OpenAI Astra math solutions solved ten open problems in mathematics and theoretical computer science. The company said the internal version of Astra handled work that had seen no progress for at least a decade in most cases. That makes the model's first public math showing less about a demo and more about proof generation.
OpenAI Astra and ten problems
OpenAI released its math report this week and used it to name Astra for the first time. The results covered high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography, and extremal combinatorics. One proof established the existence of non-sofic groups.
The company said the ten solutions came from arguments the model produced itself. Humans then worked with the same model to turn those arguments into research papers. OpenAI also said the model formalized each proof in Lean and created machine-checkable certificates of mathematical correctness.
Thomas Bloom on X
Thomas Bloom, the University of Manchester mathematician who runs erdosproblems.com, called the results "big news" on X. He said they were more significant than the counterexample to the unit distance conjecture published in May. He also wrote, "Maybe not bigger than a proof of unit distance would have been, but in terms of constructions, this is big".
Noam Brown said OpenAI had also tried and failed to crack other major problems. He wrote, "Sadly, no Millennium Prize Problems (yet)," and added, "But also, we didn't spend a lot on each problem. It's possible to push test-time compute much further." He also called the work "a major step for scientific reasoning" on X.
Lean proofs and GPT
OpenAI said the tokens used to generate all ten solutions would have cost about $2,000 at Sol's API rates. The company said its researchers helped prepare the papers and formalize the proofs. OpenAI said it takes responsibility for the accuracy of the papers and proofs.
The part to watch next is whether Astra stays a research system or becomes the model family that follows GPT. OpenAI said the new Astra family is meant to be far more capable at long-running tasks than anything it has shipped so far, but it did not tie the name to GPT-6 or any other label.
