OpenAI's internal Astra model proves 10 open math theorems for $2,000

OpenAI says internal model Astra produced machine-verified Lean 4 proofs for 10 problems open at least a decade, including the first explicit construction of a non-sofic group (open since 1999), at roughly $2,000 in Sol API tokens. A 249-page manuscript and proof certificates shipped on GitHub; math head Sébastien Bubeck called the results "beautiful."

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