OpenAI's Unreleased Astra Model Solved Ten Decades-Old Math Problems for About $2,000

OpenAI has not released its next major model, code-named Astra, and has not said whether it will ship under the GPT-6 label or as another point release. But the company used Astra on August 1 to produce a striking demonstration: solutions to ten open problems in mathematics and theoretical computer science that had each gone unsolved for at least a decade, according to Forbes and the-decoder.

The results span group theory, high-dimensional geometry, coding theory, quantum complexity, lattice cryptography, and extremal combinatorics. Among the more notable: an explicit construction of a non-sofic group, closing a question that had been open since mathematician Mikhail Gromov defined the concept of soficity in 1999. Other results include a disproof of Connes's rigidity conjecture on von Neumann algebras, a proof of Ehrhart's volume conjecture, and solutions to three problems from mathematician Paul Erdős's catalog, including problem 183 on multicolor Ramsey numbers.

OpenAI published a 249-page manuscript along with Lean 4 proof certificates, files checked by a formal proof-verification program, on GitHub under an Apache 2.0 license. According to thezvi's analysis, the repository's automated "sorry" count, which flags unverified proof steps, is zero across all ten formalized results. That means the proofs check out mechanically rather than resting on Astra's own unverified assertions. OpenAI said the total inference cost across all ten solutions was roughly $2,000 at GPT-5.6 Sol's API rates. Sam Altman, OpenAI's chief executive, reportedly gave US lawmakers and regulators a private Astra demonstration in Washington in late July, ahead of the public math release.