OpenAI要求外部专家，包括诺贝尔奖获得者，检查其在数学，计算机科学和物理领域生成的AI的证明。
OpenAI 称其内部模型反驳了计算机科学中的一个中心假设，并证明是千年奖问题之一的一部分，以及其他结果。 现在，外部专家将决定证据是否成立。
OpenAI在一篇博客文章中，称公司内部AI型号生产出证明。 OpenAI称手稿是一类需要了解的原始研究数据。
因此OpenAI要求外出专家作为"shepherds"作为结果。 根据他们的建议，公司对每个领域处理方式不同。 OpenAI 称还把数学和计算机科学证明翻译成了Lean.
精益是一种编程语言，让计算机检查证据的每一步。 这并不能保证结果没有出错利恩只检查证据是否按照利恩书写的方式建立了声明。 专家仍然必须决定这一声明是否真正反映了预期的问题。
如果 OpenAI 是正确的，计算机科学中的核心假设是错误的
计算机科学成果以 " 时间假设 " (ETH)为中心。 它涉及布尔相位性问题，或SAT. SAT处理的是逻辑公式，其变量只能是真或假。 问题是，你是否能够设置变量，这样整个公式就成真了。
只要几个变量，你就可以尝试每一个组合。 但每个新变量翻倍的可能性数。 有了100个变量，你已经看到一个31位数字。
简而言之 ETH 称没有真正的捷径你可以加快试验和出错，但在最坏的情况下，计算时间仍然呈指数增长，增加一个固定因子，每个新增变量。
OpenAI 称相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相相这是一个著名的公开问题，即一个能够被快速检查解决的问题能否被快速解决。 在SAT中，检查是很容易的，因为你只是插入一个拟议答案并做数学。 最难的就是找到一个有效的
SAT被认为是这类难题的教科书例子。 一个快速的解决方法会立刻使上千个其他问题迅速得到解决。 大多数专家认为不存在这种方法。 这种信念通过"P不等于NP"的简称来表达。
ETH比这种猜想更进一步。 称不仅SAT很难，而且有多难。 如果ETH下降，P仍然可能与NP不同，因此困难的问题不会自动变得容易。
ETH被广泛接受为真实。 在图表理论，计算生物学，数据库，和计算几何学的上百篇论文都以此为基础。 例如，它们表明，如果ETH持有，一个问题不可能比某个时间更快解决。
现在OpenAI 称它的系统已经证明ETH是虚假的。 如果证据成立这些文件就会失去基础他们的结果不会自动出错，但是他们不再被证明。
OpenAI 称的结果可以帮助研究人员找到更好的算法。 将它变成实际成果仍然需要大量的研究。
实际的回报还不清楚，但理论后果会很大
SAT在实践中很重要。 例如，称为SAT解析器的专门程序检查芯片设计是否出错并测试软件。
他们经常用数百万个变量来处理公式。 这是因为现实世界应用中的公式通常比ETH所处理的最坏情况容易得多。 加快只有最坏的情况无法自动帮助这些计划。
麻省理工学院教授瑞安·威廉姆斯(Ryan Williams)在"X"上打出类似谨慎的基调。 当一个用户问日常开发者会首先注意到什么时，还没有人知道威廉斯·称。 以目前的速度，他称，可以认为实际的SAT解答可以在12个月内看到重大的进展。 "或者，我们可能没有看到什么这样的。 我真的不知道，"他承认。
这个结果也会通过复杂性理论本身，特别是电路的研究来拉动，电路是诸如AND,OR,NOT等简单逻辑门的网络。 如果OpenAI的结果维持住，威廉斯·称就会随之而来的是，某类非常苛刻的问题无法用小回路解决。 这里"Small"的意思是，当输入翻倍的长度时，电路最多需要大约两倍的门。
那些想出ETH的人正在查是不是错了
威廉姆斯将与圣迭戈UC的罗素·英帕格利亚佐和拉马莫汉·帕图里一起独立检查和解释结果。 伊帕格利亚佐和帕图里最初与弗朗西斯·赞恩一起提出了ETH. 威廉姆斯写道，该团体没有签署任何不披露协议，正在工作无报酬，计划随即分享临时调查结果。
在一封公开信中，三人也明确表示，他们的参与并不是对索赔的认可。 这样的结果，他们需要仔细，独立的审查，写。
应集团要求，OpenAI正在发布所有原始数据，包括书面证明和取向证明。 该公司还承诺资助一次关于结果对外地意味着什么的会议。
几十年的波浪猜想现在可能存在于每一个层面
数学的结果涉及对波浪的猜想，比如在声音，光线，或地震中的波浪。 1991年数学家克里斯托弗·索格提出。
波能集中在一个单一的点上，多像放大玻璃的焦点的光。 猜想称这种极端集中只会短暂地持续。 随着时间的推移，波浪的表现比极端情况所显示的更平稳或均匀。 故取"地平分想"之名。
直到现在，它只在两个维度上被证明，因为波浪像水面。 古斯，王克同，张克同于2019年完成。 OpenAI 称它的模型现在已经为每个维度，包括空间和假设空间中甚至更维度的波浪，提供了证据。
OpenAI 称结果达到波外。 由于当地的平滑猜想对球场来说是如此地基本，因此另外两个著名的猜想也随之而来。 它们是从几何学得出的卡基亚猜想和从傅里叶分析得出的斯泰因限制猜想。 Fourier分析将声音等信号破解为单个振荡。 证明当地的平滑猜想也自动证明这两个。
卡凯亚猜想显示甚至这些后续结果都有多难。 Wang和Zahl在2025年只为三个维度证明了这一点。 OpenAI认为，这两种猜想现在都将在所有维度上被解决。
与另外两个结果不同，没有专门的团体在牧羊这个证据。 OpenAI 称确实联系了一位外聘专家来讨论这种合作。 不过，根据那个人的建议，公司直接公布了证明文本和"利恩证明". 这样，研究人员就可以自行决定如何检查结果。
OpenAI想把量子场理论放在坚实的数学地上
物理结果进入了粒子物理的基础。 物理学家用量子场理论来描述基本粒子及其之间的力量，OpenAI称之为现代理论物理中最重要的框架。 其预测极为准确，但理论缺乏精确的数学基础。
相反，物理学家们用近似方法工作，比如想象中的一连串点数，他们不断使点数变细。 这是否产生出一个独特而一致的理论，即一个理论在数学意义上是否"存在"，这仍然是一个尚未解决的问题。 它是否正确描述自然是一个单独的问题。
OpenAI 称它的AI证明了某些量子场理论在四个维度中存在，指空间加时间的三个维度。 到目前为止，没有人在粒子相互作用的理论的四个维度中拿出这样的证据。
强力坐其中心。 它将夸克结合为质子和中子，这反过来又把原子核拉在一起。 颗粒叫做克卢恩斯所证能相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相起相出相起相起相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相相出相出相出相出相出相出相出相出相出相出相出相出相出相出相出相相出相出相出相出相出相出相相出相相出相相出相出相出相出相出相出相出相出相出相出相相相相相出相出相相出相出相出相出相出相出相出相出相出相出相出相相出相出相相相相相相相相相
下步是杨米斯理论。 它只描述了葡萄干，没有夸克。 它与7个"千年奖"问题之一相挂钩，每个问题都带有克莱数学研究所100万美元的奖金。
问题有两个部分。 第一是证明杨-米尔斯理论在数学上存在。 二是显示它有所谓的"质量差距". OpenAI明确称它只解决了存在部分。 这意味着千年问题不会被完全解决。
质量差距指向了一个谜题。 在等式中，克luons没有质量，由无质量颗粒所携带的力通常会非常远。 无量光所携带的电磁力就是一例。 相形之下，强力只在微小的距离上作用，如原子核内部。 物理学家解释这一点时，说克卢恩斯会凝聚在有质量的结构中，即使是最轻的也不是无质量的。 零和最小的可能质量之间的差距称为质量差距。 计算机模拟支持它，但没有人在数学上证明它。
第二步是量子染色体动力学(QCD). 它的新增夸克并完整地描述了强大的力量。
OpenAI 称两种理论都可以在数学上存在，主要因为不对称自由。 这意味着强力随着粒子的接近而变弱。 这使得数学可以管理，即使花纹越来越细而细。
第三步通常是粒子物理学标准模型。 它描述了四种基本力量中的三种，除了重力之外的一切。 然而根据OpenAI的说法，它不能被任意地延伸至小距离上，因为它的一些力量在小距离上变得更强大而不是更弱。
因此，证据涵盖了最简单的大统一理论。 它将三力降低为一力并包括"标准模型"的力和物质粒子。 像强力一样，这种统一的力量在小距离上会变弱。 然而，没有任何实验证实这种理论。
如果证据成立，所有三个步骤都会有一个数学基础。 这不会改变任何物理的预测。 OpenAI希望它能将量子场理论变成数学上严格的学科。
一个由大卫·格罗斯领导的团体将主持这项工作。 Gross分享了2004年诺贝尔物理学奖，因为他在不对称自由方面的工作。 该团体还包括迈克尔·道格拉斯，亚瑟·贾夫，伊戈尔·克勒巴诺夫和尼基塔·涅克拉索夫。 Jaffe帮助撰写了"千年奖问题""杨-米尔斯理论".
OpenAI 称已经将"杨-米尔斯"的证明翻译为"李恩". 与计算机科学组不同的是，这个组目前一直搁置AI的材料，并计划自己编写结果。
OpenAI的审查过程融资问题本身
OpenAI承认这一过程伴随着取舍。 不管谁选了第一位牧羊人，都帮助决定谁先参与，公司写作，有些人最终比其他人更早知道。 OpenAI也叫称，尚不清楚这三种方法中哪一种效果最好。
OpenAI 称它不声称科学功劳的发现。 应该由各团体来解释结果。 公司似乎在回应Navier-Stokes公关灾难后的批评。
OpenAI还向西蒙斯基金会认捐了500万美元，以资助关于AI成果的讲习班和会议。
威廉姆斯的团体还用公开信呼吁进行超越审查的更宽泛的辩论。 问题在于如何核实AI的突破，谁能获得这些突破，谁应该得到这些突破。
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OpenAI asks outside experts, including a Nobel laureate, to check proofs its AI produced in math, computer science, and physics
OpenAI says its internal models have disproved a central assumption in computer science and proved part of one of the Millennium Prize Problems, among other results. Outside experts will now decide whether the proofs hold up.
OpenAI laid out three results from math, computer science, and physics in a blog post. The company says its internal AI models produced the proofs. OpenAI calls the manuscripts a kind of raw research data that still needs to be understood.
So OpenAI asked outside experts to act as "shepherds" for the results. Based on their advice, the company is handling each field differently. OpenAI says it also translated the math and computer science proofs into Lean.
Lean is a programming language that lets a computer check every step of a proof. That doesn't guarantee the result is error-free, though. Lean only checks whether the proof establishes the statement as it was written in Lean. Experts still have to decide whether that statement actually captures the intended problem.
If OpenAI is right, a core assumption in computer science is wrong
The computer science result centers on the Exponential Time Hypothesis (ETH). It concerns the Boolean satisfiability problem, or SAT. SAT deals with a logical formula whose variables can only be true or false. The question is whether you can set the variables so the whole formula comes out true.
With only a few variables, you can just try every combination. But each new variable doubles the number of possibilities. With 100 variables, you're already looking at a 31-digit number.
Put simply, the ETH says there's no real shortcut. You can speed up the trial and error, but in the worst case, computing time still grows exponentially, increasing by a fixed factor with every added variable.
OpenAI says the satisfiability problem is closely tied to the P versus NP problem. That's the famous open question of whether a problem whose solution can be checked quickly can also be solved quickly. With SAT, checking is easy because you just plug in a proposed answer and do the math. The hard part is finding one that works.
SAT is considered the textbook example of hard problems of this kind. A fast method for solving it would instantly make thousands of other problems fast to solve too. Most experts believe no such method exists. That belief goes by the shorthand "P does not equal NP."
The ETH goes further than that conjecture. It says not only that SAT is hard, but how hard. If the ETH falls, P could still differ from NP, so hard problems wouldn't automatically become easy.
The ETH was widely accepted as true. Hundreds of papers in graph theory, computational biology, databases, and computational geometry build on it. They show, for example, that a problem can't be solved faster than a certain time if the ETH holds.
Now OpenAI says its system has proved the ETH is false. If the proof holds, those papers lose their foundation. Their results wouldn't automatically be wrong, but they'd no longer be proven.
OpenAI says the result could help researchers find better algorithms. Turning it into practical gains would still take a lot of research, though.
The practical payoff is unclear, but the theoretical fallout would be big
SAT matters a lot in practice. Specialized programs called SAT solvers check chip designs for errors and test software, for example.
They often handle formulas with millions of variables already. That's because formulas from real-world applications are usually much easier than the worst case the ETH deals with. Speeding up only the worst case wouldn't automatically help these programs.
MIT professor Ryan Williams struck a similarly cautious tone on X. When a user asked what everyday developers would notice first, Williams said nobody knows yet. At the current pace, he said, it's plausible that practical SAT solving could see serious progress within 12 months. "Or we may see nothing of the sort. I really don't know," he admitted.
The result would also ripple through complexity theory itself, specifically the study of circuits, which are networks of simple logic gates like AND, OR, and NOT. If OpenAI's result holds, Williams says it would follow that a certain class of very demanding problems can't be solved with small circuits. "Small" here means that when the input doubles in length, the circuit needs at most about twice as many gates.
The people who came up with the ETH are checking whether it's wrong
Williams will independently check and explain the result together with Russell Impagliazzo and Ramamohan Paturi of UC San Diego. Impagliazzo and Paturi originally proposed the ETH along with Francis Zane. Williams writes that the group hasn't signed any nondisclosure agreements, is working unpaid, and plans to share interim findings as they go.
In an open letter, the three also make clear that their involvement isn't an endorsement of the claim. A result this big needs careful, independent review, they write.
At the group's request, OpenAI is publishing all the raw data, including the written proof and the Lean proof. The company has also committed to funding a conference on what the result means for the field.
A decades-old wave conjecture may now hold in every dimension
The math result concerns a conjecture about waves like those in sound, light, or earthquakes. Mathematician Christopher Sogge proposed it in 1991.
Waves can concentrate at a single spot, much like light at the focal point of a magnifying glass. The conjecture says this extreme concentration only lasts briefly. Averaged over time, waves behave more smoothly, or evenly, than the extreme case would suggest. That's why it's called the local smoothing conjecture.
Until now, it had only been proven in two dimensions, for waves on a surface like water. Guth, Wang, and Zhang did that in 2019. OpenAI says its models have now produced a proof for every dimension, including waves in space and in hypothetical spaces with even more dimensions.
OpenAI says the result reaches beyond waves. Because the local smoothing conjecture is so basic to the field, two other well-known conjectures follow from it. They are the Kakeya conjecture from geometry and Stein's restriction conjecture from Fourier analysis. Fourier analysis breaks signals like sounds into individual oscillations. Proving the local smoothing conjecture automatically proves both of these as well.
The Kakeya conjecture shows how hard even these follow-on results are. Wang and Zahl only proved it for three dimensions in 2025. According to OpenAI, both conjectures would now be solved in all dimensions.
Unlike the other two results, no dedicated group is shepherding this proof. OpenAI says it did reach out to an outside expert to discuss that kind of collaboration. On that person's advice, though, the company published the proof text and the Lean proof directly. That way, researchers can decide for themselves how to check the result.
OpenAI wants to put quantum field theory on solid mathematical ground
The physics result goes to the foundation of particle physics. Physicists describe elementary particles and the forces between them using quantum field theory, which OpenAI calls the most important framework in modern theoretical physics. Its predictions are extremely accurate, but the theories lack an exact mathematical basis.
Instead, physicists work with approximations, such as an imaginary lattice of points that they keep making finer. It's still an open question whether this produces a unique, consistent theory, meaning whether a theory "exists" in the mathematical sense. Whether it describes nature correctly is a separate question.
OpenAI says its AI has proved that certain quantum field theories exist in four dimensions, meaning three dimensions of space plus time. So far, nobody has pulled off such a proof in four dimensions for theories where particles interact with each other.
The strong force sits at the center of it. It binds quarks into protons and neutrons, which in turn holds atomic nuclei together. Particles called gluons carry it. The proof covers three theories that build on each other like steps.
The bottom step is Yang-Mills theory. It describes only gluons, without quarks. It's tied to one of the seven Millennium Prize Problems, each of which carries a $1 million prize from the Clay Mathematics Institute.
The problem has two parts. The first is proving that Yang-Mills theory exists mathematically. The second is showing that it has a so-called mass gap. OpenAI explicitly says it has solved only the existence part. That means the Millennium Problem wouldn't be fully solved.
The mass gap points to a puzzle. In the equations, gluons have no mass, and forces carried by massless particles normally reach very far. The electromagnetic force, which massless light carries, is one example. The strong force, by contrast, only acts over tiny distances, such as inside an atomic nucleus. Physicists explain this by saying gluons clump into structures that do have mass, and even the lightest of them isn't massless. The gap between zero and that smallest possible mass is called the mass gap. Computer simulations support it, but nobody has proven it mathematically.
The second step is quantum chromodynamics (QCD). It adds quarks and gives a complete description of the strong force.
OpenAI says both theories can exist mathematically mainly because of asymptotic freedom. This means the strong force gets weaker as particles get closer. That keeps the math manageable even as the lattice gets finer and finer.
The third step would normally be the Standard Model of particle physics. It describes three of the four fundamental forces, everything except gravity. According to OpenAI, though, it can't be extended to arbitrarily small distances, because some of its forces get stronger at small distances instead of weaker.
That's why the proof covers the simplest grand unified theory. It reduces the three forces to a single one and includes the Standard Model's force and matter particles. Like the strong force, this unified force can get weaker at small distances. No experiment has confirmed such theories, though.
If the proof holds, all three steps would have a mathematical foundation. That wouldn't change any of physics' predictions. OpenAI hopes it will turn quantum field theory into a mathematically rigorous discipline.
A group led by David Gross will shepherd the work. Gross shared the 2004 Nobel Prize in Physics for his work on asymptotic freedom. The group also includes Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. Jaffe helped write the Millennium Prize Problem on Yang-Mills theory.
OpenAI says it has already translated the Yang-Mills proof into Lean. Unlike the computer science group, though, this group is holding back the AI's materials for now and plans to write up the result itself.
OpenAI's review process raises questions of its own
OpenAI admits the process comes with trade-offs. Whoever picks the first shepherds helps decide who gets involved first, the company writes, and some people end up knowing more sooner than others. OpenAI also says it's not yet clear which of the three approaches works best.
OpenAI says it isn't claiming scientific credit for the discoveries. Credit should go to the groups explaining the results instead. The company appears to be responding to criticism after the PR disaster over Navier-Stokes.
OpenAI has also pledged $5 million to the Simons Foundation to fund workshops and conferences on AI results.
Williams' group also uses its open letter to call for a broader debate that goes beyond the review. The questions are how to verify AI breakthroughs, who gets access to them, and who deserves the credit.
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