OpenAI's next model Astra solved 10 unsolved math problems — and cost just $2,000 in compute

OpenAI's next major model has a name — Astra — and its debut came not through a press conference, but buried inside a research post about mathematics published August 1. The company released ten breakthrough proofs generated by an internal version of Astra, accompanied by a 249-page manuscript, step-by-step reasoning walkthroughs, and formal Lean certificates verifying each result.

The ten problems Astra cracked had seen no meaningful progress for at least a decade, and most had been stuck for far longer. The results span high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography, and extremal combinatorics — some of the hardest active areas in pure mathematics and theoretical computer science.

What Astra actually proved

Among the most significant achievements: Astra disproved Connes's rigidity conjecture on von Neumann algebras, a problem that had stood since the 1970s. It proved Ehrhart's volume conjecture and resolved three problems from Paul Erdős's famous open-problem catalogue, including Erdős problem #183 on multicoloured Ramsey numbers. The model also produced the first improvement to the general upper bound on high-dimensional sphere-packing density since 1978 — more than 45 years without progress on that result.

Other proofs included a parallel repetition theorem for two-player quantum games and new lower bounds on the circuit complexity of computing the permanent. The existence of non-sofic groups, a fundamental question in geometric group theory, was also established.

According to OpenAI, the mathematical arguments themselves originated from Astra. Human researchers then formalized the proofs and prepared them for publication, but the core reasoning was machine-generated. The total compute cost for all ten solutions was approximately $2,000 at Sol API rates — a striking number given the decades researchers spent on these problems without success.

A tease, not a release

OpenAI has not announced a public release date or confirmed the final name. Astra could ship as GPT-5.7, GPT-6, or under another designation entirely. The company mentioned tiered access is being considered, similar to Anthropic's model structure.

Notably, Astra is expected to be the first model reviewed under the Trump administration's new AI safety framework, which requires federal government sign-off before a frontier model can be publicly released. That requirement adds an unpredictable timeline to what would otherwise be a straightforward product launch.

OpenAI had previewed some of this capability in May 2026, when an internal general-purpose model used ideas from algebraic number theory to disprove the long-standing Erdős unit-distance conjecture. The August release makes clear that was not a one-off — it was Astra learning to do mathematics at a level that exceeds what most human specialists can accomplish, across a broad range of subfields simultaneously.

As first reported by The Next Web, the announcement effectively smuggled a major model reveal into what looked like a routine research publication.