OpenAI’s Astra solves open math problems

OpenAI announced on August 1, 2026 that an internal version of Astra, its next major model family, solved ten previously open problems in mathematics and theoretical computer science for roughly $2,000 in compute. The results included a construction proving the existence of non-sofic groups and new sphere-packing bounds, with formal Lean proofs published on GitHub for independent verification.

Mathematicians including Noga Alon, Timothy Gowers, Arul Shankar and Jacob Tsimerman assessed the work, and Gowers said he would recommend one proof from the model family for Annals of Mathematics without hesitation. The achievement was framed as a real research milestone, but not AGI, since the problems sat in domains with clear rules, verifiable answers and conditions well suited to AI strengths.

Other developments reinforced the same theme of rapid capability gains paired with unresolved safeguards. OpenAI and academic partners reported AI coding agents modernized research software with speedups of up to 60 times, while Epoch AI projected AI chip deployments will double every nine months. OpenAI also reportedly showed Astra to Washington policymakers as regulation loomed, and Hugging Face CEO Clem Delangue called for developer accountability when autonomous AI systems cause harm.