OpenAI announced Saturday that an internal version of its next major AI model, called Astra, generated solutions to ten longstanding unsolved problems spanning mathematics and theoretical computer science—each unresolved for at least a decade. The company says the model doesn't just answer hard questions but can help create new mathematics. The compute cost to generate the raw output for all ten solutions totaled roughly $2,000 at GPT-5.6 Sol API rates, according to the announcement.
The targeted problems covered quantum complexity, high-dimensional sphere packing, lattice cryptography, and group theory. OpenAI released a 249-page collection of manuscripts alongside computer-verifiable Lean 4 proof certificates on GitHub to support its claims. The repository's "sorry" count—the marker Lean uses when a proof step remains unproven—stands at zero, meaning the compiler verified every logical step. The most notable result is an explicit construction of a non-sofic group, settling a fundamental question in group theory that mathematician Mikhail Gromov introduced in 1999. Astra also produced a counterexample to Connes's rigidity conjecture about group von Neumann algebras, proved Ehrhart's volume conjecture, and resolved three items from Paul Erdős's famous problem catalog, including problem 183 on multicolor Ramsey numbers.
According to OpenAI, while Astra handled the underlying mathematical reasoning, human researchers transformed the model's outputs into formal papers suitable for publication, after which the model formalized each argument into Lean code. The company notes that none of the ten findings have undergone traditional academic peer review yet, and human mathematicians must still confirm that the formalized statements accurately map to the original open questions and evaluate the broader significance of the findings. Public access to Astra remains pending because the system must clear a newly established federal AI safety review process in the United States before launch.
The announcement reflects a dramatic shift in the economics of scientific research. Solving ten historic mathematical problems for the price of a mid-tier laptop shows that deep academic reasoning is quickly becoming a cheap commodity. When high-level problem-solving costs thousands of dollars instead of millions in research grants, the report says the primary bottleneck in science shifts from generating breakthrough ideas to human validation. Tech firms and research institutions will soon need to adapt to an environment where machines churn out complex theoretical frameworks faster than human experts can evaluate them, forcing a fundamental rethink of academic publishing, research budgets, and intellectual property.
The timing adds tension: the International Mathematical Union endorsed the Leiden Declaration in June, which warns that AI developers risk eroding standards around proof, consent, and scientific credit. Tech firms and research institutions now face competing pressures—machines can produce theoretical breakthroughs at commodity prices, but the infrastructure to validate those breakthroughs at scale doesn't yet exist. The academic establishment's capacity to verify claims will determine whether automated discovery accelerates progress or simply floods journals with unvetted conjecture.