OpenAI's Unreleased Model Astra Solves Ten Major Open Mathematics Problems

A Hacker News discussion examines OpenAI’s claim that an unreleased model, code-named Astra, produced new results on ten major open mathematics problems. OpenAI says an internal version of the model found the results using roughly $2,000 worth of computation at Sol API rates; humans prepared the arguments into manuscripts, and the model then formalized each argument in Lean certificates. The reported results span sphere packing, coding theory, group theory, arithmetic circuit complexity, quantum games, lattice problems, convex geometry, Ramsey theory, and extremal graph theory, including claimed resolutions of several Erdős problems. The discussion treats the announcement as potentially significant evidence of a sharp advance in AI-assisted mathematical research, particularly for well-defined problems with extensive existing theory and relatively easy verification. However, Astra has not been released, the results have not yet been independently validated in the supplied reporting, and commenters note that a Lean proof certificate does not by itself establish that every claimed result has been correctly interpreted or that all ten claims are sound. OpenAI also said it tried other,5

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