内容来源：https://www.quantamagazine.org/is-ai-the-end-of-math-as-we-know-it-20261005/

内容总结：

2026年9月8日，OpenAI宣布其AI模型解决了一个著名数学难题，在数学界引发剧烈震荡。此前整个夏天，AI模型每周都在给出数十年前数学猜想的证明。这一消息令许多数学家感到措手不及，德克萨斯大学奥斯汀分校的斯科特·阿伦森在博客中写道：“人类数学家永远不再是地球上主要的定理证明者。”加州大学伯克利分校的一场讲座上，约150名学生和研究人员对数学家肯·小野投身AI初创公司表达了愤怒与焦虑，原定50分钟的活动延长至两个多小时。

文章作者指出，公众对数学家情绪反应的困惑，暴露出一个长期问题：许多人并不了解数学的本质及其价值所在。纯粹数学介于科学与艺术之间，重视逻辑与确定性，但核心却是美、直觉与深度这些更模糊的概念。数学研究的价值不在于答案本身，而在于探索过程中产生的工具、联系和新问题。然而AI模型直接跳到终点给出证明，数学家虽能通过逻辑验证系统确认证明为真，却无法理解其所以然，缺失了数学最核心的“理解”。

数学文化几乎完全围绕解题构建，研究生通过证明定理获得发表、职位和认可。AI解题能力的突破使这一激励体系面临瓦解。OpenAI和Anthropic等公司竞相证明定理并从学术界挖人，却无意撰写清晰论文解释结果，OpenAI甚至宣布将100多项重要成果保密。这严重损害了开放科学。数学家们不再在论文末尾发布公开猜想以免被AI抓取，期刊和预印本网站arxiv.org被AI生成或辅助的证明淹没，MathOverflow论坛活跃度大幅下降。

多伦多大学的丹尼尔·利特警告，若不作改变，50年后可能无人再做数学。加州理工学院的马蒂尔德·马尔科利则指出，若坚持将猜想攻克作为唯一目标和回报，数学专业可能因想象力的终结而消亡。MIT的帕维尔·埃廷戈夫则较为乐观，认为数学家将转向解读和理解AI产出的结果，仍有大量有趣工作可做。

然而，新一代数学家是否愿意从事“解释者”的角色尚不确定。许多人进入数学是为了解决问题、探索前沿，而非花费数十年训练后只为翻译和重写AI的证明。AI本身也在削弱从事该角色所需的教育基础。麦吉尔大学的博士生马塞尔·高将当前形势比作《指环王》中被无限知识和权力腐蚀的萨鲁曼，他与越来越多数学家开始有意识地限制AI使用。他说：“我觉得船正在下沉，但我已经决定尽可能留在船上。”

尽管如此，仍有希望。数学家们已成立“人类数学协会”等组织，推动政策提案和工具来应对危机。利特认为，若成功适应，数学界可能变得更强——“人们做着有史以来最酷的事情，拥有一个真正充满活力、深刻理解事物的社区。”若无法适应，他问道：“那是谁的错？”

中文翻译：

人工智能是我们所知数学的终结吗？
引言
整个2026年夏天，种种迹象早已预示着即将到来的变化。似乎每周都有AI模型给出几十年前数学猜想的证明。因此，9月8日发生的事本不该让人完全意外。然而对许多人来说，它来得太突然，几乎像一记重击。OpenAI宣布其模型解决了数学中最著名的难题之一——随即引发了关于署名权和标准的争议。数学从此将面目全非。
“在我余下的岁月里，我不指望自己还会因为真的有人需要我来证明某个定理而去证明它，”德克萨斯大学奥斯汀分校的斯科特·阿伦森在博客中写道。“人类数学家将永远被废黜，不再是地球上进行定理证明的主要实体。”其他网络文章表达了乐观情绪，但许多则流露出悲伤、困惑和恐惧的交织。
宣布两天后，我发现自己坐在加州大学伯克利分校的一间教室里，周围是约150名学生、博士后和教授。数学家肯·小野——他已离开学术界，加入了一家名为Axiom Math的AI初创公司——预定发表演讲。“你们可能正毕业进入一个或许根本不会存在的职业，或者一个与你们预期截然不同的职业，”小野对他们说。“你们需要做好准备。”
观众的反应是愤怒和沮丧。有人窃窃私语，有人交换眼神；小野没有一页幻灯片能顺利讲完，每一页都会引发新一轮提问。“我不太确定我们到底该从中得到什么，”一名学生说。另一名学生问小野和他的初创公司将如何为“AI公司对待数学的可耻方式”承担责任。
当小野说数学家们将尽“最大努力”避免学生们所设想的黯淡未来时，第三个人双手颤抖着反驳道：“你在做什么？你的‘最大努力’是什么？”这场演讲包括提问时间原本安排了50分钟；由于问答环节延长，最终持续了两个多小时。许多学生事后仍徘徊不去，互相倾诉和安慰。
对我来说，这些情绪反应的原因显而易见。年轻数学家们意识到，他们的领域要么改变，要么面临消亡。真正让我意外的是，当我回到纽约，在与朋友或家人的谈话中提起此事时，他们看不到问题所在。他们想象着各种惊人的发现即将到来。这不正是重点吗？
这些对话暴露了一个长期存在的问题：许多人不知道数学究竟是什么，也不知道数学家为什么要做数学。现在，数学家们需要为自己回答这个问题，并迅速向全世界解释。他们如何回答将决定接下来会发生什么。
本科时，我同时学习数学和文学。我一直觉得“纯数学”——为数学概念本身而研究它们，不在乎实际应用——存在于科学与艺术之间的某个地带。它崇尚逻辑和确定性，但其核心却蕴含着美、直觉和深度这些更模糊的概念。“数学要么是最具科学气质的人文学科，要么是最具人文气质的科学，取决于你问谁，”麦吉尔大学博士生马塞尔·高说。通常它完全无用，然而一次又一次，它的抽象概念在物理学及更广泛领域的应用中展现出“不合理的有效性”。
在数学中，“过程比结果更重要”并非陈词滥调。提出问题，与其说是因为答案会实用和重要，不如说是因为它们代表着有趣的旅程。希望在于，当数学家们努力解决一个问题时，他们会想出引人入胜的工具和联系，偶然发现新颖的想法和方向，走上富有成果的弯路，并回答他们从未想过要提出的新问题。
“从来都不是关于定理本身，”高说。“而是为了传承一种尽管没有市场价值却造福了社会的传统。去深入推理，去理解世界……并传播那种知识。”
AI模型直接跳到终点。目前，它们的证明几乎无法阅读。它们省略关键细节，却在无关概念上浪费篇幅。它们无法展示新工作如何建立在数学文献中其他成果之上，或如何与之关联。数学家们知道这些证明是正确的——它们由检查逻辑的系统验证过——但完全不知道为什么正确。缺失的是理解，而理解正是数学家们所交换的货币。如果说有一段旅程，人类并未被邀请同行。
这就好比你被瞬移到了一座高山的顶峰。四周雾茫茫，你不知道自己在哪里，也不知道周围有什么。你不知道你的山如何与其他山相连，你没有任何设备帮助你探索，也没有办法让别人加入你。如果你是自己爬上这座山的，你会体验到人体如何适应海拔和氧气水平的变化。你可能不得不发明工具来导航、攀爬陡峭的悬崖，或者搭建庇护所。你可能遇到了一位同行探险者，一起在隐蔽的山谷中迷路，然后发现了一种可以制成救命药物的植物。
而你却栖息在山巅，身处黑暗之中，而瞬移机器的制造者告诉你，它比任何人类都更擅长探索荒野。
数学家们一直知道，理解比答案更有价值。那么，为什么一台AI答题机应该让人感到如此大的威胁？
部分原因在于数学发展的方式。几个世纪以来，证明定理和理解证明一直相辅相成。如果有人解决了一个数学界认定为核心、重要且困难的问题，那个解答就被视为深刻洞察力和创造力的体现。
因此，数学文化几乎完全围绕解决问题而发展。研究生们从大型复杂问题的简化版本入手磨练自己，然后寻求发表作品、找到好工作、赢得认可和声誉——所有这些都以他们证明的定理来衡量。驱动数学界的激励机制，并非为一个解决问题容易但理解答案仍然困难的世界而设计。“这打破了我们这个系统，”加州理工学院博士生塔斯敏·朱说。“它把系统推到了极限，然后摧毁了它。”
过去几个月里，我听到了许多数学家的声音，既有学生也有资深研究者，谈论这种摧毁的形态。
OpenAI和Anthropic等公司正在与数学家直接竞争（并从他们中挖走许多人）来快速证明定理，却几乎不花力气撰写清晰的论文来解释这些结果或将其置于背景中。大多数数学家目前根本不知道这些公司到底证明了什么；OpenAI已宣布将100多项重要结果保密。（这还产生了进一步的效果：让数学家们不愿研究可能已经失去意义的问题。）
“正在发生的是对开放科学的巨大伤害，”朱说。这件事唯一可能的价值就是股东价值。它完全忽视了数学的核心事业——更糟糕的是，它试图覆盖它。
许多数学家已停止在论文末尾发布公开猜想和潜在想法，因为担心它们会被机器人抓取并喂入AI模型。其他人则在论文尚未成熟时就发布，以避免被人抢先。期刊和在线预印本服务器arxiv.org已被AI辅助或AI生成的证明淹没，没有人能妥善消化或核查这些证明，这迫使研究者去做艰难且目前无人感激的工作——重写这些证明，使它们真正能惠及数学界。（即使模型不断改进，那些论文变得更易阅读，其 sheer volume 也将压垮现有系统——这些系统负责筛选新工作并判断什么有趣、什么重要。与此同时，arxiv.org已开始限制作者每月最多提交两篇。）当《机器学习研究汇刊》的一位编辑联系10篇拟被拒稿论文的作者时，大多数人要么没有回复，要么无法回答关于他们声称属于自己的工作的基本问题。
与此同时，MathOverflow——一个数学家互相回答问题的在线论坛，将著名研究者与年轻学生连接起来，留下多年交流供后人阅读和学习——活动量正大幅下降，因为学生们私下向AI模型提问。其他人则不愿在一个暴露于机器人的空间里分享想法。
这种情况令人心碎。数学之所以如此美妙，部分原因在于它开放而诚实的合作，以及它独立于政治或企业利益。这并不是说数学文化中没有其他问题——不平等和机会缺失等等——但如果不从根本上改变这个领域的激励机制，这种文化的独特之处将面临巨大风险。
“现有的平衡已经打破，”多伦多大学数学家丹尼尔·利特说。“我们必须找到新的平衡。”
根据数学家们集体如何回应——或不回应——这个时刻，存在一系列可能的未来。
在一种未来中，“一旦这个职业完成代际更替，你得到的将是一群被训练成按下按钮却不阅读输出结果的数学家，”利特说，而不是被训练去提出有趣的问题并与结果互动。“有一个糟糕的未来：如果我们不adapt，50年后就没有数学了。没有人在做，连机器也不做。
“我不是说这很可能，”他继续说。“我们不会梦游般走进那个未来。但我认为，如果我们什么都不改变，世界大概就是那样。”
正如加州理工学院的玛蒂尔德·马尔科利在为《伦敦数学学会通讯》撰写的文章中所写：“如果我们坚持把整个职业的重心仅仅放在攻克猜想上，将其作为唯一的目标和回报，那么我们可能很快就会消亡——不是因为数学的终结，而是因为我们想象力的终结。”
还有一个更乐观的替代方案——假设有一种新的激励机制，将解决问题和证明定理与工作、晋升和认可脱钩。“数学家们将花更少的时间试图在永久冻土上啄食，费尽全力挖出数学宝石，”麻省理工学院的帕维尔·埃廷戈夫说。“他们会把这种啄食更多地交给AI，并试图解释、理解和学习由此产生的结果。将有更多的数学需要理解。数学家将有大量工作——也许与以前不同，但绝对是有趣的工作。”
这种工作在一定程度上将涉及研究AI撰写的证明——就像每个本科生学习教科书中的已知证明一样。许多数学家预计，AI生成的论证很快就会从粗制滥造毕业到更优雅的写作；也许在几年内，利特说，“我们读到的是极其有趣结果的美妙阐述。对我来说，那就是梦想。那就是我进入这一行的原因。”
这些未来的数学家将有很多事要做。毕竟，利特补充说，“再好的文字也无法让你理解数学。”他们将不得不重写AI证明，找到更优雅的论证，提出理论和框架及定义，提出问题，提出新猜想，培养对什么有趣、什么重要的判断力。他们将是构建研究项目、围绕某些想法创建社区、并将知识传给他人的人。（这让我想起文学理论家罗兰·巴特1967年的著名文章《作者之死》，他在文中主张，是读者而非作者，在积极创造作品意义方面拥有最终控制权和能动性。）
“如果AI证明了所有可能的定理，而没有数学家知道这些定理，它就不能成为文化的一部分，因为文化本质上是人类的，”埃廷戈夫说。“那些论文只有当某个人类阅读它们、理解它们并从中有所收获时，才会成为数学文化的一部分。”
问题在于，下一代数学家是否愿意。甚至是否能够。
数学家们已经在重新思考如何培养学生、如何接受论文发表（他们目前正在试验要求附带领读报告），以及如何做出招聘决定。对于理解、沟通和远见这类更模糊的技能，没有简单的答案。但利害关系足够大，我认为他们会成功。
我不太确定的是，新一代数学家是否会被这个被重塑的学科所吸引。
许多人被数学吸引，是因为他们想解决问题、探索前沿，并成为第一个发现某种新真理的人。他们是否愿意为“解释者”这份工作投入数十年的训练？他们仍然会阅读和翻译证明，并期望重写它们。但他们似乎不太可能频繁体验到那种豁然开朗的时刻或创造性所有权的感觉。
“许多人做纯数学的原因，尽管薪水比工业界低得多，是因为你可以创作自己的创造性贡献，然后把它们交给一个欣赏其智识之美的社区，”朱说。“这种数学话语以机器说话、人类倾听为中心的环境，我不认为它很有吸引力。”
而AI本身正在削弱那种角色所需的教育。这在伯克利的座谈会上也被提到了。“存在一个严重风险：20年、30年、40年后，周围将没有人接受过同样的经典数学训练，”一名学生说。“我担心一个完整的数学知识体系变得无法触及的世界。”
结果可能是一代人的迷失。高是许多年轻数学家之一，他们正与这种未来产生的焦虑作斗争，也与他所看到的在职数学家（至少直到最近）缺乏努力去重塑激励机制以避免这种未来而作斗争。
“这种文化有些病态，”他告诉我。“我以前不这么认为，但现在我这么认为了。”
高对一些人未经充分批判性思考就采纳AI感到警觉，他也感到压力，不得不用它，以免被落下。“我对此非常沮丧，”他说。“那对我来说并不鼓舞人心……本来不必如此。”
他把这比作《指环王》中的萨鲁曼，被无限知识和力量的承诺所腐蚀。高和越来越多的数学家开始将自己视为AI“素食者”，有意识地节制使用这项技术。他们认为，把自己的认知外包给机器，没有任何回报、趣味或乐趣可言。
高很坚定，宁愿离开这个领域，也不愿在创造性工作中使用AI。“我认为这艘船正在下沉，”他承认，“但我已经决定尽可能久地留在船上。”
在这一切之中，仍有理由怀抱希望。数学家们看到了这些问题，并感受到集体的担忧（如果不是恐慌），因此他们正在努力为本领域的人创造有吸引力的条件——既包括对使用AI感兴趣的人，也包括不想使用的人。例如，朱和其他人成立了人类数学协会，因为“我们现在真正需要的不是更多数学，而是政策建议和工具……来应对这场危机并改变我们的生态系统。”
这将很难。惯性是强大的。但数学可能会因此变得比以前更强大。被迫说出并优先考虑人们热爱和珍视这个领域的什么，现在和未来的数学家可以强调以前被降级对待的技能：沟通和分享知识的能力，发展广阔视野的能力，实验原创想法而不觉得需要一篇接一篇发表定理的能力。深入思考。
“我认为有一个好的未来，我们最终远远超越现在的位置，学到大量有趣的数学，”利特说。“我们有人在做他们做过的最酷的事情。我们有一个真正充满活力的社区，人们深刻理解事物。”
如果我们无法适应，他补充说，“那是谁的错？”
编者按：斯科特·阿伦森是《量子杂志》顾问委员会成员。

英文来源：

Is AI the End of Math As We Know It?
Introduction
Throughout the summer of 2026, there were plenty of signs of what was to come. Every week, it seemed, artificial intelligence models were offering proofs of decades-old mathematical conjectures. So what happened on September 8 shouldn’t have been a complete surprise. And yet to many it felt sudden, almost violent. OpenAI announced that its models had solved one of math’s most famous problems — and immediately sparked a controversy over authorship and standards. Mathematics would never be the same.
“In whatever years I have left, I don’t expect that I’ll ever again prove a theorem because I’m actually needed to prove it,” Scott Aaronson of the University of Texas, Austin wrote on his blog. “Human mathematicians are forevermore dethroned as the main theorem-proving entities on planet earth.” Other online missives expressed optimism, but many revealed some combination of grief, confusion, and fear.
Two days after the announcement, I found myself in a classroom at the University of California, Berkeley, surrounded by some 150 students, postdocs, and professors. The mathematician Ken Ono, who left academia for an AI start-up called Axiom Math, was scheduled to give a talk. “You might be graduating into a profession that might not even exist, or that will be very different than what you expected,” Ono told them. “You need to brace.”
The audience responded with anger and frustration. There were whispers and exchanged glances; Ono couldn’t make it through a single slide without a fresh wave of questions. “I’m not entirely sure what our takeaway is supposed to be,” one student said. Another asked how Ono and his start-up would take responsibility in light of “the shameful way that AI companies are treating mathematics.”
When Ono said that mathematicians would do their “very best” to avoid the bleak future the students were envisioning, a third retorted, hands trembling: “What are you doing? What is your ‘very best’?” The talk, including time for questions, had been allotted 50 minutes; with the extended Q&A, it went on for more than two hours. Many students lingered afterward, to vent and console one another.
To me, the reasons for these emotional reactions were obvious. The young mathematicians recognized that their field would have to change or risk extinction. What did surprise me was that when I returned to New York and brought it up in conversations with friends or family, they didn’t see what the problem was. All sorts of amazing discoveries are around the corner, they imagined. Wasn’t that the point?
These conversations exposed a long-standing problem: Many people don’t know what mathematics really is, or why mathematicians do it. Now mathematicians need to answer that question for themselves and explain it to the rest of the world — quickly. How they answer will determine what happens next.
As an undergraduate, I studied both mathematics and literature. I always found that “pure math” — the study of mathematical concepts for their own sake, without a care for real-world applications — existed somewhere between the sciences and the arts. It prizes logic and certainty, but at its core lie fuzzier notions of beauty, intuition, and depth. “Math is either the most science-y humanities or the most humanities-type science, depending who you ask,” said Marcel Goh, a doctoral student at McGill University. Usually it’s utterly useless, yet time and again its abstractions demonstrate “unreasonable effectiveness” in applications to physics and beyond.
In mathematics, it’s not a cliché that the journey matters more than the destination. Problems are posed not so much because their answers will be practical and important, but because they represent interesting journeys. The hope is that as mathematicians struggle to solve a problem, they’ll come up with intriguing tools and connections, stumble on novel ideas and directions, take fruitful detours, and answer new questions they never would have thought to ask.
“It was never about the theorems,” Goh said. “It’s to carry on a tradition that has benefited society despite not having any market value. To reason deeply, to understand the world … and to spread that knowledge.”
AI models skip to the end. At the moment, their proofs are nearly impossible to read. They elide salient details and waste pages on irrelevant concepts. They fail to demonstrate how the new work builds on or connects to other results in the mathematical literature. Mathematicians know that the proofs are true — they’re verified by a system that checks their logic — but have no idea why. What’s missing is understanding, the currency that mathematicians trade in. If there is a journey, humans are not invited along for the ride.
It’s as if you were teleported to the peak of a tall mountain. Surrounded by fog, you have no idea where you are, or what’s around you. You do not know how your mountain connects to others, and you have no equipment to help you explore, no way to help someone else join you. If you had climbed the mountain yourself, you would have experienced how the human body adapts to altitude and changes in oxygen levels. You might have had to invent tools to navigate, to climb steep cliffs, or to make a shelter. You might have encountered a fellow explorer, gotten lost together in a hidden valley, and found a plant that could be turned into a life-saving medicine.
Instead you’re perched on the peak but in the dark, while the maker of the teleportation machine tells you that it can explore the wilderness better than any human.
Mathematicians have always known that understanding is more valuable than an answer. So why should an AI answer machine feel like such a threat?
In part, it’s because of the way mathematics has evolved. For centuries, proving theorems and understanding those proofs have gone hand in hand. If someone solves a problem that the mathematical community has decided is central and important and hard, that solution is considered a reflection of deep insight and creativity.
So mathematical culture has developed almost entirely around problem-solving. Graduate students cut their teeth on simpler versions of big, complex problems, then seek to get their work published, find good jobs, and earn credit and recognition — all of which are assessed in terms of the theorems they prove. The incentive structures that power the mathematical community are not set up for a world where solving problems is easy and understanding their answers remains hard. “It breaks our system,” said Tasmin Chu, a doctoral student at the California Institute of Technology. “It just takes it to its absolute limit and destroys it.”
Over the past few months, I’ve heard from lots of mathematicians, students and senior researchers alike, about the shape of this destruction.
Companies such as OpenAI and Anthropic are competing directly against mathematicians (and poaching many of them) to quickly prove theorems, while putting little effort into writing clear papers to explain those results or put them in context. Most mathematicians have no idea what these companies have even proved at this point; OpenAI has announced that it’s keeping more than 100 important results secret. (This has the further effect of discouraging mathematicians from working on questions that might already be moot.)
“What is happening is a huge damage to open science,” Chu said. The only possible value of this is shareholder value. It completely overlooks the central mathematical enterprise — and, even worse, it seeks to overwrite it.
Many mathematicians have stopped posting open conjectures and potential ideas at the end of their papers, for fear that they’ll be scraped by bots and fed into AI models. Others are posting their papers before they’re ready in order to avoid getting scooped. Journals and the online preprint server arxiv.org have been overrun with AI-assisted or AI-generated proofs that no one can properly digest or check, which forces researchers to do the hard, currently thankless work of rewriting the proofs so they can actually benefit the mathematical community. (Even as models improve and those papers get easier to read, their sheer volume will overwhelm current systems for sorting through new work and deciding what’s interesting and important. In the meantime, arxiv.org has started limiting authors to two submissions per month.) When an editor of Transactions on Machine Learning Research reached out to the authors of 10 papers slated for rejection, most either did not respond or could not answer basic questions about work they’d claimed as their own.
At the same time, MathOverflow, an online forum where mathematicians answer each other’s questions — connecting famous researchers with young students and leaving years of exchanges for future generations to read and learn from — is seeing a massive decline in activity, as students privately ask AI models their questions. Others don’t want to share ideas in another space exposed to bots.
The situation is heartbreaking. Part of what is so wonderful about mathematics is its open and honest collaboration, and its independence from political or corporate concerns. That’s not to say that there haven’t been other problems with the culture of mathematics — inequity and lack of access, among other things — but what’s special about that culture is at great risk without a signal change in the field’s incentive structure.
“The existing equilibrium has broken,” said Daniel Litt, a mathematician at the University of Toronto. “We’ll have to find a new one.”
There’s a range of possible futures based on how mathematicians collectively respond — or don’t respond — to this moment.
In one, “once the profession turns over, you have a collection of mathematicians who are trained in pushing a button without reading the outputs,” Litt said, rather than being trained to ask interesting questions and engage with the results. “There’s a bad future where if we don’t adapt, there’s just no more math in 50 years. No one is doing it, not even the machines.
“I’m not saying it’s likely,” he continued. “We’re not going to sleepwalk into that. But I think the world where we change nothing probably looks like that.”
As Matilde Marcolli of Caltech wrote in an essay for the London Mathematical Society Newsletter, “If we insist on focusing our entire profession solely on the tackling of conjectures as the unique goal and reward, then we may be out of business quite fast, not because of the end of mathematics but because of the end of our imagination.”
There is a more optimistic alternative — assuming a new incentive structure that disengages problem-solving and theorem-proving from jobs, advancement, and recognition. “Mathematicians will be spending less time trying to peck on the permafrost, getting out mathematical gems with great effort,” said Pavel Etingof of the Massachusetts Institute of Technology. “They’ll be sourcing that kind of pecking more to AI and trying to interpret and understand and learn the results that will come from that. There will be a lot more mathematics to make sense of. And there will be a lot of work for mathematicians — maybe different work from before, but definitely interesting work.”
That work will involve, to some extent, studying proofs written by AI — the way every undergraduate learns the known proofs in their textbooks. Many mathematicians expect AI-generated arguments to graduate from slop to more elegant writing soon enough; perhaps within a few years, Litt said, “we’re reading beautifully written expositions of highly interesting results. To me, that’s the dream. That’s why I got into it.”
These future mathematicians will have much to do. After all, Litt added, “there’s no amount of well-writtenness that lets you understand math.” They’ll have to rewrite AI proofs, find more elegant arguments, come up with theories and frameworks and definitions, ask questions, formulate new conjectures, develop a sense of what’s interesting and important. They’ll be the ones building research programs, creating communities around certain ideas, and passing that knowledge on to others. (I am reminded of the literary theorist Roland Barthes’ famous 1967 essay “The Death of the Author,” in which he argues that it is the reader, and not the writer, who has ultimate control and agency in actively creating a work’s meaning.)
“If AI proves all possible theorems, and no mathematicians know about these theorems, it cannot be part of culture, because culture is inherently human,” Etingof said. “Those papers will only become a part of mathematical culture when some human reads them and understands them and gets something out of them.”
The question is whether the next generation of mathematicians will want to. Or even be able to.
Mathematicians are already rethinking how they’ll train their students, accept papers for publication (they’re currently experimenting with requiring accompanying talks), and make hiring decisions. There aren’t easy answers for more nebulous skills such as understanding, communication, and vision. But the stakes are high enough that I think they’ll succeed.
I’m less certain about whether new generations of mathematicians will be attracted to this remade discipline.
Many people are drawn to math because they want to solve problems, explore frontiers, and be the first to discover some new truth. Will they be willing to put in decades of training for the job of interpreter? They’ll still read and translate proofs and expect to rewrite them. But it seems less likely that they will frequently experience the same moments of clarity or sense of creative ownership.
“A lot of the reason why people do pure math, even though it pays so much less than industry, is because you get to author your own creative contributions and then give them to a community that appreciates them for their intellectual beauty,” Chu said. “This environment where mathematical discourse is centered around machines talking and humans listening, I don’t think it’s a very attractive one.”
And AI is itself undermining the kind of education that would be necessary for that role. This came up at the Berkeley colloquium, too. “There’s a serious risk that 20, 30, 40 years from now, there will be no people around who have the same classical mathematics training,” one student said. “I’m worried about a world where the full body of mathematical knowledge is inaccessible.”
The result could be a lost generation. Goh is one of many young mathematicians struggling with the angst such a future is producing, and with what he sees as a lack of effort on the part of working mathematicians (at least until very recently) to remake the incentives to avoid it.
“There’s something sick about the culture,” he told me. “I didn’t think so, but now I do.”
Goh is alarmed by how some have taken up AI without enough critical thought, and he feels pressured to use it so that he doesn’t get left behind. “I was just very depressed about that,” he said. “That doesn’t feel inspiring to me. … It didn’t have to be this way.”
He likens it to Saruman from The Lord of the Rings, corrupted by the promise of unlimited knowledge and power. Goh and a growing number of mathematicians are starting to consider themselves AI “vegetarians,” consciously measured in their use of the technology. There’s nothing rewarding or interesting or fun about offloading their cognition to a machine, they argue.
Goh is determined and would rather leave the field than use AI in his creative work. “I think the ship is sinking,” he admitted, “but I’ve already made my decision to stay on board as long as I can.”
There is, through all of this, reason for hope. Mathematicians see these problems and feel a collective sense of concern (if not panic), so they are working now to create attractive conditions for people in their field — both those interested in using AI and those who don’t want to. Chu and others have formed the Association for Human Mathematics, for example, because “what we need right now actually is not more mathematics but policy proposals and tools … to deal with this crisis and change our ecosystem.”
It will be hard. Inertia is powerful. But mathematics could come out of this stronger than before. Forced to name and prioritize what people love and value about the field, current and future mathematicians can emphasize skills that have previously been deprioritized: the ability to communicate and share knowledge, to develop a broad vision, to experiment with original ideas without feeling the need to publish theorem after theorem. To think deeply.
“I think there is a good future where we come out way ahead of where we are now, where we learn a huge amount of interesting math,” Litt said. “We have people doing the coolest stuff they’ve ever done. We have a really vibrant community of people who deeply understand stuff.”
If we can’t adapt, he added, “whose fault is that?”
Editor’s note: Scott Aaronson is a member of Quanta Magazine’s advisory board.