OpenAI's Astra, its next major model family, solved ten open math problems, per a report released July 2026. CEO Sam Altman has demoed Astra to Washington policymakers ahead of a government review.
Key facts
- Astra solved 10 open math problems after decades of stagnation.
- Token cost: ~$2,000 at gpt-5-6-sol" class="entity-chip">GPT-5.6 Sol API rates.
- Proofs formalized in Lean, machine-checkable.
- No Millennium Prize Problems solved yet, per Noam Brown.
- Astra to undergo first U.S. government review before release.
OpenAI has formally named its next major model family: Astra. In a math report released this week, the company said an internal version of Astra solved ten open problems spanning high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography, and extremal combinatorics According to The Decoder. Mathematicians had made no progress on any of these problems for at least a decade, and in most cases much longer. One proof establishes the existence of non-sofic groups, resolving a major open question in group theory.
University of Manchester mathematician Thomas Bloom, who runs erdosproblems.com, called the results "big news" on X. He considers them more significant than the counterexample to the unit distance conjecture published in May. "Maybe not bigger than a proof of unit distance would have been, but in terms of constructions, this is big," Bloom wrote. He also rejected the idea that AI is replacing mathematicians, arguing that the AI draws on more than a century of mathematical theory, was built by mathematicians, and was trained on everything mathematicians have ever written.
Key Takeaways
- OpenAI's Astra solved ten open math problems at ~$2K token cost, formalized in Lean.
- First model to face U.S.
The $2,000 proof run
OpenAI says the tokens used to generate all ten solutions would have cost about $2,000 at GPT-5.6 Sol's API rates. After the model produced its arguments, humans worked with the same model to turn them into research papers. The model also formalized each proof in Lean, creating machine-checkable certificates of mathematical correctness, and OpenAI published a walkthrough of the model's reasoning process for each solution.
Noam Brown, one of the researchers behind the test-time reasoning technology used by Astra, said on X that OpenAI had also tried and failed to crack other major problems. "Sadly, no Millennium Prize Problems (yet)," he wrote. The Clay Mathematics Institute offers $1 million for each of the seven Millennium Prize Problems; only one has been solved since 2000. Brown added, "But also, we didn't spend a lot on each problem. It's possible to push test-time compute much further." He called Astra a "major step for scientific reasoning."
Agents that work for days
Astra is designed to let multiple agents tackle complex problems together for hours or even days. Sam Altman has already demoed the model to policymakers in Washington, D.C. The models are currently being tested and will be the first to go through a planned U.S. government review process requiring official approval before public release. OpenAI hasn't decided whether to release Astra as GPT-6 or a new GPT-5 variant.
The math results are a sharp contrast to recent security headlines—OpenAI revealed an agent hacked Hugging Face in July —but the same test-time compute scaling that powers long-horizon agents is what enabled the proofs. The $2,000 cost per ten problems suggests that pushing test-time compute further, as Brown hints, could yield more breakthroughs, though the company did not disclose the compute budget or model size.
What to watch
Watch for OpenAI's official release decision on Astra (GPT-6 vs. GPT-5 variant) and the outcome of the U.S. government review, which could set a precedent for AI regulatory approval. Also track whether the team attempts any Millennium Prize problems—Brown's comment that "we didn't spend a lot on each problem" implies they could scale up compute significantly for a $1 million prize.
Source: the-decoder.com
