原帖引用 · AI 翻译
OpenAI 声称，其新的 AI 证明涵盖了一道千禧年大奖难题的一半、Kakeya 猜想以及一个核心复杂性假说。
> 这些问题涉及数学、计算机科学和物理学，顶尖专家已研究了几十年。
> 其中最重大的是：约 25 年来，指数时间假说认为，某些逻辑难题所需的求解时间会随着问题规模增大而急剧增长。OpenAI 的 AI 称已证明该假说是错误的，而数百篇研究论文都以它为基础。
> 在数学领域，AI 声称破解了局部光滑化猜想。这是一道已有 35 年历史、关于波如何聚焦的难题；这一成果也解决了著名的 Kakeya 猜想。此前，人类只解决了规模较小的版本。
> 在物理领域，AI 声称以完全严格的数学证明表明，量子色动力学——解释将原子核维系在一起的作用力的理论——具有坚实的数学基础。它对杨-米尔斯理论的证明涵盖了奖金为 100 万美元的“杨-米尔斯理论的存在性与质量间隙”千禧年大奖难题的一半。
原文
OpenAI claims new AI proofs covering half a Millennium Prize problem, the Kakeya conjecture and a core complexity hypothesis. > These problems are in math, computer science and physics, problems top experts had worked on for decades. > The biggest: for about 25 years, the Exponential Time Hypothesis held that certain logic puzzles take time that explodes as they grow. OpenAI’s AI says it proved the hypothesis false, and hundreds of research papers rest on it. > In math, the AI claims to have cracked the local smoothing conjecture, a 35-year-old puzzle about how waves focus, which also settles the famous Kakeya conjecture. Humans had only solved smaller versions. > In physics, the AI claims it proved, with full mathematical rigor, that quantum chromodynamics, the theory of the force holding atoms’ cores together, stands on solid math. Its Yang-Mills proof covers half of the $1M “Yang-Mills Existence and Mass Gap” Millennium Prize problem.