OpenAI Names Astra as Its Next Major Model — Pre-Release Solves 10 Unsolved Math Problems
OpenAI has officially named its next major model: Astra. The confirmation arrived not via a product launch but through a math paper — an internal build of Astra resolved ten open problems in pure and applied mathematics, all unsolved for at least a decade and several open for far longer.
The ten results, published Friday alongside Lean certificates on GitHub, span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. Total compute to find the solutions: roughly $2,000 at Sol API rates. Humans then prepared the manuscripts with the same model; the model formalized each argument in Lean independently.
The Ten Problems
| Problem | Result |
|---|---|
| High-dimensional sphere packing | New upper bounds down to the Cohn-Elkies threshold |
| Binary and spherical codes | Exponentially improved max-code-size bounds at any prescribed distance |
| Non-sofic groups | Construction establishing the existence of non-sofic groups |
| Connes’s rigidity conjecture | Disproof: certain groups are not uniquely determined by their von Neumann algebras |
| Arithmetic circuit complexity | New lower bounds for computing the permanent; formula lower bound of n^4/log n |
| Quantum parallel repetition | Exponential parallel repetition theorem for general two-player quantum games |
| Closest vector problem | Polynomial-factor hardness of approximation (related to post-quantum cryptography) |
| Ehrhart’s volume conjecture | Maximum convex-body volume whose centroid is its only interior lattice point, solved in every dimension |
| Multicolor Ramsey numbers | Superexponential lower bound for multicolor triangle Ramsey numbers (Erdős problem 183) |
| Extremal number conjectures | Compactness and degeneracy conjectures resolved (Erdős problems 146 and 180) |
Each result is described as substantively new by the respective mathematical communities. Several — including the non-sofic groups construction and the Connes conjecture disproof — are broadly significant across mathematics as a whole. The closest-vector-problem hardness result bears directly on the security foundations of post-quantum cryptography.
The Astra Context
This is the first time OpenAI has officially confirmed “Astra” as a model name in any public communication. The company has been evaluating it internally before release. In May, the same evaluation pipeline surfaced an AI-generated disproof of the Erdős unit-distance conjecture. That disproof has already generated follow-on work; Friday’s paper is the next tranche from that evaluation track.
The Lean formalization is notable. It is not enough to publish an argument; the model also generates machine-checkable proofs from axioms. OpenAI released the Lean certificates to GitHub alongside the paper. The combination — new results plus formal verification — sets a floor on correctness that informal math papers cannot reach.
Attribution and the Leiden Declaration
OpenAI explicitly addressed attribution. The company is not claiming human authorship for proofs generated entirely by an AI system. The paper states: “the mathematical arguments themselves were generated by an internal version of Astra.” Human collaborators prepared manuscripts and verified correctness; the intellectual content is attributed to the model.
The post acknowledges the Leiden Declaration on AI and Mathematics, signed by mathematicians who have raised concerns about AI’s effect on the discipline. OpenAI’s position: AI-generated proofs should be attributed honestly, and claiming human authorship for model-generated arguments misrepresents both the system and the nature of human intellectual work.
What Comes Next
OpenAI announced ChatGPT for Academic Researchers alongside the math paper, giving 100,000 scientists free access to its best ChatGPT models. The research initiative positions Astra as a scientific tool before it reaches the product tier.
Astra’s timeline to public release was not disclosed. What is now on record: at current pre-release capability, a single model can resolve open problems across at least eight distinct mathematical domains at a cost orders of magnitude below what a funded research group would spend on the same questions.
Key Numbers
- Problems solved: 10 open problems, each open for at least a decade
- Compute cost: approximately $2,000 at Sol API rates for all ten
- Formalization: Lean certificates published to GitHub for each proof
- Fields covered: geometry, coding theory, group theory, operator algebras, quantum complexity, lattice cryptography, combinatorics
- Previous result: Erdős unit-distance conjecture disproof (May 2026, same evaluation track)