OpenAI's Astra Solves 10 Long-Standing Math Problems
OpenAI Astra solves 10 math and CS problems, with Lean-verified proofs and major breakthroughs See how the model tackled group theory, quantum complexity, and more for researchers
OpenAI said its internal model Astra solved 10 longopen problems in mathematics and theoretical computer science, including work in geometry, group theory, and quantum complexity. The announcement was reported on Aug. 3, 2026.
According to the article, the problems included a proof that nonsofic groups exist, along with progress on conjectures tied to Alain Connes and Ehrhart, plus several problems from Paul Erdős’s list. OpenAI said the proofs were verified in Lean, and the total token cost for successful runs was about $2,000.
The report also said Anthropic researcher Levent Alpoge claimed he reproduced five of the proofs within 24 hours using another model. The article frames the development as part of a broader debate about how AI could help tackle longstanding research problems in fields beyond math, including drug discovery and materials science.