这可能是今年最炸裂的科技新闻，甚至没有之一。
Claude更是直言，如果这些结果成立，这将是数学和理论计算机领域历史上最重要的一天。
其中，数学突破与菲尔茨奖得主王虹此前在挂谷猜想上的工作高度相关，而物理突破可能是三者中最重要的，或解决了诺奖得主杨振宁遗留的难题。
而这次要说的是计算机领域的突破：指数时间假设不成立。
按照 Claude 的说法，这是一个图灵奖级别的颠覆性成果，“如果声明正确无误，这将改变计算机科学”。
现OpenAI研究员、原微软人工智能副总裁兼杰出科学家Sebastien Bubeck称赞这位“20 年来见过的最大惊喜”。
而且，是在同一天，是两个AI，几乎同时宣布取得这一突破！
OpenAI与Anthropic两大AI巨头，几乎在同一时间，宣布自家内部模型推翻了统治理论计算机科学长达27年的“指数时间假设”（ETH）！
更让人细思极恐的是：Anthropic甩出的论文里，明确标注核心算法由内部模型Claude在零人类干预的情况下独立推演发现。
这篇可能载入人类科学史册的论文，署名的唯一作者，只有Claude。
理论计算机界的“天”塌了，这到底意味着什么？
简单来说，1999年，指数时间假设（ETH）由加州大学圣地亚哥分校的Russell Impagliazzo和Ramamohan Paturi提出。
你可以把它想象成一把有n个开关的密码锁，也就是3SAT问题。
半个世纪以来，无数绝顶聪明的大脑想尽办法去开锁，但没人能打破一件事：破解这把锁的时间，永远随着开关数量的增加呈“指数级”暴涨。
举个例子，假设一把锁需要填入n个数字，每个数字都在1到9之间。每个位置都有9种选择，因此总共有9ⁿ种可能，也就是9连乘n次。
我们可以通过穷举所有9ⁿ种可能来解决这个谜题。但这种方法极其低效：对于一个需要填入n = 100个数字的数独谜题，即使用上世界上所有的计算机，也要等到太阳冷却之后才能完成。
长期以来，人们一直试图找到运行时间随 n 增长得比 9ⁿ 更慢的算法，却始终没有成功。
1999年，学者们把这种集体直觉写成了一个正式假设：3SAT不存在亚指数时间算法。
你可以改进一点点速度，但永远翻不过这堵“指数墙”。这就好比物理学里的“光速不可超越”一样。
这个猜想提出已经二十多年了，过去有数百篇论文以 ETH 成立为前提，去研究各种计算问题的复杂性下界。
从图论、组合优化，到数据库和计算生物学，很多研究都建立在这个假设之上。
黎曼猜想如果被推翻，倒的是数论；ETH 被推翻，倒的是复杂度和参数化算法。
ETH 的分量没到“P vs NP”或黎曼猜想这种千禧年级别。
但它比 P≠NP 更强、更具体：如果ETH成立，就能推出 P≠NP；但 ETH 被推翻，并不能推出 P=NP。
大量依赖ETH的条件性研究结论，都需要重新评估了。
AI 领域的新一批“受害者”已经出现了——
群里还有个哥们儿，他之前写的一篇论文就是以 ETH 成立为前提的。
现在这个前提可能直接没了，论文的结论要重新审视。
你想象一下，你花了几年时间研究一个问题，写论文、做证明，甚至一个领域的学者围绕这个假设研究了二十多年（比如图里这个教授）。
结果有一天，一个AI模型告诉你，大家一直以来相信的前提可能就是错的。
跨越科学研究的卢比孔河：唯一作者 Claude
戏剧性的一幕紧接着就出现了。
OpenAI总裁Greg Brockman前脚刚发帖官宣，老对手Anthropic后脚直接甩出了一篇同题论文，正面硬刚，当场撞车！
Anthropic表示：巧了这不是，我们的Claude内部模型在10月16日就已经独立推翻了ETH！
而且，Anthropic在论文页面上留下了一段“来源声明”：
核心算法由一个内部Claude研究模型于10月16日找到，消耗1400万输出Token，没有任何人类输入。
这意味着，AI彻底跨越了科学研究的卢比孔河——它不再是人类的工具，而是成为了真正的“第一作者”。
1400万Token是个什么概念？一本《三体》全集大约90万字。1400万Token，相当于Claude一口气疯狂推演了十几套《三体》厚度的草稿。
多位顶尖学者评估后表示：这相当于一个AI模型在几天之内，不吃不喝、不眠不休地完成了一个人类顶级博士后一到两年的科研量级！
在这几天里，Claude自己摸索路径，自己推演公式，自己验证逻辑，甚至跨界调用了八竿子打不着的冷门数学工具，最终把一份证明拍在了人类面前。
这一次，不是“AI帮数学家查文献”，更不是“AI做对了一道奥赛题”。
这是AI在人类最硬核、最纯粹的理论学科里，单枪匹马捅破了天。
祖师爷连夜被叫醒，数学家化身“审计员”极速瘦身
AI说推翻了就推翻了吗？会不会是AI在“一本正经地胡说八道（幻觉）”？
最魔幻的一幕发生了。两家公司为了自证清白，都没有仅仅扔出一篇PDF，而是同时公开了Lean形式化证明代码。
Lean是一位“铁面无私的电子审稿人”，哪怕有一步逻辑跳跃，它都会直接报错。既然代码能跑通，说明逻辑底层几乎封死了出错的可能。交出“机器可验”的卷子，这是AI无可辩驳的底气。
但这还不能完全确认证明的正确性。
当年提出ETH猜想的两位奠基人——Russell Impagliazzo与Ramamohan Paturi，据传已被紧急请出山。
27年前，两位学者写下一个猜想；27年后，他们被叫醒，去检查一个AI是怎么把它推翻的。
这大概是学术史上最复杂的一种心情。
目前，这两位泰斗正联合MIT等高校的顶级团队，对两家的代码展开逐行审验。
与此同时，另一条战线也在飞速推进。
面对AI产出的这份长达60多页的“外星”证明，人类大脑读起来极其吃力。
英伟达高级AI架构师Shiva Kintali连夜爆肝，将OpenAI原版60多页的ETH证伪证明，硬生生压缩成22页的精简版！
他砍掉了AI繁琐的步骤，不追求最优的对数因子，只求干净利落地证伪基本陈述，并补充了算例。
他的目标只有一个：“让人类同行能真正看懂。”
现在，一个前所未有的学术奇观出现了：
AI负责攻坚：在几天里撞开一道27年没人撞开的门；
人类负责消化：把AI冗长的推演，提炼成人类能理解、能继续往下推的知识。
现在，轮到人类给AI的作业打分、做精简了。
基础科研的“主客易位”
早在2023年3月，OpenAI曾发布过一份轰动一时的《AI对就业市场影响预测报告》。在这份榜单里，高居“被AI冲击最大职业”榜首的，赫然是数学家 。
当时，大多数人对此嗤之以鼻：数学需要人类最顶级的严密逻辑，满嘴跑火车的AI怎么可能做得了理论数学？
然而，整整三年后的今天，伴随着ETH被AI连夜证伪、Kakeya猜想接连被模型攻破……
这颗三年前射出的子弹，终于正中了人类理论科研的眉心。
这是否意味着科学家们要集体失业了？并不。
正如北大校友、学者Weijie Su在三年前所洞察的那样：AI不会简单粗暴地“取代”任何领域，而是会重塑它们。未来的科研，将极大奖励那些能与现实世界挑战、以及其他学科产生深度连接的人。
就像照相机发明后，画家不再需要比拼“谁画得更像”，于是诞生了印象派和现代艺术。
当AI接管了“算与证”的苦力活，人类终于可以把宝贵的精力花在更根本的问题上：寻找下一个值得探索的问题，建立跨越学科的现实连接。
27年前，当那两位学者写下ETH猜想时，绝对想不到，终结它的不是人类。
更想不到，会是两个AI在同一天交卷。
“世界不是正在被AI改变，而是已经被改变了。”
本文由 AI图鉴自动抓取并翻译，版权归原作者所有；如需查看原文请点下方链接。
It's probably one of the worst news stories of the year.
Claude is even more forthright, and if these results are established, it will be the most important day in the history of mathematics and theoretical computers.
Among them, mathematical breakthroughs are highly related to the previous work of the Fields Prize winner, Wang Rainbow, in the Hang Valley, and physical breakthroughs may be the most important of all three, or solve the difficult legacy of the Nobel laureate Yang Jinning.
And this is the breakthrough in the computer sector: the index time scenario is not valid.
According to Claude, this is a subversive outcome at the Turing Prize level, “if the statement is correct, it will change computer science”.
Now Open AI researcher, former Vice President of Microsoft Artificial Intelligence and distinguished scientist Sebastien Bubeck praises the “greatest surprise ever seen in 20 years”.
And, on the same day, two AIs, almost simultaneously, declared this breakthrough!
Open AI and Anthropic are two AI giants who, at almost the same time, declared their own internal models to overturn the 27-year-old "indexed time scenario" of dominant theory computer science!
Even more alarming is the fact that in the paper that Anthropic throws, it is clear that the core algorithm is being independently extrapolated by the internal model Claude, with zero human intervention.
This paper, which may be included in the history of human science, is signed by the only author, Claude.
Theoretic computer world has collapsed. What does that mean?
In short, in 1999, the index time scenario (ETH) was proposed by Russell Impagliazzo and Ramamohan Paturi of the University of California, Santiago.
You can imagine it as a code lock with an n switch, a 3SAT problem.
For half a century, countless brilliant brains have tried their best to unlock the lock, but no one can break one thing: the time to break the lock is always a “indexy” surge as the number of switches increases.
For example, it is assumed that a lock would need to be filled in a number of n, each between 1 and 9. There are nine options for each location, so there are a total of nine possibilities, i.e. nine millimeters.
We can solve this puzzle by overusing all the 9n possibilities. However, this method is extremely inefficient: it will not be complete until the sun cools for a unique puzzle that needs to be filled in n = 100 numbers, that is, using all the computers in the world.
For a long time, people have tried to find algorithms that run faster than 9n over time, but never succeeded.
In 1999, scholars made this collective intuition a formal assumption: 3SATs do not have sub-index time algorithms.
You can improve a little speed, but you'll never be able to get through this “index wall”. It's like "the speed of light cannot be exceeded" in physics.
It's been more than 20 years since the idea was put forward, and hundreds of papers in the past, premised on the establishment of ETH, have been studying the complexity of the various computational issues.
Many studies are based on this assumption, from graphics, portfolio optimization, to databases and computational biology.
Lehman assumed that, if overturned, it would be the theory of numbers; ETH would be overturned, and complexity and parameterization.
ETH does not have the weight of “P vs NP” or Lehman imagines this millennium level.
But it's stronger and more specific than P≠NP: if ETH is set up, it's possible to launch P≠NP; but ETH is overturned and not P=NP.
The findings of the extensive reliance on ETH conditional studies need to be reassessed.
A new group of "victims" in the AI field has emerged:
There's a guy in the group who wrote a paper that was based on ETH.
Now that this premise may be gone, the conclusions of the paper need to be revisited.
Imagine you spent a few years working on a problem, writing papers, proving it, and even a field of scholars studying that hypothesis for over 20 years.
And then one day, an AI model tells you that the premise you've always believed is probably wrong.
Crossing the Rupicon River: the only author, Claude
A dramatic scene followed.
Open AI president Greg Brockman's ex-legging secretary declared that the old opponent, Anthropic, had thrown a cosmological paper straight out of the back of his foot.
Anthropic says it's not by chance that our Claude internal model has independently overturned ETH on October 16th!
Moreover, Anthropic left a “source statement” on the paper page:
The core algorithm was found on 16 October by an in-house Claude study model, which consumed $14 million to export Token without any human input.
This means that AI has completely crossed the Rupicon River for scientific research — it is no longer a tool of humanity but a true “first author”.
What's 14 million Token? It's about 900,000 words. 14 million Tokens, equivalent to Claude's one-square draft of a dozen sets of Three Bodies.
Many leading scholars have assessed that this is equivalent to an AI model that, in a few days, has completed a scientific scale of one to two years after a top human doctorate without eating or drinking or sleeping.
In those days, Claude himself groped the path, pushed the formula himself, validated the logic himself, even crossed the border using cold-door mathematical tools that could not be hit by eight poles, and finally filmed a certificate in front of humanity.
This time, it's not "AI to help mathematicians look at the literature," it's not "AI to do an Osei question right."
It's the first time that AI's in the most hard-core, purest theoretical discipline of mankind has broken it alone.
Grand Master was awakened all night, and the mathematician turned into an "Adviser" with extremely thinness.
Did AI turn it down? Could it be that AI is saying "a serious nonsense"?
The most magical scene happened. In order to prove themselves innocent, neither company simply threw out a PDF but at the same time disclosed Lean's formalized certificate code.
Lean is an “iron-faced electronic reader” who, even if he makes a logical leap, will report a direct error. Now that the code runs, it means that the bottom of the logic is almost blocking the possibility of error. This is the irrefutable background of AI.
However, this does not fully confirm the validity of the certificate.
The two founders, Russell Impagliazzo and Ramamohan Paturi, who had raised their suspicions in the same year, were reportedly called out of the mountain on an urgent basis.
Twenty-seven years ago, two scholars wrote their next guess; 27 years later, they were woken up to see how an AI had overturned it.
This is probably the most complex mood in academic history.
At present, the two Thai schools, together with the top teams of higher education institutions such as MIT, are conducting a line-by-line review of their codes.
At the same time, another front is advancing at a fast pace.
This 60-page “extraterrestrial” in the face of AI output proves that the human brain is extremely hard to read.
Shiva Kintali, Senior AI Architect, Yin Weida, blew up over 60 pages of ETH perjury in the original Open AI, compressing the hard-body into a 22-page streamlined version!
He cut down the cumbersome steps of AI, not pursuing the best logarithmic factor, but simply seeking cleanness to testify against the basic statement and adding the calculation.
His goal is only one: "Let our fellow human beings truly understand."
Now, an unprecedented academic wonder has emerged:
AI is responsible for the attack: in a few days, a 27-year-old door was broken.
Humans are responsible for indigestion: the lengthy evolution of AI is based on knowledge that humans understand and can continue to push down.
Now, it's humans' turn to score and streamline AI.
"Major Diversion" for Basic Science
As early as March 2023, Open AI had a sensational report entitled " AI Impact Forecast on the Employment Market ". In this list, mathematicians are most likely to be at the top of the list of "the occupation hit most by AI".
At that time, most people snout at it: math required the highest human logic, and how could AI, with its mouth full of trains, do theoretical mathematics?
However, today, three years later, along with ETH's false testimony by AI, and Kakeya's assumption that it's being broken by the model...
This bullet, which was fired three years ago, finally caught the eye of human theoretical research.
Does this mean that scientists are collectively unemployed? No.
As Weijie Su, a North University alumni and scholar, saw three years ago: AI will not simply “replace” any field, but will reshape it. Future research will greatly reward those who can be connected to real world challenges and to other disciplines.
Like when the camera was invented, painters no longer needed to spell “who painted more like”, so Impressors and modern art were born.
When AI took over the hard work of “calculating and proving”, human beings could finally devote valuable energy to a more fundamental issue: finding the next issue worth exploring and building a reality that transcends disciplines.
Twenty-seven years ago, when those two scholars wrote their ETH guess, it was never humans who ended it.
Not to mention, it's gonna be two AIs on the same day.
“The world is not being changed by AI, but has been changed.”
Auto-fetched and translated by AI Atlas. All rights belong to the original author.