OpenAI发布了其下一代AI模型Astra在数学领域的重大突破。该模型在包括高维几何、编码理论、算术电路复杂度、群论和算子代数等领域共解决了10个数学难题[1]。其中包括终结长达27年的非sofic群猜想——该猜想由Gromov于1999年提出[1]；首次突破1978年以来的极限，精确计算了Cohn-Elkies线性规划的指数衰减率，从而解决高维球体堆积问题[1]；以及推翻1982年菲尔兹奖得主Alain Connes的刚性猜想，构造出无穷可数群家族以证明存在非同构但代数结构相同的群[1]。
这些成果的研究成本显著低廉。生成全部10项突破性成果的总成本约2000美元，按Sol API价格计算，平均每个难题需要200美元[1]。OpenAI已开源包含249页的论文及其Lean形式化验证证明[1]。
数学家Thomas Bloom评价此次突破比OpenAI之前证伪单位距离猜想更为重要[1]。Claude Fable 5则表示，按菲尔兹奖标准，任何一项成果都足以获奖[1]。OpenAI核心创始人Noam Brown表示，模型测试时的计算资源远未封顶，连百万美元级别的千禧年难题也可能被攻克[1]。
OpenAI has announced major breakthroughs by its next-generation AI model Astra in solving ten significant mathematics problems across multiple disciplines [1]. The achievements span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, and operator algebra [1].
Among the most notable accomplishments, Astra constructed an infinite finitely presented non-sofic group, resolving a conjecture first posed by Gromov in 1999 that had remained unsolved for 27 years [1]. The model also achieved the first breakthrough since 1978 in calculating the exponential decay rate of the Cohn-Elkies linear programming bound, advancing solutions to the high-dimensional sphere packing problem [1]. Additionally, Astra refuted the rigidity conjecture proposed by 1982 Fields Medal recipient Alain Connes by constructing infinite countable families of groups with identical algebraic structures but non-isomorphic relationships [1].
OpenAI published a 249-page paper documenting these results and has made the Lean formalized proofs publicly available [1]. The total computational cost for generating all ten breakthroughs was approximately 2,000 US dollars, averaging 200 dollars per problem based on Sol API pricing [1]. Mathematician Thomas Bloom characterized this breakthrough as more significant than OpenAI's previous disproof of the unit distance conjecture [1]. Claude Fable 5 assessed that any single result would meet the standards for a Fields Medal [1]. Noam Brown, a core founder of OpenAI, noted that the model's computational capacity during testing remains far from saturated, suggesting that even million-dollar-class Millennium Prize problems could potentially be solved [1].
