OpenAI has revealed Astra, its next major model, by dropping a striking demonstration: an internal version solved 10 open problems in mathematics and theoretical computer science that had resisted human progress for a decade or more. Every proof came with a machine-checkable certificate. The results are impressive, and the cost, about $2,000 in compute, may be the most startling part.

Key Takeaways

• OpenAI unveiled Astra, described as its next major model family
• An internal version solved 10 long-open math and CS problems
• Each result came with a Lean-verified, machine-checkable proof
• The total compute cost was roughly $2,000 at Sol API rates
• The results are not yet peer-reviewed, and debate is underway

What OpenAI Revealed

In a research post, OpenAI introduced Astra as its next major model and used a batch of mathematical breakthroughs to announce it. The company said the problems had seen no progress on their central results for at least a decade, and in most cases much longer.

The scope of the work:

• Fields covered: High-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, quantum complexity, lattice cryptography, and extremal combinatorics
• Standout results: An explicit construction of a non-sofic group, a disproof of Connes’s rigidity conjecture and a proof of Ehrhart’s volume conjecture, plus improved bounds on high-dimensional sphere packing
• The output: A 249-page manuscript collection published alongside Lean 4 certificates and model-generated walkthroughs of the reasoning, posted to GitHub
• The ask: OpenAI wants the mathematical community to examine the discoveries, establish their significance, and build on the underlying ideas

Astra is described as a model family built for long-running workloads, designed to let AI agents collaborate on different parts of a larger problem. The Information independently confirmed OpenAI is working on it.

The $2,000 Detail

The cost figure is what turned heads across the field. OpenAI emphasized that it did not spend enormous amounts of compute to achieve these results.

The economics, as OpenAI described them:

• The total tokens needed to find all 10 solutions would cost roughly $2,000 at GPT-5.6 Sol API rates
• After the model found solutions, human researchers used the same model to prepare the arguments as manuscripts
• Astra then formalized every argument in Lean, allowing the proofs to be checked by the theorem-proving system

Noam Brown, a researcher behind the test-time reasoning technology Astra uses, noted the model didn’t crack everything. “Sadly, no Millennium Prize Problems (yet),” he wrote, adding that OpenAI didn’t spend much per problem and that test-time compute could be pushed much further.

Why the Machine-Checkable Proofs Matter

The Lean certificates are central to why these claims carry weight. Unlike a chatbot asserting an answer, a Lean-verified proof can be mechanically checked for correctness.

What verification does and doesn’t settle:

• Settles: Whether the logical steps of each proof hold together, checkable by the Lean system rather than trust
• Doesn’t settle: Whether the results have passed refereed journal peer review, which none have yet
• Doesn’t settle: Independent replication of the discovery process, as opposed to verification of the proofs, which is hard to do right now

OpenAI says it takes responsibility for the manuscripts and Lean formalizations, while attributing the mathematical arguments themselves to the model, an authorship arrangement the field is still negotiating.

The Expert Reaction

Response from mathematicians has been a mix of genuine excitement and careful caveats. This is where the nuance matters most.

The positive read:

• OpenAI math research head Sébastien Bubeck confirmed the results on X, calling each one “beautiful,” while Noam Brown called them a major step for scientific reasoning
• The non-sofic groups construction is the standout, the first of its kind after 27 years where no one had one at all, with a technique expected to generalize
• Several other results, like the sphere-packing bound and a closest-vector-problem hardness result, are direct improvements to standing bounds, not mere counterexamples

The skeptical read:

• Roughly half the ten are outright resolutions of named conjectures, while the rest are improved bounds, a real contribution but not the same as “solved”
• All ten results come from one lab, one unreleased model, and one coordinated manuscript, so independent scrutiny matters
• No peer review has happened yet, so significance remains informally assessed from preprints, and authorship is still being negotiated

What It Signals About Astra

The math showcase is really a preview of a broader ambition. OpenAI frames Astra as a step-change in scientific reasoning, not just a math tool.

The capabilities the demonstration hints at:

• Working on problems continuously for hours or even days at a time
• Letting multiple AI agents collaborate on parts of a larger problem
• Applying the same low-cost, verifiable approach beyond math into domains like drug discovery and materials science

OpenAI hasn’t decided whether the model will ship as GPT-5.7, GPT-6, or under another name, and the wider release timeline remains unclear. For now, Astra exists as an internal system OpenAI is using to make a point about where scientific reasoning is heading.

Why It Matters

The significance runs deeper than 10 proofs. If a well-posed open problem can be handed to a model and checked in Lean for a few thousand dollars, the bottleneck in parts of mathematics could shift from producing arguments to posing the right questions.

The broader stakes:

• For math: The most immediate change may be in what mathematicians choose to spend their time on, moving from proving toward framing and verifying
• For science: The same cheap, verifiable approach could accelerate fields far beyond math, if it generalizes
• For the AI race: Astra positions OpenAI’s next model around scientific reasoning, a high-value frontier rivals are also chasing

The honest takeaway is measured optimism. The proofs are real and verifiable, but they’re unreviewed, built on a century of human work, and limited to problems that can be cleanly formalized. Astra is a genuine milestone worth watching closely, not a declaration that AI has replaced the mathematician. As these results get picked apart by the field in the coming weeks and months, their true significance will come into focus.

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