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  "title": {
    "zh": "OpenAI宣称破解纳维-斯托克斯问题，对手数学家质疑成果归属",
    "en": "OpenAI Says It Solved a $1M Math Problem. A Rival Mathematician Says He Did It First"
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    "zh": "OpenAI宣布，其内部AI模型以约一万个智能体协同工作88小时，生成了一个经过Lean验证的证明，表明纳维-斯托克斯流体方程可以发生爆破。就在数小时前，纽约大学数学家Tristan Buckmaster指责OpenAI试图为他与Anthropic研究员Levent Alpöge已完成的成果抢占优先权。\n\n纳维-斯托克斯问题是克莱数学研究所七个千禧年大奖难题之一，每个奖金为100万美元，因此经过验证的爆破证明将是数学领域的里程碑，也是AI在形式推理方面的惊人展示。优先权之争还引发了对科研伦理以及AI实验室在激烈竞争环境中如何处理未发表工作的重要拷问。\n\nBuckmaster声称，他在9月将未发表证明的细节告知了一位OpenAI数学家，此后OpenAI的Sébastien Bubeck先提出协调发表，但随后又施压，并提到OpenAI内部已完成一份100页的强制纳维-斯托克斯爆破证明。OpenAI、Bubeck和Sam Altman均否认指控，Bubeck还公开了短信记录，称这些消息表明他曾真诚提议进行协调发布。",
    "en": "OpenAI claims its AI solved a $1M math problem, but a rival mathematician says he did it first and accuses OpenAI of racing to claim credit."
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      "title_zh": "OpenAI宣称破解纳维-斯托克斯问题，对手数学家质疑成果归属",
      "title_en": "OpenAI Says It Solved a $1M Math Problem. A Rival Mathematician Says He Did It First",
      "what_changed_zh": "OpenAI宣布，其内部AI模型以约一万个智能体协同工作88小时，生成了一个经过Lean验证的证明，表明纳维-斯托克斯流体方程可以发生爆破。就在数小时前，纽约大学数学家Tristan Buckmaster指责OpenAI试图为他与Anthropic研究员Levent Alpöge已完成的成果抢占优先权。\n\n纳维-斯托克斯问题是克莱数学研究所七个千禧年大奖难题之一，每个奖金为100万美元，因此经过验证的爆破证明将是数学领域的里程碑，也是AI在形式推理方面的惊人展示。优先权之争还引发了对科研伦理以及AI实验室在激烈竞争环境中如何处理未发表工作的重要拷问。\n\nBuckmaster声称，他在9月将未发表证明的细节告知了一位OpenAI数学家，此后OpenAI的Sébastien Bubeck先提出协调发表，但随后又施压，并提到OpenAI内部已完成一份100页的强制纳维-斯托克斯爆破证明。OpenAI、Bubeck和Sam Altman均否认指控，Bubeck还公开了短信记录，称这些消息表明他曾真诚提议进行协调发布。",
      "what_changed_en": "OpenAI claims its AI solved a $1M math problem, but a rival mathematician says he did it first and accuses OpenAI of racing to claim credit.",
      "current_state_zh": "OpenAI宣布，其内部AI模型以约一万个智能体协同工作88小时，生成了一个经过Lean验证的证明，表明纳维-斯托克斯流体方程可以发生爆破。就在数小时前，纽约大学数学家Tristan Buckmaster指责OpenAI试图为他与Anthropic研究员Levent Alpöge已完成的成果抢占优先权。\n\n纳维-斯托克斯问题是克莱数学研究所七个千禧年大奖难题之一，每个奖金为100万美元，因此经过验证的爆破证明将是数学领域的里程碑，也是AI在形式推理方面的惊人展示。优先权之争还引发了对科研伦理以及AI实验室在激烈竞争环境中如何处理未发表工作的重要拷问。\n\nBuckmaster声称，他在9月将未发表证明的细节告知了一位OpenAI数学家，此后OpenAI的Sébastien Bubeck先提出协调发表，但随后又施压，并提到OpenAI内部已完成一份100页的强制纳维-斯托克斯爆破证明。OpenAI、Bubeck和Sam Altman均否认指控，Bubeck还公开了短信记录，称这些消息表明他曾真诚提议进行协调发布。",
      "current_state_en": "OpenAI claims its AI solved a $1M math problem, but a rival mathematician says he did it first and accuses OpenAI of racing to claim credit.",
      "detailed_summary_zh": "OpenAI claims its AI solved a $1M math problem, but a rival mathematician says he did it first and accuses OpenAI of racing to claim credit.",
      "detailed_summary_en": "OpenAI claims its AI solved a $1M math problem, but a rival mathematician says he did it first and accuses OpenAI of racing to claim credit.",
      "background_zh": "纳维-斯托克斯方程描述流体运动，其存在性与光滑性问题问的是三维空间中光滑解是否总是存在，还是会发生破裂，例如数学上预测无限速度的“爆破”。Lean是一个开源证明助手，可以逐步验证数学证明，因此经Lean验证的结果通常被认为是可形式化检查的。Buckmaster是纽约大学库朗数学研究所教授，曾因纳维-斯托克斯方程的相关研究获得2019年克莱研究奖。",
      "background_en": "The Navier-Stokes equations describe the motion of fluids, and the Navier-Stokes existence and smoothness problem asks whether smooth solutions always exist in three dimensions or can break down, such as via 'blow-up' where the math predicts infinite velocity. Lean is an open-source proof assistant that verifies every step of a mathematical proof, so a Lean-verified result is considered formally checkable. Buckmaster is a professor at NYU's Courant Institute who received the 2019 Clay Research Award for related work on Navier-Stokes equations.",
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          "url": "https://en.wikipedia.org/wiki/Lean_(proof_assistant)",
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        {
          "url": "https://en.wikipedia.org/wiki/Navier–Stokes_equations",
          "title": "Navier–Stokes equations - Wikipedia"
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