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OpenAI's Astra Solved Decades-Old Math Problems For $2,000

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4 weeks 2 days ago
An anonymous reader quotes a report from Forbes: The cost of producing new results on ten longstanding mathematical problems just fell to $2,000, according to OpenAI, which says its Astra model generated machine-checkable proofs for questions that had resisted human progress for decades. OpenAI published the work on August 1 and used it to give its next major model family a name: Astra. The results run across group theory, high-dimensional geometry, coding theory, quantum complexity, lattice cryptography and extremal combinatorics. They arrived as a 249-page manuscript collection and, alongside it, something the field has not seen attached to an AI claim before at this scale: a machine-checkable certificate for every single result. The problems were not textbook exercises dressed up as discoveries. Each had been open for at least ten years, most of them far longer, and several sit at the center of their subfields: - A construction establishing the existence of non-sofic groups, a question that has occupied group theorists for years. - A disproof of Connes's rigidity conjecture, a long-standing problem in the theory of von Neumann algebras. - An improvement to the general upper bound on sphere-packing density in high dimensions, a bound that had stood since 1978. - Three problems come from the catalogue of open questions left behind by Paul Erdos. The announcement follows another result from May, when OpenAI used a similar reasoning model to produce an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdos in 1946.

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