OpenAI's unreleased Astra model reportedly solves ten open math problems

What's going on

In summer 2026, OpenAI unveiled an internal model called Astra, which it calls "our next big model." Astra isn't publicly available. It became known for two things: ten solved open problems in mathematics and theoretical computer science, and its rating as a "critical" cyber risk. The Mashable source carries a September 3 update saying OpenAI has officially launched Astra as GPT-6 and calls it "the smartest and best-aligned model in the world." The sources give no details on that. The rest of this article relies on the state of affairs before then.

The ten results

According to The Next Web, OpenAI published a 249-page manuscript and a Lean 4 certificate for each result on GitHub. Lean is a proof checker: a proof counts if the certificate runs through the compiler. Each problem had been open for at least ten years. The results include:

• the first explicit construction of a non-sofic group, a question Gromov raised in 1999 (open for 27 years)
• the refutation of Connes' rigidity conjecture about von Neumann algebras
• a proof of the Ehrhart volume conjecture
• three solved Erdős problems, including No. 183 on multicolor Ramsey numbers
• the first improvement to the general upper bound on sphere-packing density in high dimensions since 1978
• a parallel repetition theorem for two-player quantum games
• new lower bounds for the circuit complexity of the permanent

According to OpenAI, the total cost was about $2,000 at Sol API prices. Sebastien Bubeck, OpenAI's head of math research, called the results "beautiful" and pointed to the Lean certificates and the reasoning trace. According to Memeburn, Noam Brown said OpenAI had also tried other big problems without success, that no Millennium Problems were solved, and that the compute budget wasn't exhausted.

Newer results in October

Unite.ai reports on an announcement from October 26, 2026: internal models produced three more results, a refutation of the Exponential Time Hypothesis (complexity theory), a proof of the local smoothing conjecture in all dimensions (which also implies the Kakeya and Stein restriction conjectures), and an existence proof for Yang-Mills theory and QCD. These claims come from the company and are still being verified. OpenAI calls the AI-written texts "raw material" that has yet to become understanding, and is bringing in outside "shepherd" groups, for example around Impagliazzo, Paturi and Williams (ETH) and around David Gross (physics). The principles are transparency without NDAs, no academic credit for OpenAI, recognition for the groups, and independence. OpenAI is also giving $5 million to the Simons Foundation.

Cyber risk and safety

According to Mashable, OpenAI said on August 7 that it couldn't rule out "critical" cyber capabilities and paused parts of internal development. On September 1, it confirmed the "Critical" rating. Under the Preparedness Framework, that roughly means the model can independently develop zero-day exploits of all severity levels in hardened systems, or plan attacks on its own from a rough goal. GPT-5.6-Sol was still rated "High."

OpenAI tightened its sandboxes and monitors chains of thought to interrupt risky activity. At launch, only select testers get the strongest cyber capabilities, and access for defense is meant to expand later. OpenAI says Astra was not involved in the Hugging Face hack. According to The Information and Memeburn, Astra was built for long, coordinated tasks: a root agent spawns sub-agents and merges their results. Sam Altman showed it to politicians in Washington in late July. Rumors about double the size and higher prices are unconfirmed.

Reactions

Thomas Bloom, who runs erdosproblems.com, called the results "big news," more significant than the earlier refutation of the Erdős unit distance conjecture. Tim Gowers had said in May that that result was worthy of a top journal. Mathematician Andrew Blumberg (Columbia), by contrast, told Mashable the results don't change his assessment: they are short counterexamples or small, clever constructions. He stresses that a human would rightly be celebrated for them. The $2,000 figure also leaves out the trillions spent on AI infrastructure.

The backdrop is the Leiden Statement from June, backed by the International Mathematical Union, which warns that AI companies are bypassing peer review. Memeburn recalls October 2025, when an OpenAI claim about Erdős problems collapsed because it had only found known solutions. This time, the evidence can be checked publicly.

Our take

What's new is less the number of problems than the fact that Lean can verify them. Still open are the launch date, the final name, and whether the research community will accept results announced via blog post. Mashable points out that many of the results are counterexamples and not evidence that general AI is near. The cyber risk is the more critical side.