OpenAI近日公布了一份62页的核心手稿《How the Ideas Came Together》，详细记录了其下一代模型Astra解决十大数学难题的完整推演过程[1]。这些难题涵盖高维球体堆积、二元码与球面码、群论、Connes刚性猜想、算术电路下界、量子并行重复、最近向量问题、Ehrhart体积猜想、多色Ramsey数以及极值图论等领域[1]，被认为具有菲尔兹奖级别的学术价值。
在具体成果中，高维球体堆积密度的上界从原来的0.5991推进到0.6044005442916776954，打破了46年未有实质性进展的局面[1]。此外，AI还成功构造了非sofic群，这是27年来首次构造成功[1]。手稿由AI模型独立撰写，OpenAI团队完全没有参与其中[1]，整个研究过程仅耗费约2000美元的Token成本[1]。
OpenAI研究人员Mo Bavarian对此评价称："这一刻，比任何时候都更像奇点前夜"[1]。
OpenAI has publicly released a 62-page manuscript titled "How the Ideas Came Together," which documents how its next-generation model Astra tackled ten major unsolved mathematics problems [1]. The manuscript presents the complete derivation process and demonstrates the AI's thought progression, including obstacles encountered and perspective shifts throughout the problem-solving journey [1].
The problems addressed span multiple mathematical domains, including high-dimensional sphere packing, binary codes and spherical codes, group theory, the Connes rigidity conjecture, arithmetic circuit lower bounds, quantum parallel repetition, the closest vector problem, the Ehrhart volume conjecture, multicolor Ramsey numbers, and extremal graph theory [1]. For the high-dimensional sphere packing challenge, the AI advanced the upper bound on packing density from 0.5991 to 0.6044005442916776954, marking the first substantial progress in 46 years [1]. Another achievement involved constructing non-sofic groups, a problem that had remained unsolved for 27 years [1].
Notably, the manuscript was entirely authored by the AI model independently, with the OpenAI team playing no role in its creation [1]. The computational cost for generating these results was approximately 2,000 dollars in tokens [1]. Mo Bavarian commented on the significance of this moment, stating: "This moment feels more like the eve of the singularity than ever before" [1].
