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2026-08-02 0 浏览 会员

AI 不断攻克未解数学难题,数学家们心情复杂

AI 模型正在破解困扰人类数十年的数学猜想,从推翻单位距离猜想到解决拉姆齐理论问题。数学家们反应不一,有人视为工具,有人担忧淘汰。

SOURCE / AI小生意项目库 MIN / 9 ACCESS / 会员 POST / 2026-08-02 00:01:31

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作者:Matthias Bastian 来源站点:the-decoder.com 原贴时间:

原文

AI models are cracking conjectures that stumped humans for decades. Reactions in the math community range from shrugs to an existential crisis as the profession grapples with its own possible obsolescence. In May 2026, OpenAI published a counterexample to the "Unit Distance Conjecture," disproving a conjecture in geometric graph theory that had remained open since 1946. It was one of hundreds of open problems linked to Hungarian mathematician Paul Erdos . AI had already helped solve other math problems, including other Erdos problems, but many mathematicians considered this the most significant example yet. Just one week later, human researchers adapted the core proof technique and used it to disprove another major conjecture . Since then, the floodgates have been open, and barely a day goes by without more news about AI in mathematics . Models are finding counterexamples, spotting broader patterns, and helping researchers turn arguments into machine-checkable proofs. Epoch AI, the research group best known for its demanding "FrontierMath" AI benchmark , recently announced the second solution in "FrontierMath: Open Problems," a test drawn from major unsolved questions in math. OpenAI's new Astra model also appears designed for this work: The lab introduced it with ten solutions of varying difficulty. Abhishek Saha, a math professor at Queen Mary University of London, writes on X , "At the moment, in my area of research mathematics, frontier AI models are at least as good as a solid and indefatigable PhD student." Saha spent a full day using GPT-5.5 Pro for routine work that would previously have taken weeks. The experience left him "increasingly playing the role of conductor, rather than doubling up as the whole orchestra." Saha said most mathematicians don't realize this is already possible, and he expects the field to split over how it responds. "Some will adapt soon, and find boundless possibilities," he wrote. He expects others to resist, adding, "Other academics will continue to be AI-sceptical until the very end, like the folklore hero John Henry." The American folk hero worked himself to death competing against a steam drill. Saha represents a group of researchers who treat AI as a productivity tool rather than an attack on their field. Writing in The Conversation , mathematician Trefor Bazett says AI and human ingenuity could usher in a new golden age of mathematics. He cites an April 2026 paper from a team of Carnegie Mellon University mathematicians that solved an open problem in Ramsey theory by combining SAT solvers, code generated by language models, and formal proof verification. The paper explicitly connects that result to a "golden age" that Fields Medal winner Timothy Gowers predicted in 2000 . Gowers imagined computers handling routine checks while mathematicians focused on deeper ideas. "In other words, computers would still do the boring bits for us, but these would not be quite as boring as they are now," he wrote. The Carnegie Mellon researchers believe that period has now begun. "We believe that we are now entering this golden age, thanks to the combination of several technologies," they write.

中文翻译

AI 不断攻克未解数学难题,数学家们心情复杂

AI 模型正在破解困扰人类数十年的猜想。数学界的反应从耸肩到存在主义危机不一而足,因为这一行业正努力应对自身可能被淘汰的局面。

2026 年 5 月,OpenAI 发布了“单位距离猜想”的一个反例,推翻了一个自 1946 年以来一直悬而未决的几何图论猜想。这是与匈牙利数学家保罗·埃尔德什相关的数百个开放问题之一。AI 此前已经帮助解决了其他数学问题,包括其他埃尔德什问题,但许多数学家认为这是迄今为止最重要的例子。仅仅一周后,人类研究人员改编了核心证明技术,并用它推翻了另一个重大猜想。此后,闸门大开,几乎每天都有关于数学领域 AI 的新消息。

模型正在寻找反例、发现更广泛的模式,并帮助研究人员将论证转化为机器可检验的证明。以要求严格的“FrontierMath”AI 基准而闻名的研究小组 Epoch AI 最近宣布了“FrontierMath:开放问题”中的第二个解决方案,该测试取自数学领域的重大未解问题。OpenAI 的新 Astra 模型似乎也是为此设计的:该实验室推出了它,并附带了十个难度各异的解决方案。

伦敦玛丽女王大学数学教授 Abhishek Saha 在 X 上写道:“目前,在我的研究数学领域,前沿 AI 模型至少相当于一个扎实且不知疲倦的博士生。”Saha 花了一整天使用 GPT-5.5 Pro 处理以前需要数周的日常事务。这段经历让他“越来越像指挥家,而不是兼做整个乐团”。Saha 说大多数数学家没有意识到这已经成为可能,他预计该领域将因应对方式而分裂。“有些人会很快适应,并发现无限的可能性,”他写道。他预计其他人会抵制,并补充说:“其他学者将继续对 AI 持怀疑态度,直到最后,就像民间英雄约翰·亨利一样。”这位美国民间英雄在与蒸汽钻的竞争中劳累致死。Saha 代表了一群将 AI 视为生产力工具而非对其领域攻击的研究人员。

数学家 Trefor Bazett 在《The Conversation》上撰文称,AI 和人类的聪明才智可能会开启数学的新黄金时代。他引用了卡内基梅隆大学数学团队 2026 年 4 月的一篇论文,该团队通过结合 SAT 求解器、语言模型生成的代码和形式化证明验证,解决了拉姆齐理论中的一个开放问题。该论文明确将这一结果与菲尔兹奖得主蒂莫西·高尔斯在 2000 年预测的“黄金时代”联系起来。高尔斯设想计算机处理日常检查,而数学家专注于更深层次的思想。“换句话说,计算机仍然会为我们做无聊的部分,但这些部分不会像现在这么无聊,”他写道。卡内基梅隆大学的研究人员认为,那个时代现在已经开始了。“我们相信,由于多种技术的结合,我们现在正在进入这个黄金时代,”他们写道。

核心信息

AI 模型正在破解困扰人类数十年的数学猜想,从推翻单位距离猜想到解决拉姆齐理论问题。数学家们反应不一,有人视为工具,有人担忧淘汰。

  • AI 模型正在破解困扰人类数十年的数学猜想,从推翻单位距离猜想到解决拉姆齐理论问题。数学家们反应不一,有人视为工具,有人担忧淘汰。
  • 原贴提到:AI models are cracking conjectures that stumped humans for decades. Reac
  • 来源:the-decoder.com
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