OpenAI has introduced its next-generation AI model, Astra, saying it generated new results on 10 open mathematical problems that had remained unsolved for at least a decade, with some dating back several decades.
In a research paper published on August 1, OpenAI said an unreleased internal version of Astra produced original mathematical results spanning high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography and extremal combinatorics.
According to the company, the model generated the core mathematical arguments, while human researchers refined the final manuscripts. Astra also produced formal Lean proof certificates, allowing the results to be independently verified using automated proof-checking tools.
The complete research release spans 249 pages, with OpenAI estimating the total inference cost for solving the 10 problems at approximately $2,000.
Among the reported results are new upper bounds on sphere-packing density, a construction establishing the existence of non-sofic groups, a disproof of Connes' rigidity conjecture, and progress on problems originally posed by mathematician Paul Erdős.
The announcement drew attention across the AI research community. While Anthropic's Fable 5 reportedly compared the work to Fields Medal-level research, experts cautioned that Astra's findings still require peer review and independent verification. The announcement follows similar mathematical breakthroughs claimed by rival AI companies, including Anthropic and Harmonic.
OpenAI has not disclosed when Astra will be publicly released or whether it will be integrated into GPT-6 or another future product. The company described Astra as a multi-agent research system designed for long-duration reasoning tasks, positioning advanced mathematics as one of its primary evaluation benchmarks.
