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OpenAI Unveils Ten Advances in Math and Theoretical CS, Token Cost ~$2,000
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- DeepHorus
OpenAI today announced ten major advances in mathematics and theoretical computer science, with core research on these previously unsolved problems having seen no substantial breakthroughs for at least a decade. According to the official introduction, these results were computed by an internal version of the next-generation core model Astra. At Sol API rates, the token cost consumed to find solutions was approximately $2,000 (about 13,500 RMB).
These problems span multiple branches of mathematics, including high-dimensional sphere packing, binary and spherical codes, non-flexible groups, and the Connes rigidity conjecture. For example, on non-flexible groups, the AI proposed a construction method that proved the existence of non-flexible groups, answering a core open problem in group theory; on the Connes rigidity conjecture, the system disproved a long-standing conjecture, showing that certain groups are not uniquely determined by their von Neumann algebras.
Other results include new lower bounds for arithmetic circuit complexity, a quantum parallel repetition theorem, and the approximate hardness of the closest vector problem. Among them, the closest vector problem is directly related to post-quantum cryptography, and proving its hardness has fundamental significance for cryptographic security. In addition, the AI solved Erdős problems 146 and 180 in extremal graph theory and gave superexponential lower bounds for multicolor Ramsey numbers.
OpenAI emphasized that human researchers assisted in writing the paper manuscripts and formally verified the proofs in the Lean language, taking responsibility for correctness, but the mathematical arguments themselves were all generated by the AI system. The company believes that authorship should truthfully reflect the process of research result generation. If proofs independently generated by AI were claimed as human-written, it would both erase the system's contribution and distort the essence of genuine human intellectual labor.
The significance of these results lies not only in solving specific problems, but also in demonstrating AI's potential in mathematical research. In fields that traditionally rely on human intuition and creativity, AI can now provide breakthrough ideas at relatively low cost. However, this also raises discussions about academic integrity and research ethics; how to appropriately attribute AI contributions has become a new issue facing the academic community.
Looking forward, as model capabilities improve, AI may play a role in more fundamental scientific fields. OpenAI's announcement this time is only the beginning; more detailed papers and methods may be released later. For the mathematical community, these AI-generated proofs need to pass rigorous verification and review before they can become part of the recognized mathematical knowledge system.
