OpenAI: its unreleased Astra model solved ten open math problems, including the first example of a "non-sofic" groupHistory·GPT-6 Astra: release, risks and mathematical results
SI has stopped merely retelling what is known: it finds proofs that humans failed to find for decades, and they can be checked by a program, which means science is accelerating.
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OpenAI said an internal version of its next major model, Astra, solved ten problems, each of which had stayed open for at least ten years. The headline result is the first explicit construction of a non-sofic group (the question was posed in 1999); also disproved was Connes's rigidity conjecture, proved was Ehrhart's volume conjecture, three problems from the Erdős catalog were solved, and for the first time since 1978 the upper bound on sphere packing density in high dimensions was improved. Each result comes with machine-checkable proofs in Lean 4 (GitHub) and a 249-page manuscript. By OpenAI's estimate, all ten solutions cost about $2,000 in compute at GPT-5.6 Sol API rates. OpenAI's head of mathematics research Sébastien Bubeck confirmed the results. The public release date of Astra has not been announced; according to Tech Times, the model will undergo a voluntary pre-release review by the US government before wide availability.