An unreleased OpenAI model called Astra has produced verified solutions to ten mathematics and theoretical computer science problems that had gone unsolved for at least a decade, according to the company, at a compute cost of roughly $2,000 across all ten. The results span high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography and extremal combinatorics.
Unlike a chatbot answer that has to be taken on faith, each solution comes with a proof formalized in the Lean 4 programming language, meaning the logic can be checked mechanically rather than by trusting OpenAI's claims. The company published the formalized proofs on GitHub under an Apache 2.0 license, alongside reasoning walkthroughs, so outside mathematicians can audit the work directly.
Outside mathematicians are taking it seriously
The most significant single result is the first explicit construction of a non-sofic group, a question that had been open since 1999 and had resisted 27 years of attempts by human mathematicians. Thomas Bloom, a mathematician at the University of Manchester, called the results "big news" and said they are more significant than the counterexample to the unit distance conjecture published earlier this year — a comparison to one of 2026's other notable results in the field.
Big news — more significant than the counterexample to the unit distance conjecture published in May.
Thomas Bloom, mathematician, University of Manchester
None of the ten problems was a Millennium Prize Problem, and OpenAI researcher Noam Brown has said the results likely understate what additional test-time compute could produce. Astra itself has no announced price or release date. Under a new U.S. regulatory framework for advanced models, it will be the first system required to pass a government safety review before any public rollout — a process that has no fixed timeline of its own.
The episode marks one of the clearer public examples yet of a large language model contributing original, independently verifiable results to open problems in a hard science, rather than summarizing or recombining work that already existed. That distinction — verifiable proof versus persuasive-sounding text — is likely to shape how skeptical mathematicians and computer scientists remain willing to be about similar claims from other labs going forward.
