OpenAI’s Astra solves 10 long-open math problems and publishes the proofs
OpenAI Group PBC revealed Saturday that an internal version of Astra, the model family it calls its next major release, produced new results for 10 problems in mathematics and theoretical computer science that had been open for at least a decade, and it published machine-checkable proofs alongside the claim. The company posted a 249-page manuscript […] The post OpenAI’s Astra solves 10 long-open…
OpenAI's Astra, the company's next major release of its AI model family, has reportedly solved 10 long-standing mathematical problems and published machine-checkable proofs for each. The 249-page manuscript collection, along with model-written reasoning walkthroughs and Lean 4 certificates for all 10 results, is available on GitHub under an Apache 2.0 license.
The most significant achievement is the construction of a non-sofic group, a question left open since Mikhail Gromov introduced soficity in 1999. Other notable results include disproving Connes's rigidity conjecture and proving Ehrhart's volume conjecture. Additionally, Astra has provided counterexamples in extremal graph theory, resolving two more Erdős problems.
The Lean certificates ensure the proofs are machine-checkable, reducing trust in the model to a simple binary verdict.
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