这是 AI 首次在数学核心难题上生成全新知识，做数学研究或 AI 基础研究的团队值得关注——它可能改变我们对 AI 创造力的认知。
OpenAI 在著名的组合几何问题——Erdős 1946 年提出的平面单位距离问题上取得重大突破，AI 模型找到了构造 n 个点使得单位距离对数超线性增长的方法。此前所有已知构造的单位距离对数都接近线性，而新方法实现了 n^{1+δ} 的常数 δ 增长（后续改进显示 δ=0.014）。这是 AI 首次在数学核心难题上做出实质性新知识生成，而非仅验证已知结果。数学家表示“很难入睡”，认为这是 AGI 的征兆。
our math result is a milestone in new knowledge generation by AI. very exciting to imagine similar r...
our math result is a milestone in new knowledge generation by AI. very exciting to imagine similar results in other scientific fields. "It's very hard to sleep, man" is a pretty good reaction. Alex Dimakis @AlexGDimakis A breakthrough by OpenAI in a very famous Combinatorics problem, the Planar Unit Distance problem by Erdos 1946. The problem is amazing because it can be described to a first-grader: Find a way to place n points on the plane to maximize the number of pairs that have distance exactly 1. For example, if you have n=4 points on a square (of side-length 1) you have 4 pairs of distance 1. The diagonals have length sqrt(2) so don't count. But you can squeeze one diagonal and create a point-set with n=4 points and 5 pairs of distance 1. And you can't get more than 5 pairs from n=4 points, so we are done with n=4 points. Now, if you place n points on a line, you have n-1 pairs of distance 1. In general, all known constructions of n points had a number of pairs scaling essentially linearly: n^{1+something vanishing} It seems that the model found a way to place n points on the plane so that their unit distances scale super-linearly: like n^{1+delta} for some *constant* delta. Delta was not explicitly specified apparently, but a forthcoming refinement by Will Sawin shows delta=0.014 works, according to the announcement. This is incredible progress for mathematics, since this is (unlike previous Erdos problems solved by AI) a major breakthrough, in one of the most studied problems in combinatorial geometry. If you're in mathematics research now, you feel the AGI. Lijie Chen said it honestly in the video: "It's very hard to sleep, man" 🔗 View Quoted Tweet 💬 23 🔄 6 ❤️ 152 👀 12084 📊 27 ⚡