今年 9 月，OpenAI 宣称其模型攻克纳维-斯托克斯方程，25 位菲尔兹奖得主随即联名发出公开信，将 AI 与数学之争推向公众视野；10 月 6 日，OpenAI 又一次性发布 722 篇由 AI 生成的数学预印本，次日因符号错误撤回三篇；10 月 8 日的成果更新日志进一步显示，另有 14 篇被修订、13 篇更新引用，手稿总数从 722 降至 719。彼时舆论的核心问题是：AI 会不会取代数学家。（参见文章：AI一次甩出722篇数学论文，25位菲尔兹奖得主坐不住了）
如今，事件有了新的进展。近日，在陶哲轩发起的非营利机构 SAIR Foundation 的播客节目中，两位身处争议中心的数学家，SAIR 主席、菲尔兹奖得主陶哲轩，与今年新晋菲尔兹奖得主、芝加哥大学教授邓煜，就 AI 与数学的未来展开了一场对谈。事件的前后经过，可参见下图的时间线。
这场对话没有停留在“AI 能不能做题”的层面，而是把讨论推进到了更根本的位置：AI 做出的数学，谁来负责理解；被批量生产的证明，如何回到数学的传统之中。
解题不等于理解：两条边界开始分离
先看这两位对谈者为何有资格回应这场争议。陶哲轩是 UCLA 教授，31 岁获得菲尔兹奖，也是 SAIR 基金会的创办人之一，近年来持续关注形式化验证与 AI 辅助研究；邓煜则在深圳长大，2006 年拿下国际奥数金牌，今年 7 月与北大校友王虹一同获得菲尔兹奖，因在希尔伯特第六问题上的关键进展而广受瞩目。联名公开信的签署者中，两人都位列其中。由“最会做题的人”来讨论“做题的意义”，本身就构成了这场对谈的张力。
对谈中最具启发性的判断，来自邓煜对数学“边界”的重新刻画。他说，做数学是为了理解世界，其中存在两条边界：一条是已经有证明的问题的边界，另一条是人类能够理解证明的边界。
在过去几个世纪里，这两条边界基本重合。一个人解出一道难题，通常也真正弄懂了它：能讲清楚证明，能从中提出新问题，能带出学生。陶哲轩进一步指出，数学界奖励“解题”，实际奖励的是这一整套活动，解题只是其中最容易衡量的指标。
AI 改变的正是这个前提。当机器可以在短时间内生成大量证明，“得到解答”与“掌握背后逻辑”开始变成两件不同的事。邓煜将其概括为：AI 使第二条边界显现了出来。他的看法是：AI 的证明令人惊叹，其中蕴藏着很好的新思路；AI 正在学习人类的思路，也在创造自己能够被理解的新思路，这是人类与 AI 的共同演进。但前提是，这些证明必须进入人类能理解的范围。
这个框架也解释了为什么顶尖数学家并未陷入“AI 取代人类”的恐慌。真正值得关注的问题不是 AI 解决了多少新问题，而是这些证明能否被理解、能否验证、能否在此基础上继续探索。陶哲轩直言，OpenAI 发布的成果中有十来个问题他都很关心，之后会去看，但眼下不在他的优先级里；按目前的解释方式，还未能打动他。
不过，这批成果并非全是水分。其中与编号 003 的准黎曼猜想相关的结果，将 zeta 函数零点的无零点区域推进到 7/8（此前人类只能确立一条随虚部增大不断变窄、无限贴近实部 1 的无零点区域，甚至无法排除在实部大于 0.99 的竖直带状区域内存在反常零点的可能），陶哲轩称之为“该问题五十年来最大进展”，并认为这个由三四个既有想法拼出的安排“恐怕没有一位在世数学家能独自组装出来”。这恰恰说明，问题不在成果不行，而在发布方式。
被切断的传承链：溯源危机比解题更重要
理解缺口并非杞人忧天，这场争议中已经出现了量化证据。按发布初期对仓库形式化目录的统计，722 篇预印本中经过 Lean 等形式化验证的比例仅约 22%，且 10 月 3 日至 6 日新增的 143 篇中，没有一篇经过 Lean 形式化验证。更深一层的问题在于，Lean 只验证形式化后的陈述，并不保证它与原问题一致，正如澎湃新闻的转述：“Lean 说你的代码没有 bug，不等于你的代码实现了你想要的功能。”这一现象被陶哲轩称为“证明消化不良”：产出的速度远远跑在了消化能力的前面。
如果说“理解缺口”是学科内部的隐忧，对谈揭示的第二个问题则关乎整个学术系统的运转：思想的溯源链条正在断裂。
陶哲轩指出，科技公司利用 AI 研究数学，本质上是在提炼他人的研究成果，从别人的论文和研究中获取数据。学术界遵循开放科学的原则已有数百年：论文是公共财富，引用让思想可以被追溯，科学正是这样进步的。但 AI 将数千年积累的文献“不透明地转化为答案”，有时能指出参考了哪些文献，有时则无法追溯。技术公司有动机淡化这一点，让人以为答案是凭空出现的。
邓煜给出了更具体的例证：已经出现有人直接使用他人在 ChatGPT 中输入的想法来生成证明的情况。他主张，AI 至少应该公开自己的思维链，让人知道它参考了什么材料；连思维链都看不到，“太荒唐了”。
这个问题与 9 月的公开信一脉相承。信中集中批评过，AI 公司以越来越快的节奏大规模生产“真/假”陈述，绕开同行评议，而验证与消化的成本却由数学共同体承担。学界内部也有更强硬的声音：10 月 7 日，人类数学协会（AHM）发表声明，称“一次性发布 700 多份文件，展示的不是学术研究，而是权力展示”，并敦促数学家停止与 OpenAI 的合作，陶哲轩在个人博客转发了这份声明。陶哲轩在本次对谈中说得更直白：批量解题产出的成果成了某种副产物，甚至可以说是“有毒废料”，接着它们得想办法处理，或者由数学家来处理。
国内学界也作出了回应。10 月 11 日，“丘成桐数学与人工智能实验室联盟”在清华大学成立，丘成桐在求真书院回应这场争议时说：“就像海啸来了，我们该如何应对海啸。”何旭华则认为，这批内容“并非全部符合学术规范，但其中有很多值得吸收的想法和成果”。
从“事后收拾”到“事前参与”：激励需要重新定价
针对这些结构性问题，两位数学家给出的方案核心是改变激励，而不是拒绝技术。
第一，改变成果进入学术文献的标准。陶哲轩主张，如果一项 AI 产出的成果只给出答案，而不附带理解、解释和可追溯的引用，它就不应该成为数学文献的一部分。这类产出需要先经过形式化验证，并留出人类的消化期。
第二，让数学家事前参与，而非事后收拾残局。陶哲轩认为，理想状态是 AI 公司在项目启动时就与数学家协作，帮助理解证明、标注来源，而不是发布之后再请学界兜底。中青在线 10 月 21 日即以“AI 公司应邀请数学家事前参与，而非事后收拾残局”为题报道这场对谈。
第三，重新分配“验证劳动”的价值。过去，解题意味着一整套理解活动的完成，指标与目的尚未脱节；现在，“解题”本身正在成为被追逐的目标。借用古德哈特定律的说法，一个指标一旦成为追逐的目标，它就不再是好指标。学术评价需要看见更广泛的理解与洞见，形式化验证、成果阐释这些劳动必须被定价。
开放数学模型：把工具交给共同体
对谈中另一个重要信息，是 SAIR 启动的 Open Math OS 项目。按照陶哲轩的介绍，其愿景是为数学社群提供由社群自己开发、符合自身价值观和目标的工具：起步阶段不发布自研新模型，先整合现有开源模型与研究工具，同时汇聚数据、训练资源和算力，希望几个月后在开源模型的基础上做出自己的模型。
邓煜参与这个项目的动机与陶哲轩一致：建立一个能够真正追溯思想来源、不依赖大公司的工具。在他看来，AI 是工具，好坏取决于围绕它形成的体系；保持开放，AI 才能健康发展并持续造福社区。
这一选择有其现实针对性。普林斯顿高等研究院“数学与人工智能顾问小组”9 月底发布的建议中曾警告，专有模型可能造成“实验室跑赢整个领域”的两级体系，使工具拥有者实际上设定整个学科的研究议程；该小组 9 名成员中包括高尔斯（Gowers）、海尔（Hairer）、威滕（Witten）三位菲尔兹奖得主。开源的数学模型正是对这种可能性的预防：当工具由社群共同拥有，研究议程的设定权就不会集中到少数几家公司手中。
值得注意的是，两人都没有把“慢”与“快”对立起来。陶哲轩强调，不应简单分成支持与反对两派，理想是兼得“慢科学”与快速方法的好处：保留慢节奏科研带来的深度理解、强大的共同体和人类对学科的持续掌握，同时使用能加速研究的工具。速度不是唯一需要优化的目标。
留给研究者的问题：什么仍然属于人
对谈反复回到一个话题：AI 时代，数学研究者还需要培养什么能力。两人的答案高度一致，提出有价值的问题、设计整体证明路线、发展新思想、做出价值判断，这些仍然是人的关键能力。
邓煜特别强调，“理解”是使用 AI 的前提：AI 能把事情做好，前提是人类对问题已有充分理解；理解既用于引导 AI，也让人在离开 AI 时依然能独立工作。当人类已经有了解题路线图，只是实现细节过于繁琐时，AI 可以接手推导，把研究者的时间留给更根本的问题。
陶哲轩对年轻一代的态度则在克制中透出乐观。他承认，数学领域许多老规矩正在变化，年轻一代眼下有很多焦虑甚至绝望。但他认为，当工具真正到了他们手里，他们就会想出极富创意的新做法。“我对年轻一代充满希望，只要有合适的工具，他们就能做出惊人的成果。”
这些能力的落点，也正在进入制度层面的讨论。此前，由国际数学联盟支持、2411 名数学家签署的《人工智能与数学莱顿宣言》（2026 年 6 月发布）已建议：论文应增设“工具与计算资源披露”部分，并在可行时提供形式化证明；对青年学者而言，与其在解题这条已被机器打通的赛道上竞争，不如把精力转向提出新问题、判断成果价值这些机器暂不擅长的环节。对谈虽未逐条重申这些建议，但两位得主给出的方向与之完全一致。
从 722 篇预印本引发的震动，到两位菲尔兹奖得主的这场对谈，讨论的落点已经从“AI 能否做数学”转向“数学共同体需要什么样的 AI”。这或许是本轮争论最有价值的转向：问题不再是非此即彼的站队，而是如何在开放、溯源、理解和激励这几个维度上，重建一套与新工具相容的学术秩序。
数学以恒久立身。它消化过集合论危机，也催生了计算机科学。这一次，它面临的不是被取代的危机，而是一个更朴素的要求：无论证明由谁写出，理解它的责任，仍然在人。（本文首发钛媒体APP，作者 | 硅谷Tech-news，编辑 | 焦燕）
- 参考资料：https://weibo.com/tv/show/1034:5355948643123203?from=old_pc_videoshow
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In September this year, Open AI declared that its model was the Knavi-Stokes equation, and 25 Fields Prize laureates sent a joint open letter to push AI and mathematics into public view; on October 6, Open AI made another one-time publish 722 mathematical preprints generated by AI, which were withdrawn the following day by mistake of symbols; the results update log on October 8 further showed that another 14 were revised, 13 updated references, and the total number of manuscripts dropped from 722 to 719. The central question in public opinion is whether AI will replace mathematicians. (See article: AI. threw out 722 math papers at once, 25 Fields winners couldn't sit down.)
Now there are new developments. In recent days, in a podcast by SAIR Foundation, a non-profit organization launched by Tao Cheol, two mathematicians at the centre of the controversy, SAIR President and Fields Laureate Tao Cheol-hyol, engaged in a conversation with the new Fields winner this year and Professor Deng Zheng, University of Chicago, about AI and the future of mathematics. The history of the events can be found in the time line shown below.
The conversation did not stop at the "Ai can't do it" level, but moved the discussion to a more fundamental point: the math that AI makes, who is responsible for understanding; the proof of mass production, how to get back to math.
The solution does not mean understanding: the two borders begin to separate.
Let us first see why these two interlocutors are qualified to respond to this controversy. At 31 years of age, he was a UCLA professor and one of the founders of the SAIR Foundation. In recent years, he has continued to focus on formalization certification and AI support research; Deng has grown up in Shenzhen, where he won the International Odium medal in 2006, and in July this year, he won the Fields Prize with a North University alumni Wang. Two of the signatories of the joint open letter were among them. The discussion of “the meaning of the question” by “the most competent person” constitutes in itself the tension in this conversation.
The most enlightening judgement of the conversation comes from the redrawing of the mathematical “boundary”. He said that mathematics was intended to understand the world, where there were two boundaries: one where the problem had already been proven, and the other where humans could understand it.
In the past few centuries, the two borders have largely coincided. One solves a problem, which is often understood: it is clear that new problems can be raised and students brought out. It was further noted that the mathematics community rewards the “problem” and that the actual reward is this set of activities, which are only the most easily measurable indicators.
AI changed that premise. When machines can produce a large amount of proof in a short period of time, “to get answers” and “to take control of the logic behind them” begin to become two different things. Dumbledore summed it up: AI made the second boundary visible. His view was that the testimony of AI was impressive and contained good new ideas; AI was learning the human mind and was also creating new ideas that it could understand, which was a common evolution between human beings and AI. But the premise is that these proofs must come within the reach of human understanding.
This framework also explains why top mathematicians are not caught up in the fear of "AI instead of humans." The real concern is not how many new problems AI has solved, but whether these certificates can be understood, validated and pursued on this basis. Tout-chul put it bluntly, Open AI publish had a dozen issues of concern to him that he would look at later, but not at the moment in his priority; he had not been touched by the current interpretation.
However, not all of the results were water. The results associated with the quasi-Liman guess No. 003 pushed the zero-point area of the zeta function to 7/8 (previously humans could only establish a zero-point area that was ever narrower and closer to the real part with the vantage point, and could not even exclude the possibility of an abnormal zero in a vertical zone larger than 0.99), which Tao Chulzhu called “the greatest advance of the problem in 50 years” and considered that the arrangement, which was co-mingled by three or four well-established ideas, “I am afraid that no one of the world's mathematicians can assemble alone”. That is precisely why the problem is not one of results, but of the publish approach.
Cut-off transmission chains: Retrace crisis is more important than solving the problem.
Understanding the gaps is not a matter of concern, and evidence of quantization has appeared in this dispute. According to the initial publish inventory of warehouse formalization, only about 22 per cent of 722 pre-prints were formally certified, such as Lean, and none of the 143 new ones from 3 to 6 October were formally certified by Lean. The deeper problem is that Lean only validates formalized statements, and it doesn't guarantee their consistency with the original problem, as the news repeats: "Lean says your code doesn't have bugs, it doesn't mean that your code does the function you want." This phenomenon has been referred to by Tao Chul Xin as “proved indigestion”: the rate of output is well ahead of the capacity to digest.
If the “understanding gap” is a concern within the discipline, the second issue revealed by the conversation concerns the functioning of the entire academic system: the retrospective chain of thought is breaking.
According to Tao Chul-hyun, technology companies use AI to study mathematics, essentially to extract research from others and to extract data from others ' papers and studies. The academic community has followed the principle of open science for hundreds of years: thesis is a public asset, and it is science that advances by quoting ideas that can be traced. AI, however, “transparently translates” the thousands of years of accumulated literature into answers, sometimes pointing to references and sometimes not traceable. Technology companies have a motive to dilute this, which gives the impression that the answer is empty.
Dumbledore gives a more specific example: there have been cases in which people have directly used ideas entered by others in ChatGPT to produce proof. He argued that AI should at least open up its own thinking chain to show what it refers to; even the thought chain could not be seen, “it is absurd”.
The problem goes hand in hand with the open letter of September. The letter focused on criticism that AI produces “real/false” statements at an increasingly rapid pace, bypassing peer reviews, while the costs of validation and digestion are borne by the mathematical community. There is also a stronger voice within the academic community: on October 7, the Association of Human Mathematics (AHM) issued a statement stating that “more than publish 700 documents are one-off, showing not academic research, but a demonstration of power” and urging mathematicians to stop working with Open AI, which Tao Zheix transmitted to his personal blog. Tao Cheol-chul is even more straightforward in this conversation: the results of bulk solving outputs become some sort of by-product, or even a “toxic waste”, and then they have to be dealt with somehow or by mathematicians.
In-country academia has also responded. On October 11th, the “Alliance of Mathematics and Artificial Intelligence Laboratories” was founded at the University of Tsinghua, and Chu responded to the controversy by saying, “Just as the tsunami came, how should we respond to it.” For his part, He Xue believed that the content was “not entirely in line with academic norms, but that there were many ideas and results to be absorbed”.
From “back-to-back” to “pre-engagement”: incentives need to be reprioritized
In response to these structural problems, the core of the programme offered by two mathematicians was to change incentives rather than reject technology.
First, changing the standards of entry into academic literature. Tao Chul-hyun argued that an AI output should not be part of the mathematical literature if it gave only answers without understanding, interpretation and retroactive references. Such outputs need to be formally validated and allowed for human digestion.
Second, involve mathematicians before, not after. Tao Chul-hyun believes that the ideal state is for AI to work with mathematicians at the start of the project to help understand the certificate, to mark the source, and not to go to the bottom after publish. On October 21st, China Online reported this conversation on the theme “AI should invite mathematicians to participate before, not to clean up after”.
Thirdly, the value of “validation” is redistributed. In the past, problem solving had meant the completion of a set of understanding activities, and indicators had not yet been disconnected from the purpose; now, the “problem” itself was being pursued. In the words of the Goodha-specific law, once an indicator is targeted, it is no longer a good indicator. Academic evaluations need to see a broader understanding and insight, and formal validation and interpretation of results must be priced.
Open Math Model: Handing over tools to the Community
Another important message in the conversation is the Open Math OS project started by SAIR. According to Tao Chul-hyun, the vision is to provide the mathematical community with tools developed by the community itself that are consistent with its values and goals: The start-up phase does not involve the self-study of the publish model, first consolidating existing open-source models and research tools, while pooling data, training resources and calculations, and hoping to build on the open-source model in a few months.
The motivation for Deng to be involved in this project is consistent with Tao Cheol-chul: to create a tool that can truly trace the source of ideas without relying on large companies. In his view, AI was a tool, and good or bad depended on the system that was built around it; keeping it open would enable AI to develop healthyly and to continue to benefit communities.
This option is realistic and relevant. At the Princeton Institute of Higher Studies, the Mathematics and Artificial Intelligence Advisory Group, in its recommendations at the end of the month, publish warned that proprietary models could create a two-tier system of “laboratories win the whole field” that would allow tool owners to actually set the research agenda for the whole discipline; 9 members of the group included three Fields winners. Open-source mathematical models are the prevention of this possibility: when tools are shared by communities, the setting of the research agenda will not be concentrated in a few companies.
It is worth noting that neither of them has put “slow” against “fast”. Tao Chul-hyun stressed that there should be no simple division between pro- and anti-ratuits, and that the ideal was a combination of “slow science” and the benefits of a fast-track approach: retention of the deep understanding of slow-paced science, a strong community and continued human mastery of discipline, and the use of tools to accelerate research. Speed is not the only objective that needs to be optimized.
The question left to researchers: what is still human?
The conversation has come back to the subject of the AI era where mathematical researchers need to develop competencies. Their answers are highly consistent, raising valuable questions, designing overall proof of course, developing new ideas and making value judgements, which remain critical human capabilities.
In particular, Deng stressed that “understanding” is a prerequisite for the use of AI: AI can do things well if humans have a full understanding of the problem; understanding is used both to guide AI and to keep people working independently when they leave AI. When humans already have a road map for understanding the subject, but the details are too cumbersome to achieve, AI can take over and leave the time of researchers to more fundamental questions.
The attitude of Tao Cheol-hyun towards the younger generation is optimistic in restraint. He acknowledged that many old rules were changing in the field of mathematics and that the younger generation was in a state of anxiety and even despair. But he believes that when the tools are actually in their hands, they will come up with innovative new approaches. “I am hopeful that the younger generation, with the right tools, will be able to do amazing things.”
The fallout from these capacities is also entering into institutional discussions. Previously, the Leiden Declaration on Artificial Intelligence and Mathematics (publish, June 2026), supported by the International Mathematics Union and signed by 2411 mathematicians, had recommended that the paper should include a “tool and calculator resource disclosure” section and, where feasible, provide formalized proof; for young scholars, instead of competing on a machine-enabled track, it would be better to turn their energies to the pieces of machinery that are not good at raising new questions and judging the value of results. While the proposals were not reiterated article by article, the two recipients gave exactly the same direction.
From the shock triggered by 722 pre-prints to this conversation between the two Fields winners, the point of discussion has shifted from "Ai can do math" to "Ai what the math community needs." This is perhaps the most valuable shift in the debate in this round: the question is no longer one of standing on the other, but of how to re-establish an academic order that is compatible with new tools in terms of openness, traceability, understanding and motivation.
Mathematics stands for eternity. It digests the acoustic crisis and gives rise to computer science. This time, it is not facing a crisis that has been replaced, but a more modest demand: Whoever wrote it, understood its responsibility is still human. (This article starts with titanium media app, by | Silicon Valley Tech-news, editor | Joo Yon)
- References: https://weibo.com/tv/show/1034: 535594864312303? from=old pc videoshow
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