An internal version of OpenAI’s next-generation model, Astra, successfully tackled ten long-standing open problems in mathematics and theoretical computer science. These challenges had stumped researchers for at least a decade, and in many cases much longer. Among the breakthroughs: an explicit construction proving the existence of non-sofic groups (a central question in group theory), a disproof of Connes’ rigidity conjecture, new upper bounds on the density of high-dimensional sphere packings (the first improvement since 1978), and advances in coding theory, arithmetic circuit complexity, and quantum complexity. ixbt.com +3
What sets this apart is OpenAI’s approach to verification. The company didn’t just publish the results; it formalized each proof using Lean — a language that allows for machine-checkable, step-by-step verification. OpenAI then open-sourced these Lean certificates on GitHub, enabling mathematicians worldwide to independently confirm the correctness of the arguments. The company also shared a walkthrough of the model’s reasoning process. OpenAI emphasized that while the model generated the mathematical arguments, human researchers collaborated to prepare the manuscripts and ensure the presentation. The total compute cost for these successes was roughly $2,000 at Sol API rates. This marks a significant step: AI is no longer just solving benchmark tasks but contributing to genuine research frontiers.
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