OpenAI官方宣布推出下一代模型Astra，并公布其内部版本在数学与理论计算机科学领域取得的10项新成果[1]。这些突破涉及高维几何、群论、量子复杂性等多个研究方向，所涉问题均为长期未解难题，其中部分已悬而未决至少十年[1]。
其中，高维球体堆积指数自1978年以来首次实现改进[1]，而针对非sofic群的构造推翻了自2000年前后提出的长期猜想[1]。这些研究成果由模型生成、经人类整理后形成一份249页的论文和62页的解题说明[1]，寻找全部解法所消耗的计算成本按Sol API费率计算约为2000美元[1]。
OpenAI方面表示，公司参与了论文的论证整理与Lean形式化验证工作，对相关结果的正确性负责[1]。本周，OpenAI首席执行官萨姆·奥尔特曼向美国华盛顿的白宫官员、内阁成员和国会议员预览了Astra[1]。
OpenAI has announced its next-generation model, Astra, revealing that an internal version has achieved ten significant new results in mathematics and theoretical computer science.[1] These breakthroughs address long-standing unsolved problems spanning high-dimensional geometry, group theory, quantum complexity, and other domains, with each problem remaining open for at least a decade.[1]
Among the key accomplishments, the model improved the sphere-packing exponent for high-dimensional spheres for the first time since 1978.[1] Additionally, it constructed non-sofic groups that overturn a long-standing conjecture proposed around 2000.[1] The research findings have been formalized into a comprehensive 249-page paper accompanied by 62 pages of solution explanations, with the token cost for finding all solutions calculated at approximately 2,000 US dollars based on the Sol API pricing structure.[1]
OpenAI emphasized its responsibility for the results' accuracy, stating that the company participated in argumentation, organization, and Lean formal verification of the findings.[1] Earlier this week, OpenAI CEO Sam Altman previewed Astra to White House officials, cabinet members, and congressional representatives in Washington.[1]
