OpenAI Model Solves Ten Long-Standing Math and CS Problems

OpenAI's unreleased model solved ten long-standing open problems in math and theoretical computer science. The number worth staring at is not ten. It is $200 per problem.

The results

The model is called Astra, an internal version. Reported results include:

• The first explicit non-sofic group, a problem open for 27 years (paper title: Nonsofic Groups Exist)
• A counterexample disproving Connes's rigidity conjecture
• High-dimensional sphere packing: the exact strength of the Cohn-Elkies method
• Quantum parallel repetition for all entangled games
• Ramsey lower bounds, CVP hardness, Ehrhart-related results
• Three Erdős problems resolved

Some of these had been sitting there since the 1940s. This is the same model that disproved an Erdős conjecture in May, and the same one Sam Altman has been demoing for Congress. OpenAI's Noam Brown called it a major step for scientific reasoning.

The number that matters

Total cost to solve all ten, at GPT-5.6 Sol API pricing: about $2,000. Roughly $200 per problem.

Andrew Wiles spent seven years on Fermat's Last Theorem, a problem nobody solved for 350 years. Different difficulty class, so the comparison is unfair. But the direction is right, and direction matters more than precision here.

Someone asked the correct follow-up: what happens if you throw $20,000 of compute at harder problems? $200,000?

Why this matters if you build things

I watch token prices daily because we run a model gateway. Last week DeepSeek shipped at $0.14 per million input tokens. The week before, OpenAI cut one of its models by 80 percent. Inference cost is collapsing on a quarterly cycle.

Stack that against $200 per proof and you get an uncomfortable conclusion:

Compute budget has stopped being a finance line item. It is a research strategy variable.

Deciding whether to attack a hard problem used to depend on finding a sufficiently brilliant person and convincing them to spend five years. There is now a second path: deciding how much you are willing to pay. Discovery has acquired a purchasable component.

The detail everyone skipped

Every proof shipped with a machine-checkable certificate.

That is the foundation the $200 stands on. If a model hands you a result and you need three PhDs and two months to confirm it, then $200 was never the real price. Verification was. When the proof checks itself, verification cost collapses along with inference cost.

Which points at the pattern I keep hitting:

The bottleneck is moving from "can we produce it" to "can we verify it."

Mathematics is the cleanest demonstration, because it is one of very few domains where verification can be fully formalized. Most businesses are not that lucky.

So the practical question is not whether AI will do your work. It is which steps in your process still require a human to confirm the output. Those steps are your actual ceiling on throughput, and cheaper inference does not move them at all.

Three takeaways

1. Watch $200, not 10. Ten proves the capability exists. $200 proves it can be bought with a budget.
2. Machine-checkable proofs are the foundation. Without them, $200 just moves cost from inference to review.
3. The bottleneck is shifting to verification. Wherever you still verify by hand is your real ceiling.

None of this means mathematicians are finished. The opposite. Choosing which problem is worth attacking, and judging whether a result matters, just became the scarce skill.

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Based on OpenAI's public announcement of Astra and statements from Noam Brown (@polynoamial). Cost figures are estimates at GPT-5.6 Sol API pricing from public reporting. Results and numbers per OpenAI.