OpenAI’s Astra model solves ten long-standing math problems
OpenAI reports that its unreleased Astra model has produced solutions to ten open problems in mathematics and computer science, verified with formal proofs.
· AI · 2 min read
OpenAI said this week that its internal Astra model has generated solutions to ten open problems in mathematics, quantum complexity, and theoretical computer science. The company claims the advances were achieved using an unreleased version of Astra, which then formalized each proof for independent verification.
What happened
According to OpenAI, Astra constructed the core arguments for each solution, then converted them into Lean certificates—formal proofs that can be checked step by step by external software. The proofs were published on GitHub. This process allows independent mathematicians and computer scientists to verify the results without relying on OpenAI’s word alone. The company estimated that the compute required to generate all ten solutions would cost around $2,000 at current Sol API rates.
Researchers have responded with a mix of surprise and caution. Some see Astra’s results as a sign of acceleration in mathematical research, provided the work is documented and explained clearly. Others have called for more transparency and improved write-ups to ensure the broader community can interpret, verify, and build on these advances.
Why it matters
If confirmed, these results would mark a significant milestone for AI in fundamental research, demonstrating the ability to contribute new knowledge rather than simply process existing information. The use of formal proof certificates also addresses concerns about trust and verification in machine-generated research. The event has prompted renewed debate about AI’s role in scientific discovery and the need for rigorous standards around transparency and reproducibility.