The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” said Michael Harris, a mathematician at Columbia University and an author of the declaration, in a New York Times interview. He also spoke of the declaration attempting to “recover control of the narrative about the values and goals of mathematics from the AI industry.” “科技行业按照商业逻辑行事，这与数学的价值观背道而驰，”哥伦比亚大学数学家、该宣言的作者之一迈克尔·哈里斯（Michael Harris）在接受《纽约时报》采访时表示。他还提到，该宣言旨在“从人工智能行业手中夺回对数学价值观和目标的话语权。”
OpenAI uploaded a research paper describing its AI model’s mathematical proof along with commentary from independent mathematicians. But the company did not disclose information about prompts, AI training data, and the amount of computational resources used to solve the mathematics problems in question, said Rodrigo Ochigame, a historian and anthropologist of computing and artificial intelligence at Leiden University and another author of the declaration. OpenAI 上传了一篇描述其人工智能模型数学证明的研究论文，并附上了独立数学家的评论。但该宣言的另一位作者、莱顿大学计算与人工智能历史学家兼人类学家罗德里戈·奥奇加梅（Rodrigo Ochigame）表示，该公司并未披露有关提示词（prompts）、人工智能训练数据以及解决相关数学问题所使用的计算资源量的信息。
“The AI model is proprietary and unavailable to anyone outside the company,” Ochigame told The New York Times. “We get a flashy promotional video, while basic information needed to assess the scientific meaning of the result is kept secret.” “该人工智能模型是专有的，公司外部的任何人无法使用，”奥奇加梅告诉《纽约时报》。“我们得到的是一段华丽的宣传视频，而评估结果科学意义所需的基本信息却被保密了。”
The OpenAI achievement was “remarkable” but likely involved substantial compute resources, said Ursula Martin, a mathematician and computer scientist at Oxford University and an author of the declaration, in The New York Times interview. She suggested that similar quantities of equivalent effort from human mathematicians would have probably solved the problems in the same way—and she cautioned that mathematics is also about the “cultivation of ideas, understanding, judgment and human.” 牛津大学数学家兼计算机科学家、该宣言的作者之一厄休拉·马丁（Ursula Martin）在接受《纽约时报》采访时表示，OpenAI 的成就“令人瞩目”，但很可能涉及了大量的计算资源。她认为，人类数学家投入同等数量的努力，很可能也能以同样的方式解决这些问题——她并告诫说，数学同样关乎“思想、理解、判断和人类的培养”。