OpenAI’s Astra Solved 10 Open Math Problems for $2,000
2 min readAn unreleased OpenAI model has done something no AI system had managed before. It produced original mathematics that human experts could not, and it did so for roughly the price of a laptop. On August 1, 2026, OpenAI announced that an internal version of Astra, its next major model family, solved ten previously open problems in mathematics and theoretical computer science.
What OpenAI Announced
The results sit in genuine research territory. They include a construction establishing the existence of non-sofic groups, a long-standing open question in group theory, and new upper bounds on sphere-packing density down to the Cohn-Elkies threshold. OpenAI published formal Lean proofs on GitHub for the results, and the total compute bill came to about $2,000.
Lean is a formal proof language that a computer can check automatically. That detail is the whole story. AI models are known for producing confident but wrong output, so a lab claiming its system cracked open problems would normally deserve heavy skepticism. A Lean proof removes the need for trust. If the verifier accepts it, the logic holds, no matter who or what wrote it.
What Mathematicians Said
OpenAI included assessments from prominent mathematicians including Noga Alon, Timothy Gowers, Arul Shankar and Jacob Tsimerman. Gowers, a Fields Medalist, said he would recommend one of the model family proofs for the Annals of Mathematics without hesitation. That is close to the highest praise a proof can receive.
The same experts supplied the caveat. These problems sit in areas that reward systematic search and construction, which is exactly where AI is strongest. The results are real, but they are not evidence that AI can now do all of mathematics, and they are not AGI.
Why It Matters
The $2,000 figure may end up mattering more than the proofs themselves. If certain research problems can be attacked for a few thousand dollars each, organizations can pursue many of them in parallel, bounded by budget rather than by how many brilliant mathematicians they can hire. Pair that with projections that AI chip deployments are doubling every nine months, and the pace of this kind of work could climb sharply.
OpenAI also demonstrated Astra to Washington policymakers, timing that lands while a White House frontier AI framework is being finalized. Astra itself remains unreleased, so the next things to watch are independent scrutiny of the published proofs and any public launch date.