朋友们，今天的Cao，我需要先深呼吸一下。
OpenAI干了一件事：派出大约1万个AI智能体，花了88个小时，用Lean形式化验证语言，「解决」了纳维-斯托克斯方程的千禧年难题。官方博客的用词是"a solution"——注意，不是"a step toward"，不是"progress on"，是"a solution"。
千禧年难题是什么？Clay数学研究所悬赏的七大数学难题，每个悬赏100万美元。纳维-斯托克斯方程是其中之一——它描述流体运动的基本规律，但数学家们证明（或证伪）其解的存在性与光滑性已经努力了将近100年。全球能真正理解这个问题的数学家，可能不超过几百人。
然后OpenAI说：我用1万个AI搞定了。88小时。
数学界的心情：震惊、怀疑、还有点酸
消息一出，数学界的反应堪称一部大型连续剧。
第一阶段是震惊。千禧年难题啊！陶哲轩、佩雷尔曼级别的数学家奋斗多年都只推进了一小步，你一个AI公司88小时就搞定了？
第二阶段是怀疑。等一下，Lean的形式化验证虽然严格，但前提是你得把整个证明过程正确地翻译成Lean代码。1万个智能体协作写出的证明，其中任何一个智能体犯了错，整个证明就废了。验证通过只说明代码自洽，不说明数学证明本身正确。
第三阶段是酸。有数学家在社交媒体上说：「如果AI真的解决了千禧年难题，那我这辈子读的数学PhD算什么？」也有人说：「1万个智能体88小时，用掉的电费可能比100万奖金还多。」
陶哲轩本人倒是比较冷静，他在博客上说需要时间仔细审查这份证明，目前不做判断。
「不领奖金」是什么操作
OpenAI在公告中特别强调：不会申领千禧年难题的100万美元奖金。
这操作很OpenAI。一方面，100万美元对OpenAI来说是零钱中的零钱——它一轮融资就是几十亿美元。另一方面，不领奖金避免了一个尴尬的问题：AI解决了数学难题，奖金该给谁？给OpenAI公司？给写代码的工程师？给那1万个智能体？这个问题在法律和伦理上都没有先例。
但更深层的原因可能是优先权争议。千禧年难题的奖金规则是：解决方案必须在学术期刊上发表，并经过两年的学术审查期。如果OpenAI领了奖金，就意味着它要接受全世界最顶尖数学家为期两年的严格审查。任何一个逻辑漏洞都会被揪出来。以目前AI生成证明的可靠性水平来看，这个风险相当大。
不领奖金，OpenAI就立于不败之地：如果证明是对的，它是「AI攻克千禧年难题」的先驱；如果证明有错，它可以甩锅给「探索性研究」。
这件事真正的意义
抛开争议，这件事有一个不可忽视的信号：AI辅助数学研究的方式正在发生根本性变化。
以前AI在数学中的角色是「计算器」——帮你算、帮你验证。现在它变成了「研究员」——帮你探索证明路径、帮你组织逻辑链条、帮你把直觉变成严格的形式化证明。1万个智能体的协作模式，本质上是一种「暴力搜索」——在证明空间中同时探索大量可能的路径，直到找到一条可行的。这种方法对人类数学家来说是不可能的（你没法同时想1万条路），但对AI来说完全可行。
当然，「暴力搜索」找到的证明，人类能不能理解、有没有洞察力、能不能推广到其他问题，是另一回事。但至少它打开了一扇门：有些数学问题，AI可能比人类先找到答案。
至于纳维-斯托克斯的证明到底对不对——且听下回分解。
今天就Cao到这里，明天继续。
Folks, today's Cao — I need to take a deep breath first.
OpenAI did something: sent approximately 10,000 AI agents, spent 88 hours, used the Lean formal verification language, and "solved" the Navier-Stokes Millennium Prize problem. The official blog's wording is "a solution" — note, not "a step toward," not "progress on," but "a solution."
What's a Millennium Prize problem? Seven mathematical problems posed by the Clay Mathematics Institute, each with a $1 million bounty. Navier-Stokes is one of them — it describes the fundamental laws of fluid motion, but mathematicians have been trying to prove (or disprove) the existence and smoothness of its solutions for nearly 100 years. The number of mathematicians worldwide who truly understand this problem probably doesn't exceed a few hundred.
Then OpenAI says: I cracked it with 10,000 AIs. 88 hours.
The Math World's Mood: Shock, Skepticism, and a Little Salt
When the news broke, the math world's reaction was practically a serialized drama.
Stage one: shock. A Millennium Prize problem! Terence Tao, Perelman-level mathematicians working for years only moved the needle a tiny bit, and an AI company solved it in 88 hours?
Stage two: skepticism. Wait — Lean's formal verification is rigorous, but the premise is that the entire proof process must be correctly translated into Lean code. With 10,000 agents collaborating to write a proof, if any single agent makes an error, the entire proof is invalid. Passing verification only means the code is self-consistent, not that the mathematical proof itself is correct.
Stage three: salt. Mathematicians on social media said things like: "If AI really solved a Millennium Prize problem, what was my math PhD worth?" Others noted: "10,000 agents for 88 hours — the electricity bill might be more than the $1M prize."
Tao himself was relatively measured, saying on his blog that he needs time to carefully review the proof and won't make a judgment yet.
"Won't Claim the Prize" — What Kind of Move Is That?
OpenAI's announcement specifically emphasized: it will not claim the Millennium Prize's $1 million bounty.
This is such an OpenAI move. On one hand, $1 million is pocket change for OpenAI — a single funding round is billions. On the other hand, not claiming the prize sidesteps an awkward question: if AI solved a math problem, who gets the money? The OpenAI company? The engineers who wrote the code? The 10,000 agents? There's no legal or ethical precedent for this.
But the deeper reason might be priority disputes. The Millennium Prize rules state: the solution must be published in an academic journal and undergo a two-year academic review period. If OpenAI claimed the prize, it would mean accepting the world's top mathematicians' rigorous scrutiny for two years. Any logical flaw would be exposed. Given current AI-generated proof reliability levels, that risk is considerable.
By not claiming the prize, OpenAI stays invincible: if the proof is correct, it's the pioneer of "AI cracking a Millennium Prize problem"; if the proof has errors, it can deflect to "exploratory research."
The Real Significance of This
Setting aside the controversy, there's an undeniable signal: the way AI assists mathematical research is fundamentally changing.
Previously, AI's role in math was "calculator" — helping you compute and verify. Now it's becoming "researcher" — helping you explore proof paths, organize logical chains, and turn intuition into rigorous formal proofs. The 10,000-agent collaboration model is essentially "brute-force search" — simultaneously exploring a massive number of possible paths through proof space until a viable one is found. This approach is impossible for human mathematicians (you can't think 10,000 paths at once), but entirely feasible for AI.
Of course, whether humans can understand the proofs found by "brute-force search," whether they offer insight, whether they generalize to other problems — that's another matter. But at least it's opened a door: for some mathematical problems, AI might find the answer before humans do.
As for whether the Navier-Stokes proof is actually correct — stay tuned.
That's all for today's Cao — more tomorrow.
1万个智能体88小时搞定了数学家们努力了100年的问题——不管证明对不对，这件事本身就已经改变了游戏规则。
—— Dawn Vision编辑部
10,000 agents cracked in 88 hours what mathematicians have worked on for 100 years — regardless of whether the proof is correct, this alone has changed the game.
— The Dawn Vision Editorial Desk
实用提醒：第一，别急着转发「AI解了千禧年难题」的消息——先等数学界同行评审。第二，1万Agent协作的方式值得关注，但暴力搜索≠数学洞察。第三，如果你是做AI研究的，Lean形式化验证是未来趋势，值得现在就开始学。
Practical tips: First, don't rush to share "AI solved a Millennium Prize" — wait for peer review from mathematicians. Second, the 10K-agent collaboration model is worth watching, but brute-force search ≠ mathematical insight. Third, if you're in AI research, Lean formal verification is a future trend worth learning now.
OpenAI · Navier-Stokes · Millennium Prize · 10K agents · 88 hours · Lean · formal verification · Terence Tao · mathematics
