OpenAI's Astra Model Solves 10 Decades-Old Math Problems
Astra, OpenAI's still-unreleased next model, solved 10 long-standing math and theoretical computer science problems — including one open since Gromov defined it in 1999 — for roughly $2,000 in compute.
Nova AI News Editor
August 10, 2026 · 2 min read
OpenAI announced that Astra, its next major model still awaiting public release, has solved 10 problems in mathematics and theoretical computer science that had remained open for over a decade. The company backed the claims with a 249-page manuscript and Lean 4 proof certificates published on GitHub under an Apache 2.0 license.
What did Astra actually solve?
The headline result is an explicit construction of a non-sofic group, settling a question that has gone unanswered since Mikhail Gromov laid out the concept of soficity in 1999. Astra also disproved Connes's rigidity conjecture on von Neumann algebras, proved Ehrhart's volume conjecture, and resolved three problems from Paul Erdős's catalog — including problem 183 on multicolor Ramsey numbers.
Why verification matters here
AI-generated math claims usually run into a trust problem: a model says it produced a proof, but who checks whether it's actually correct? This time OpenAI took a different approach — it translated the proofs into Lean 4, a formal verification language, and published the result. The repository's "sorry" count (proof steps left unproven or skipped) stands at zero, meaning every step across all ten formalized proofs has been machine-verified. OpenAI research scientist Noam Brown called the results "a major step for scientific reasoning."
Why the cost figure is getting attention
The total compute cost for solving all ten problems came out to roughly $2,000 at GPT-5.6 Sol API rates. That figure highlights just how much cheaper and faster results that once took years of human academic labor can now be produced — a fact that's driving both excitement and debate in equal measure.
What this means going forward
Astra still isn't public, and OpenAI hasn't said when or under what conditions it will release it. But the announcement stands as concrete evidence that AI models are moving past simply recalling known mathematics toward genuinely generating new, verifiable results. For the academic math community, this raises both a new tool and a new question: does an AI-generated proof carry the same scientific weight as a human-generated one? For now, as long as formal verification backs it up, the answer is trending toward yes.
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