{"@context":"https://schema.org","@type":"NewsArticle","generatedAt":"2026-09-28T06:03:00.468Z","headline":"OpenAI 宣布以内部 AI 系统给出 Navier-Stokes 千禧年问题解答","description":"OpenAI 宣布其内部 AI 系统给出 Navier-Stokes 存在与光滑性问题的解答，证明初始光滑的流体可在有限时间内形成奇点，并附证明文稿与 Lean 形式化验证。","url":"https://www.aioga.com/news/cmtszna9e04isro5woti0ixg6/","mainEntityOfPage":"https://www.aioga.com/news/cmtszna9e04isro5woti0ixg6/","datePublished":"2026-09-08T10:00:00.000Z","dateModified":"2026-09-08T10:00:00.000Z","inLanguage":"zh-CN","publisher":{"@type":"NewsMediaOrganization","name":"Aioga","url":"https://www.aioga.com"},"citation":["https://openai.com/index/navier-stokes-solution","https://aihot.news/items/cmtszna9e04isro5woti0ixg6"],"canonicalUrl":"https://www.aioga.com/news/cmtszna9e04isro5woti0ixg6/","directAnswer":{"@type":"Answer","text":"OpenAI宣布，其内部AI系统给出了三维不可压缩、恒密度流体Navier–Stokes存在与光滑性问题的解答：初始光滑且静止的流体在有限时间内形成奇点，并同步发布证明文稿与Lean形式化验证。","url":"https://www.aioga.com/news/cmtszna9e04isro5woti0ixg6/","dateCreated":"2026-09-08T10:00:00.000Z","author":{"@type":"Organization","@id":"https://www.aioga.com/authors/aioga-editorial/#editorial-team","name":"Aioga Editorial Team","url":"https://www.aioga.com/authors/aioga-editorial/"}},"evidence":[{"@type":"CreativeWork","name":"OpenAI source article","url":"https://openai.com/index/navier-stokes-solution","datePublished":"2026-09-08T10:00:00.000Z","provider":{"@type":"Organization","name":"OpenAI","url":"https://openai.com/index/navier-stokes-solution"}},{"@type":"CreativeWork","name":"AIHot archive record","url":"https://aihot.news/items/cmtszna9e04isro5woti0ixg6","datePublished":"2026-09-08T10:00:00.000Z","provider":{"@type":"Organization","name":"AIHot","url":"https://aihot.news/items/cmtszna9e04isro5woti0ixg6"}}],"aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","originalPublisher":{"name":"OpenAI","url":"https://openai.com/index/navier-stokes-solution"},"geoDeepAnswer":null,"article":{"id":"cmtszna9e04isro5woti0ixg6","slug":"cmtszna9e04isro5woti0ixg6","url":"https://www.aioga.com/news/cmtszna9e04isro5woti0ixg6/","title":"OpenAI 宣布以内部 AI 系统给出 Navier-Stokes 千禧年问题解答","title_en":"","summary":"OpenAI 宣布其内部 AI 系统给出 Navier-Stokes 存在与光滑性问题的解答，证明初始光滑的流体可在有限时间内形成奇点，并附证明文稿与 Lean 形式化验证。","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","sourceUrl":"https://openai.com/index/navier-stokes-solution","aiHotUrl":"https://aihot.news/items/cmtszna9e04isro5woti0ixg6","publishedAt":"2026-09-08T10:00:00.000Z","category":"行业动态","score":72,"selected":true,"articleBody":["We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean.","The Millennium Prize Problems ⁠ (opens in a new window) ：https://www.claymath.org/millennium-problems/ represent some of the deepest questions at the frontier of mathematics. The question of whether smooth three-dimensional fluid motion can break down has remained unresolved for roughly 90 years.","A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity. To solve the Navier–Stokes problem, we used an internal model that is significantly more capable than GPT‑6 Astra. We believe it is important to inform the world about the pace of AI progress and what to expect from upcoming models.","The Navier–Stokes equations use Newton’s second law of motion (“F=ma”) to describe how fluids move. Importantly, they treat a fluid as a continuous medium rather than tracking individual molecules. These equations are used for aircraft design, weather forecasting, and the study of blood flow.","A fundamental open question for these dynamical equations has been whether the continuum approximation of the fluid can break down. Specifically, can the Navier–Stokes equations for a three-dimensional incompressible fluid with constant density develop a “singularity,” even when the motion starts smoothly? Here, a singularity means the dynamics lead to speeds in the fluid growing without bound within a finite amount of time. The development of a singularity would have to happen despite the presence of viscosity, which tends to smooth out motion. Because a real fluid cannot move infinitely fast, this would mark a breakdown in how the equations model the fluid. To continue modeling the system, one would then need to track the behaviour of each particle individually.","The equations date to the nineteenth-century work of Claude-Louis Navier and George Gabriel Stokes. In 1934, Jean Leray proved that solutions exist in a generalized sense, but whether they always remain smooth became a central unanswered question. In 2000, the Clay Mathematics Institute named the Navier–Stokes existence and smoothness problem one of seven Millennium Prize Problems.","Our system produced an analytical proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity in a finite time. The fluid has a smooth force applied to it, and its energy remains finite through the entire dynamics, from rest to the formation of the singularity. This resolves the Navier–Stokes Millennium Prize problem by establishing statement “C” (and also “D”) in the official Millennium Prize formulation ⁠ (opens in a new window) ：https://www.claymath.org/wp-content/uploads/2022/06/navierstokes.pdf .","The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. This central region shrinks while it speeds up in such a way that its energy still stays finite, as required by the laws of physics. The technical challenge is for the equations to develop the breakdown through the motion of the fluid itself, rather than, for example, us putting in an infinite force by hand. More mathematically, the terms in the Navier–Stokes equations that describe the motion—acceleration, pressure gradients, momentum transfer, viscosity—must both become big yet cancel in a precise way. This detailed balance leaves a smooth external force even as the velocity of the fluid grows without bound.","A snapshot of local incompressible motion. Orange marks faster angular rotation; teal marks slower rotation. Circulating speed also depends on radius. The trajectories show inward spiraling and axial stretching.","Since August 28 we have been training a new internal model that has exhibited unprecedented performance in our benchmarks, including mathematics. This model’s training is ongoing and its performance continues to improve.","On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems.","We used a system of coordinating agents powered by our internal model. The agents had access to tools such as the ability to read from a cached version of the internet and the ability to run code. Agents were subdivided into groups with the ability to communicate within the group. The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents. At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation.","For each problem, we prompted different groups of agents with different variants of the problem statement, covering all variants of the problem. For the Navier–Stokes problem, we suggested versions “A” and “B” (particular forms of the Navier–Stokes problem which would result in a proof) and versions “C” and “D” (which would result in a disproof) to separate groups of agents.","In addition to the full Millennium Prize problems, we asked our multiagent system to try a set of “easier” problems. One of these problems was a similar blowup question for the limit of the Navier–Stokes problem with the viscosity term removed. This is known as the regularity problem for the Euler equations, and our agents surprised us by resolving this question. The specific variant of the question that they resolved was the unforced version, where no external force is applied to the fluid. Nearly 100 agents worked together for approximately 50 hours to produce our Euler regularity disproof. 1：#citation-bottom-1","Once we saw the Euler solution, we thought that Navier–Stokes was the most promising problem to work on. Thus, we decided to devote our resources to Navier–Stokes. To do so, we shifted agents away from the other Millennium Problems and prompted these agents with the Euler resolution. When a further trained version of our internal model became available over the course of the effort, we updated our agents to that model.","We encouraged different groups of agents to explore a diversity of approaches. After some time, we cross-pollinated the agent groups by using Codex to consolidate the most useful insights from each agent group. These follow-up prompts drew on the agents’ own intermediate results. The group that found the solution to Navier–Stokes was guided in such a way.","The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. Lean formalization and verification took an additional 17 hours via GPT‑6 Astra.","Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens. In the process of resolving the Navier–Stokes problem, the agents sent 2.7 million messages and used approximately 130 billion output tokens.","Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.","We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ⁠：https://openai.com/policies/how-your-data-is-used-to-improve-model-performance/ . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).","Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result.","This milestone represents substantial work by mathematicians and AI researchers. However, this is not a culmination, but rather a snapshot in time, of progress on AI development.","We believe we are now in the next period of AI progress ⁠：https://openai.com/index/research-acceleration-view-inside-openai/ , and today’s results provide further evidence of this. We are focusing on understanding this model, and using what we learn to help us guide and pace how we pursue further advances in capability. One of our key goals ⁠：https://openai.com/index/built-to-benefit-everyone-our-plan/ is to build AI systems which are steerable, accountable, and connected to people, which may require more deliberate choices about the pace of progress, as we continue our mission to ensure AGI benefits all of humanity.","Read the Euler proof paper ⁠ (opens in a new window) ：https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194ece1/euler.pdf · Link to Lean formalized proof ⁠ (opens in a new window) ：https://github.com/openai/NavierStokesAndEuler svg]:opacity-60 ms-1 scale-inline-100\" href=\"#citation-top-1\">"],"articleImages":[{"sourceUrl":"https://images.ctfassets.net/kftzwdyauwt9/75EbpsuBOy5LbUgCppWXD1/88da8c19dcf76d6f4f8fd7485dcb6346/navier-stokes-light-master.png?w=3840&q=90&fm=webp","alt":"Diagram of a swirling vortex illustrating inward spiral and axial stretching.","afterParagraph":7,"url":"/media/articles/cmtszna9e04isro5woti0ixg6/71880b46b84d8a18.webp"},{"sourceUrl":"https://images.ctfassets.net/kftzwdyauwt9/7ut3G8rKt5ia4P3yRqi2qN/6ffb429f70548a881eb46a4e7e61498e/Option_120___1080_1080.png?w=3840&q=90&fm=webp","alt":"An alien mind > Listing card","afterParagraph":23,"url":"/media/articles/cmtszna9e04isro5woti0ixg6/aa1ddc4a166b06bf.webp"},{"sourceUrl":"https://images.ctfassets.net/kftzwdyauwt9/5kS3OG1Jfdja5xLmYcRwgr/f53b9dfe985df5969aff5dc41f2d1934/Art_Card__7_.png?w=3840&q=90&fm=webp","alt":"Research acceleration: The view inside OpenAI > Cover image","afterParagraph":23,"url":"/media/articles/cmtszna9e04isro5woti0ixg6/b3a3bfa0798b09a4.webp"}],"mediaStatus":"ok","articleBodyZh":["我们正在分享关于纳维－斯托克斯存在性和平滑性问题的解决方案，这是千禧年大奖难题之一。这个由OpenAI内部系统生成的证明表明，流体运动的纳维－斯托克斯方程动力学可以在有限时间内产生奇点。我们分享了证明的书面说明以及在Lean中的形式化。","千禧年大奖难题 (在新窗口中打开)：https://www.claymath.org/millennium-problems/，代表了数学前沿的一些最深层次问题。三维平滑流体运动是否会失稳的问题大约已经悬而未决90年。","我们工作的一个主要目标是赋能科学家推进能够造福全人类的研究和技术。为了解决纳维－斯托克斯问题，我们使用了一个内部模型，该模型的能力远超GPT‑6 Astra。我们认为向世界通报人工智能的发展速度以及未来模型的预期非常重要。","纳维－斯托克斯方程使用牛顿第二运动定律（\"F=ma\"）来描述流体如何运动。重要的是，这些方程将流体视为连续介质，而不是跟踪单个分子。这些方程用于飞机设计、天气预报以及血流研究。","对于这些动力方程，一个基本的未解问题是流体的连续介质近似是否会失效。具体来说，对于三维不可压缩、密度恒定的流体，纳维－斯托克斯方程是否可能产生“奇点”，即使运动从平滑状态开始？这里的奇点意味着流体动力学会导致速度在有限时间内无限增长。奇点的发展必须发生在粘性存在的情况下，而粘性通常会平滑运动。由于真实流体不可能无限加速，这将标志着方程对流体建模的失效。为了继续建模系统，就需要开始单独跟踪每个粒子的行为。","这些方程可以追溯到十九世纪 Claude-Louis Navier 和 George Gabriel Stokes 的工作。1934 年，Jean Leray 证明了解在广义意义上存在，但它们是否总是保持光滑成为一个尚未解决的核心问题。2000 年，克雷数学研究所将 Navier–Stokes 存在性和光滑性问题列为七大千禧年大奖问题之一。","我们的系统提供了一个分析性证明和 Lean 格式化，证明了一个最初光滑且静止的流体可以在有限时间内产生奇点。流体受到平滑的力作用，其能量在整个动力过程中从静止到奇点形成仍然保持有限。这通过建立“C”命题（以及“D”命题）解决了 Navier–Stokes 千年大奖问题，详细内容可参见官方千年大奖说明：https://www.claymath.org/wp-content/uploads/2022/06/navierstokes.pdf。","解是一个涡旋，即流体的旋转涡流，它向内螺旋并越来越拉长，就像意大利面一样。中央区域在加速的同时收缩，其能量仍然保持有限，符合物理定律。技术上的挑战在于方程必须通过流体自身的运动产生崩溃，而不是例如由我们手工施加无限大的力。更数学地说，Navier–Stokes 方程中描述运动的项——加速度、压力梯度、动量传递、粘性——必须既增大又以精确的方式互相抵消。这种精细的平衡即使在流体速度无限增长时，也保持了外部力的平滑性。","不可压缩局部运动的快照。橙色表示角速度较快，青绿色表示角速度较慢。循环速度也依赖半径。轨迹显示向内螺旋和轴向拉伸。","自 8 月 28 日起，我们一直在训练一个新的内部模型，该模型在我们的基准测试中展现了前所未有的性能，包括数学领域。该模型的训练仍在进行中，其性能持续提升。","在星期二，9月1日，我们听到传言称两个千禧年大奖问题已经被解决。受这些传言以及我们内部模型性能飞跃的启发，我们启动了一项工作，对其进行评估，涵盖所有未解的千禧年大奖问题以及其他一些高影响力问题。","我们使用了一个由我们的内部模型驱动的协调代理系统。代理可以访问各种工具，例如从缓存的互联网版本中读取信息以及运行代码。代理被划分为能够在组内通信的小组。小组的规模各不相同，产生纳维–斯托克斯问题解决方案的小组大约涉及1万个并发代理。在整个过程中，我们始终维持对所有前沿模型评估施加的严格安全措施，包括监控和隔离。","对于每个问题，我们向不同的代理小组提供问题陈述的不同变体，覆盖问题的所有变体。对于纳维–斯托克斯问题，我们向不同的小组建议了“A”和“B”版本（纳维–斯托克斯问题的特定形式，会生成证明）以及“C”和“D”版本（会生成反例证明）。","除了完整的千禧年大奖问题外，我们还要求我们的多代理系统尝试一组“较简单”的问题。这些问题之一是纳维–斯托克斯问题中去除粘性项的极限膨胀问题。这被称为欧拉方程的规律性问题，而代理出人意料地解决了这个问题。他们解决的具体问题变体是无外力版本，即流体没有外力施加。约有100个代理协作工作了大约50小时，得出了我们的欧拉方程规律性反例证明。 1：#citation-bottom-1","在看到欧拉问题的解决方案后，我们认为纳维–斯托克斯问题是最有希望的工作对象。因此，我们决定将资源投入到纳维–斯托克斯问题上。为此，我们从其他千禧年问题中调配代理，并向这些代理提供欧拉问题的解决方案。当在整个过程中我们内部模型的进一步训练版本可用时，我们将代理更新为该模型。","我们鼓励不同组的代理探索多种方法。经过一段时间后，我们利用 Codex 将每个代理组的最有用见解整合起来，从而实现代理组之间的交叉授粉。这些后续提示参考了代理自身的中间结果。找到 Navier–Stokes 解的那组就是在这种指导下完成的。","代理们在 9 月 5 日星期六达成了他们的解决方案，这比最初启动的代理晚约 88 小时。通过 GPT‑6 Astra 进行精简形式化和验证又花费了 17 小时。","在所有尝试的问题中，代理总共发送了 490 万条信息，并使用了大约 3000 亿输出令牌。在解决 Navier–Stokes 问题的过程中，代理发送了 270 万条信息，并使用了大约 1300 亿输出令牌。","我们的工作始于 9 月 1 日，在听到一个传言后我们后来意识到这与 Anthropic 员工 Levent Alpöge 和 NYU 数学教授 Tristan Buckmaster 有关。在完成整个项目和 Lean 验证（9 月 6 日）后，我们根据传言认为他们也有 Navier–Stokes 的解，于是联系他们，提供同时发布我们结果的机会，并在联合公告中认可他们的优先权。那时我们发现他们已经解决了受迫 Euler 问题。在这些讨论中，我们向他们展示了我们使用的所有提示，后来又让他们看到证明。我们承认他们在受迫 Euler 问题上的工作优先权，并祝贺他们取得了卓越的数学成就。","我们（研究人员和代理）在他们公开发布之前，并未通过任何方式看到他们的工作——尤其是没有访问任何特定用户数据来解决此问题。虽然可能性不大，但我们不能排除从他们使用我们产品中获得的去标识化数据有助于改善我们的模型：https://openai.com/policies/how-your-data-is-used-to-improve-model-performance/。然而，我们的证明有显著不同，即便在 Euler 问题中的精确结果（受迫与非受迫）也不同。","我们发布此结果的目标是报道我们 AI 模型的重大进展。我们无意因这一结果申领奖励千禧年奖。","这一里程碑代表了数学家和人工智能研究人员的大量工作。然而，这并不是一个终点，而只是人工智能发展进程中的一个时间快照。","我们相信我们现在正处于人工智能进展的下一个阶段：https://openai.com/index/research-acceleration-view-inside-openai/，而今天的成果为此提供了进一步的证据。我们专注于理解这个模型，并利用所学来指导和调整我们在追求能力进一步提升时的步伐。我们的一个关键目标：https://openai.com/index/built-to-benefit-everyone-our-plan/ 是构建可被操控、可问责并与人类相连的人工智能系统，这可能需要对进展速度做出更仔细的选择，同时我们继续执行确保通用人工智能成果惠及全人类的使命。","阅读欧拉证明论文（在新窗口打开）：https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194ece1/euler.pdf · Lean形式化证明链接（在新窗口打开）：https://github.com/openai/NavierStokesAndEuler svg]:opacity-60 ms-1 scale-inline-100\" 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Astra。我们认为向世界通报人工智能的发展速度以及未来模型的预期非常重要。","纳维－斯托克斯方程使用牛顿第二运动定律（\"F=ma\"）来描述流体如何运动。重要的是，这些方程将流体视为连续介质，而不是跟踪单个分子。这些方程用于飞机设计、天气预报以及血流研究。","对于这些动力方程，一个基本的未解问题是流体的连续介质近似是否会失效。具体来说，对于三维不可压缩、密度恒定的流体，纳维－斯托克斯方程是否可能产生“奇点”，即使运动从平滑状态开始？这里的奇点意味着流体动力学会导致速度在有限时间内无限增长。奇点的发展必须发生在粘性存在的情况下，而粘性通常会平滑运动。由于真实流体不可能无限加速，这将标志着方程对流体建模的失效。为了继续建模系统，就需要开始单独跟踪每个粒子的行为。","这些方程可以追溯到十九世纪 Claude-Louis Navier 和 George Gabriel Stokes 的工作。1934 年，Jean Leray 证明了解在广义意义上存在，但它们是否总是保持光滑成为一个尚未解决的核心问题。2000 年，克雷数学研究所将 Navier–Stokes 存在性和光滑性问题列为七大千禧年大奖问题之一。","我们的系统提供了一个分析性证明和 Lean 格式化，证明了一个最初光滑且静止的流体可以在有限时间内产生奇点。流体受到平滑的力作用，其能量在整个动力过程中从静止到奇点形成仍然保持有限。这通过建立“C”命题（以及“D”命题）解决了 Navier–Stokes 千年大奖问题，详细内容可参见官方千年大奖说明：https://www.claymath.org/wp-content/uploads/2022/06/navierstokes.pdf。","解是一个涡旋，即流体的旋转涡流，它向内螺旋并越来越拉长，就像意大利面一样。中央区域在加速的同时收缩，其能量仍然保持有限，符合物理定律。技术上的挑战在于方程必须通过流体自身的运动产生崩溃，而不是例如由我们手工施加无限大的力。更数学地说，Navier–Stokes 方程中描述运动的项——加速度、压力梯度、动量传递、粘性——必须既增大又以精确的方式互相抵消。这种精细的平衡即使在流体速度无限增长时，也保持了外部力的平滑性。","不可压缩局部运动的快照。橙色表示角速度较快，青绿色表示角速度较慢。循环速度也依赖半径。轨迹显示向内螺旋和轴向拉伸。","自 8 月 28 日起，我们一直在训练一个新的内部模型，该模型在我们的基准测试中展现了前所未有的性能，包括数学领域。该模型的训练仍在进行中，其性能持续提升。","在星期二，9月1日，我们听到传言称两个千禧年大奖问题已经被解决。受这些传言以及我们内部模型性能飞跃的启发，我们启动了一项工作，对其进行评估，涵盖所有未解的千禧年大奖问题以及其他一些高影响力问题。","我们使用了一个由我们的内部模型驱动的协调代理系统。代理可以访问各种工具，例如从缓存的互联网版本中读取信息以及运行代码。代理被划分为能够在组内通信的小组。小组的规模各不相同，产生纳维–斯托克斯问题解决方案的小组大约涉及1万个并发代理。在整个过程中，我们始终维持对所有前沿模型评估施加的严格安全措施，包括监控和隔离。","对于每个问题，我们向不同的代理小组提供问题陈述的不同变体，覆盖问题的所有变体。对于纳维–斯托克斯问题，我们向不同的小组建议了“A”和“B”版本（纳维–斯托克斯问题的特定形式，会生成证明）以及“C”和“D”版本（会生成反例证明）。","除了完整的千禧年大奖问题外，我们还要求我们的多代理系统尝试一组“较简单”的问题。这些问题之一是纳维–斯托克斯问题中去除粘性项的极限膨胀问题。这被称为欧拉方程的规律性问题，而代理出人意料地解决了这个问题。他们解决的具体问题变体是无外力版本，即流体没有外力施加。约有100个代理协作工作了大约50小时，得出了我们的欧拉方程规律性反例证明。 1：#citation-bottom-1","在看到欧拉问题的解决方案后，我们认为纳维–斯托克斯问题是最有希望的工作对象。因此，我们决定将资源投入到纳维–斯托克斯问题上。为此，我们从其他千禧年问题中调配代理，并向这些代理提供欧拉问题的解决方案。当在整个过程中我们内部模型的进一步训练版本可用时，我们将代理更新为该模型。","我们鼓励不同组的代理探索多种方法。经过一段时间后，我们利用 Codex 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模型的重大进展。我们无意因这一结果申领奖励千禧年奖。","这一里程碑代表了数学家和人工智能研究人员的大量工作。然而，这并不是一个终点，而只是人工智能发展进程中的一个时间快照。","我们相信我们现在正处于人工智能进展的下一个阶段：https://openai.com/index/research-acceleration-view-inside-openai/，而今天的成果为此提供了进一步的证据。我们专注于理解这个模型，并利用所学来指导和调整我们在追求能力进一步提升时的步伐。我们的一个关键目标：https://openai.com/index/built-to-benefit-everyone-our-plan/ 是构建可被操控、可问责并与人类相连的人工智能系统，这可能需要对进展速度做出更仔细的选择，同时我们继续执行确保通用人工智能成果惠及全人类的使命。","阅读欧拉证明论文（在新窗口打开）：https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194ece1/euler.pdf · Lean形式化证明链接（在新窗口打开）：https://github.com/openai/NavierStokesAndEuler svg]:opacity-60 ms-1 scale-inline-100\" href=\"#citation-top-1\">"]},"en":{"title":"OpenAI Announces Navier-Stokes Millennium Problem Solution Using Internal AI System","summary":"OpenAI announced that its internal AI system produced a solution to the Navier-Stokes existence and smoothness problem, proving that initially smooth fluids can form singularities in finite time, accompanied by proof documents and Lean formal 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첨부했다.","url":"https://www.aioga.com/ko/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:37.622Z"},"es":{"title":"OpenAI anuncia la solución del problema del Milenio de Navier-Stokes mediante un sistema de IA interno","summary":"OpenAI anunció que su sistema de IA interno proporcionó una solución al problema de existencia y suavidad de Navier-Stokes, demostrando que un fluido inicialmente suave puede formar singularidades en tiempo finito, y adjuntó el manuscrito de prueba y la verificación formal en Lean.","category":"Industria","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI anuncia la solución del problema del Milenio de Navier-Stokes mediante un sistema de IA interno - Aioga Noticias de IA","description":"OpenAI anunció que su sistema de IA interno proporcionó una solución al problema de existencia y suavidad de Navier-Stokes, demostrando que un fluido inicialmente suave puede forma...","url":"https://www.aioga.com/es/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:37.570Z"},"fr":{"title":"OpenAI annonce qu'un système d'IA interne a fourni la solution au problème du millénaire de Navier-Stokes","summary":"OpenAI a annoncé que son système d'IA interne avait fourni la solution au problème de l'existence et de la régularité des Navier-Stokes, prouvant que les fluides initialement lisses peuvent former des singularités en un temps fini, avec un manuscrit de preuve et une vérification formelle Lean.","category":"Industrie","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI annonce qu'un système d'IA interne a fourni la solution au problème du millénaire de Navier-Stokes - Aioga Actualités IA","description":"OpenAI a annoncé que son système d'IA interne avait fourni la solution au problème de l'existence et de la régularité des Navier-Stokes, prouvant que les fluides initialement lisse...","url":"https://www.aioga.com/fr/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:42.018Z"},"de":{"title":"OpenAI kündigt Lösung des Navier-Stokes-Millennium-Problems durch internes KI-System an","summary":"OpenAI kündigte an, dass ihr internes KI-System die Frage der Existenz und Glattheit der Navier-Stokes-Gleichungen gelöst habe. Der Beweis zeige, dass eine anfänglich glatte Flüssigkeit in endlicher Zeit Singularitäten bilden könne, und enthielt die Beweisunterlagen sowie die formale Verifikation in Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI kündigt Lösung des Navier-Stokes-Millennium-Problems durch internes KI-System an - Aioga KI-News","description":"OpenAI kündigte an, dass ihr internes KI-System die Frage der Existenz und Glattheit der Navier-Stokes-Gleichungen gelöst habe. Der Beweis zeige, dass eine anfänglich glatte Flüssi...","url":"https://www.aioga.com/de/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:42.467Z"},"pt-BR":{"title":"OpenAI anuncia solução do problema do milênio de Navier-Stokes usando sistema de IA interno","summary":"A OpenAI anunciou que seu sistema de IA interno forneceu a solução para o problema da existência e suavidade de Navier-Stokes, provando que um fluido inicialmente suave pode formar singularidades em tempo finito, juntamente com a versão manuscrita da prova e a verificação formal usando Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI anuncia solução do problema do milênio de Navier-Stokes usando sistema de IA interno - Aioga Notícias de IA","description":"A OpenAI anunciou que seu sistema de IA interno forneceu a solução para o problema da existência e suavidade de Navier-Stokes, provando que um fluido inicialmente suave pode formar...","url":"https://www.aioga.com/pt-BR/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:46.990Z"},"ru":{"title":"OpenAI объявляет о решении проблемы тысячелетия Навье-Стокса с помощью внутренней AI-системы","summary":"OpenAI объявляет, что их внутренняя AI-система предоставила решение проблемы существования и гладкости уравнений Навье-Стокса, показав, что начально гладкая жидкость может образовать сингулярности за конечное время, с приложением рукописи доказательства и формальной верификации в Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI объявляет о решении проблемы тысячелетия Навье-Стокса с помощью внутренней AI-системы - Aioga Новости ИИ","description":"OpenAI объявляет, что их внутренняя AI-система предоставила решение проблемы существования и гладкости уравнений Навье-Стокса, показав, что начально гладкая жидкость может образова...","url":"https://www.aioga.com/ru/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:48.376Z"},"ar":{"title":"تعلم OpenAI عن حل مسألة نافير-ستوكس لمسابقة مسائل الألفية باستخدام نظام الذكاء الاصطناعي الداخلي الخاص بها","summary":"أعلنت OpenAI أن نظام الذكاء الاصطناعي الداخلي الخاص بها قدم حلًا لمسألة وجود وسلاسة نافير-ستوكس، مبينًا أن السائل المبدئي السلس يمكن أن يكون له نقاط فردية خلال وقت محدد، وأرفقت الإثباتات بالإضافة إلى التحقق الرسمي باستخدام Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"تعلم OpenAI عن حل مسألة نافير-ستوكس لمسابقة مسائل الألفية باستخدام نظام الذكاء الاصطناعي الداخلي الخاص بها - Aioga أخبار الذكاء الاصطناعي","description":"أعلنت OpenAI أن نظام الذكاء الاصطناعي الداخلي الخاص بها قدم حلًا لمسألة وجود وسلاسة نافير-ستوكس، مبينًا أن السائل المبدئي السلس يمكن أن يكون له نقاط فردية خلال وقت محدد، وأرفقت الإ...","url":"https://www.aioga.com/ar/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:54.108Z"},"hi":{"title":"ओपनएआई ने अपनी आंतरिक एआई प्रणाली के माध्यम से नवीयर-स्टोक्स मिलेनियम समस्या का समाधान देने की घोषणा की","summary":"ओपनएआई ने घोषणा की कि उसकी आंतरिक एआई प्रणाली ने नवीयर-स्टोक्स मौजूदगी और चिकनाई समस्या का समाधान प्रदान किया, जिससे यह साबित हुआ कि प्रारंभ में चिकनी तरलता सीमित समय में विषम बिंदु बना सकती है, साथ ही प्रमाण का दस्तावेज और लीन फॉर्मल सत्यापन भी संलग्न किया गया।","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"ओपनएआई ने अपनी आंतरिक एआई प्रणाली के माध्यम से नवीयर-स्टोक्स मिलेनियम समस्या का समाधान देने की घोषणा की - Aioga AI समाचार","description":"ओपनएआई ने घोषणा की कि उसकी आंतरिक एआई प्रणाली ने नवीयर-स्टोक्स मौजूदगी और चिकनाई समस्या का समाधान प्रदान किया, जिससे यह साबित हुआ कि प्रारंभ में चिकनी तरलता सीमित समय में विषम बिंद...","url":"https://www.aioga.com/hi/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:53.683Z"},"it":{"title":"OpenAI annuncia di fornire la soluzione del problema del Millennio di Navier-Stokes tramite sistema AI interno","summary":"OpenAI annuncia che il suo sistema AI interno ha fornito la soluzione del problema dell'esistenza e regolarità di Navier-Stokes, dimostrando che un fluido inizialmente liscio può sviluppare singolarità in tempo finito, allegando il manoscritto della dimostrazione e la verifica formalizzata in Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI annuncia di fornire la soluzione del problema del Millennio di Navier-Stokes tramite sistema AI interno - Aioga Notizie IA","description":"OpenAI annuncia che il suo sistema AI interno ha fornito la soluzione del problema dell'esistenza e regolarità di Navier-Stokes, dimostrando che un fluido inizialmente liscio può s...","url":"https://www.aioga.com/it/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:58.781Z"},"nl":{"title":"OpenAI kondigt aan dat interne AI het Navier-Stokes millenniumprobleem oplost","summary":"OpenAI kondigt aan dat hun interne AI-systeem een oplossing heeft voor het bestaan- en gladheidsprobleem van Navier-Stokes, waarbij wordt bewezen dat aanvankelijk gladde vloeistoffen in eindige tijd singulariteiten kunnen vormen, inclusief bewijsdocumenten en Lean-formalisatie van de verificatie.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI kondigt aan dat interne AI het Navier-Stokes millenniumprobleem oplost - Aioga AI-nieuws","description":"OpenAI kondigt aan dat hun interne AI-systeem een oplossing heeft voor het bestaan- en gladheidsprobleem van Navier-Stokes, waarbij wordt bewezen dat aanvankelijk gladde vloeistoff...","url":"https://www.aioga.com/nl/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:21:58.027Z"},"tr":{"title":"OpenAI, iç AI sistemiyle Navier-Stokes binyıl problemi için çözüm ürettiğini duyurdu","summary":"OpenAI, iç AI sisteminin Navier-Stokes varoluş ve düzgünlük sorununa çözüm sağladığını, kanıtın başlangıçta düzgün duran bir akışkanın sınırlı süre içinde tekil noktalar oluşturabileceğini gösterdiğini ve kanıt belgeleri ile Lean formal doğrulamasını eklediğini açıkladı.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI, iç AI sistemiyle Navier-Stokes binyıl problemi için çözüm ürettiğini duyurdu - Aioga AI Haberleri","description":"OpenAI, iç AI sisteminin Navier-Stokes varoluş ve düzgünlük sorununa çözüm sağladığını, kanıtın başlangıçta düzgün duran bir akışkanın sınırlı süre içinde tekil noktalar oluşturabi...","url":"https://www.aioga.com/tr/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:22:03.409Z"},"vi":{"title":"OpenAI công bố giải pháp cho vấn đề Nghìn năm Navier-Stokes bằng hệ thống AI nội bộ","summary":"OpenAI công bố hệ thống AI nội bộ của họ đưa ra lời giải cho vấn đề Navier-Stokes về sự tồn tại và tính mượt mà, chứng minh rằng chất lỏng ban đầu mượt mà có thể tạo thành điểm kỳ dị trong thời gian hữu hạn, kèm theo bản thảo chứng minh và xác minh hình thức Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI công bố giải pháp cho vấn đề Nghìn năm Navier-Stokes bằng hệ thống AI nội bộ - Tin tức AI Aioga","description":"OpenAI công bố hệ thống AI nội bộ của họ đưa ra lời giải cho vấn đề Navier-Stokes về sự tồn tại và tính mượt mà, chứng minh rằng chất lỏng ban đầu mượt mà có thể tạo thành điểm kỳ...","url":"https://www.aioga.com/vi/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:22:03.714Z"},"id":{"title":"OpenAI Mengumumkan Memberikan Solusi Masalah Milenium Navier-Stokes dengan Sistem AI Internal","summary":"OpenAI mengumumkan bahwa sistem AI internal mereka memberikan solusi untuk masalah eksistensi dan kehalusan Navier-Stokes, membuktikan bahwa fluida yang awalnya halus dapat membentuk singularitas dalam waktu terbatas, disertai manuskrip bukti dan verifikasi formal Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI Mengumumkan Memberikan Solusi Masalah Milenium Navier-Stokes dengan Sistem AI Internal - Berita AI Aioga","description":"OpenAI mengumumkan bahwa sistem AI internal mereka memberikan solusi untuk masalah eksistensi dan kehalusan Navier-Stokes, membuktikan bahwa fluida yang awalnya halus dapat membent...","url":"https://www.aioga.com/id/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:22:08.944Z"},"th":{"title":"OpenAI ประกาศให้คำตอบปัญหาพันปีย์ Navier-Stokes ด้วยระบบ AI ภายใน","summary":"OpenAI ประกาศว่าระบบ AI ภายในของตนให้คำตอบปัญหาการมีอยู่และความเรียบเนียนของ Navier-Stokes โดยพิสูจน์ว่าสภาพไหลเดิมที่เรียบเนียนสามารถเกิดจุดวิกฤติในเวลาจำกัด และแนบเอกสารพิสูจน์พร้อมการตรวจสอบเชิงรูปแบบด้วย Lean","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI ประกาศให้คำตอบปัญหาพันปีย์ Navier-Stokes ด้วยระบบ AI ภายใน - ข่าว AI Aioga","description":"OpenAI ประกาศว่าระบบ AI ภายในของตนให้คำตอบปัญหาการมีอยู่และความเรียบเนียนของ Navier-Stokes โดยพิสูจน์ว่าสภาพไหลเดิมที่เรียบเนียนสามารถเกิดจุดวิกฤติในเวลาจำกัด และแนบเอกสารพิสูจน์พร...","url":"https://www.aioga.com/th/news/cmtszna9e04isro5woti0ixg6/","contentTranslated":true,"sourceHash":"d80c715fa0f19038","translatedAt":"2026-09-08T18:22:09.768Z"},"pl":{"title":"OpenAI ogłasza, że ich wewnętrzny system AI dostarczył rozwiązanie Milenijnego Problemu Naviera-Stokesa","summary":"OpenAI ogłosiło, że ich wewnętrzny system AI dostarczył rozwiązanie problemu istnienia i gładkości Naviera-Stokesa, dowodząc, że początkowo gładka ciecz może tworzyć osobliwości w skończonym czasie, wraz z manuskryptem dowodu i weryfikacją formalną w Lean.","category":"行业动态","source":"OpenAI：官网动态（RSS · 排除企业/客户案例）","aggregationSource":"OpenAI：官网动态（RSS · 排除企业/客户案例）","pageTitle":"OpenAI ogłasza, że ich wewnętrzny system AI dostarczył rozwiązanie Milenijnego Problemu Naviera-Stokesa - 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