Thought Leadership
OpenAI has announced Astra as its next major AI model. An internal version of the system has reportedly tackled mathematical problems that have remained unsolved for decades.
In a research paper published on August 1, OpenAI describes Astra as its “next major model.” For the problems it addressed, there had been no progress on the respective central result for at least a decade and, in most cases, significantly longer. According to OpenAI, the results span a broad range of mathematical fields, including high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, quantum complexity, lattice-based cryptography and extremal combinatorics.
Among the individual results cited are a proof of the existence of so-called non-sofic groups, a disproof of Connes’ rigidity conjecture, new bounds on the density of sphere packings in high-dimensional spaces, and solutions to several problems posed by mathematician Paul Erdős.
According to OpenAI, the tokens required to find the solutions would have cost around $2,000 at the model’s Sol API pricing. Human researchers then used the same model to turn the underlying reasoning into formal manuscripts. Astra subsequently formalized each proof as a so-called Lean certificate, allowing the results to be machine-checked using the Lean mathematical verification system.
OpenAI has yet to decide whether the model will ultimately be released as GPT-5.7, GPT-6 or under an entirely different name.
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