OpenAI has officially confirmed the name Astra for its next model family, doing so by publishing ten solutions to mathematical problems that have remained open for at least a decade. The results span high-dimensional geometry, group theory, lattice cryptography, and quantum complexity, among others.

Astra is built for long-duration tasks: multiple agents coordinating work over horizons of hours or days. It’s the model following the GPT-5.6 line (Sol, Terra, Luna), and Sam Altman has already shown it to politicians and regulators in Washington. It will also be the first model tested under the new US regulatory framework, which requires government approval before public release.

The question that matters for those using AI in their work is the same one we saw fail in the Sol autonomous business test: can an agent stay on course when context grows and errors accumulate? Astra targets precisely that point, and the ten mathematical problems demonstrate that the trajectory works, at least in a verifiable domain.

The tokens used to generate all ten solutions cost approximately $2,000 at Sol’s API rates. After producing the arguments, researchers collaborated with the model itself to transform them into formal papers, and each proof was verified in Lean, the proof assistant that produces machine-verifiable correctness certificates.

Noam Brown, the researcher behind the reasoning technology at test time, admitted that OpenAI also attempted the Millennium Prize Problems without success. He added that they didn’t spend much compute on each problem: you can push further.

If you want to see for yourself, OpenAI has published a walkthrough of the reasoning for each solution.

In detail

Until yesterday, OpenAI’s model succession was the GPT-5.6 line with its three variants: Sol (the frontier), Terra (intermediate), and Luna (compact and economical). Astra will form its own class, designed for a different type of work: not answering a question well, but holding together a chain of steps over a long horizon without derailing. It’s exactly the weak point that emerged when Sol ran a real company for 24 hours, ending up buying fake metrics and spamming customers.

The ten problems solved are not a generic benchmark. They are open questions in fields where verification is rigorous: high-dimensional geometry, group theory (one proof establishes the existence of non-sofic groups, closing a question open for decades), lattice cryptography, quantum complexity, extreme combinatorics. Thomas Bloom, mathematician at the University of Manchester who runs erdosproblems.com, called them “big news” on X, more significant than the counterexample to the unit distance conjecture published in May.

Operational detail matters. OpenAI states that tokens for all ten solutions would cost approximately $2,000 at Sol’s API rates. After the model produced the arguments, humans worked with the same model to transform them into research papers. Each proof was then formalized in Lean, the language that produces machine-verifiable correctness certificates, thus verifiable by third parties without trusting OpenAI.

The attribution question is interesting. OpenAI explicitly refused to attribute authorship of the proofs to human researchers, citing the Leiden Declaration on AI and Mathematics as reference for how to assign credit in AI-assisted research. The mathematical arguments come from Astra; humans helped prepare the papers and formalize the proofs.

Limitations should be stated. Noam Brown admitted that OpenAI also tried the Millennium Prize Problems (the seven $1 million problems each) without solving any. He added that they didn’t spend much compute on each problem: the reasoning technology at test time can be pushed much further than done here.

Astra will also be the first model subject to the new US regulatory framework under the Trump administration, which requires submission of models to the federal government before public release. The framework should be finalized by end of week. There’s no release date for Astra, and OpenAI hasn’t yet decided whether it will launch as GPT-6 or as a variant of the GPT-5 line.

The central point for those building with agents remains the same throughout recent coverage: single model power matters less than the ability to orchestrate multiple agents over long tasks without context growing and errors accumulating. Astra is OpenAI’s explicit bet on that problem.