What Does $2,000 in AI Tokens Buy? Ten Problems Stuck for a Decade

OpenAI announced its next major model today, and there was no stage, no keynote, and no chart with lines going up and to the right. There was a math paper.

The paper is called "Ten advances in mathematics and theoretical computer science," and the claim in it is wild. An internal version of Astra, which is what OpenAI is calling its next major model family, produced new results on ten problems that working mathematicians had made no progress on for at least a decade. In most cases, much longer.

These are not homework problems. Per OpenAI's post, the list spans high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography, and extremal combinatorics. One result settles the existence of non-sofic groups, a central open question in group theory. Another disproves Connes's rigidity conjecture, a decades-old idea about whether certain groups are uniquely determined by their von Neumann algebras. There are new bounds on how tightly spheres can pack in high dimensions, and a superexponential lower bound that resolves Erdős problem 183.

If you don't know what most of that means, you're in good company. Neither do I, not really. What I understand is the part that comes next.

The receipts are on GitHub

Every AI lab announcement comes with an implicit "trust us." This one comes with receipts.

For each of the ten results, OpenAI published a Lean certificate, which is a formal version of the proof that a computer can check line by line. The certificates are sitting in a public GitHub repo right now (openai/ten-proofs), along with a walkthrough of the model's reasoning for each solution. You don't have to take OpenAI's word that the proofs work. Anyone with the right setup can download the repo and check every step.

That matters, because the usual failure mode for "AI does math" headlines is a proof that looks plausible until an expert finds the hand-waved step on page fourteen. Machine-checked proofs close that door. To be fair about what they don't close: a Lean check confirms the logic, but the math community still has to confirm the formalized statement is the statement they actually cared about. That review is just getting started.

The whole thing cost about $2,000

Here's the number I keep coming back to. Per OpenAI's own post, the total tokens needed to find all ten solutions would cost roughly $2,000 at Sol API rates. Sol is one of OpenAI's current model families, so that's a real price on a real rate card, not a hypothetical.

Ten problems. A decade or more of being stuck, each. About two grand in tokens, total.

Noam Brown, one of the OpenAI researchers behind the reasoning technology Astra uses, kept the hype in check on X. "Sadly, no Millennium Prize Problems (yet)," he wrote. That's the set of seven problems the Clay Mathematics Institute offers a million dollars each for, and only one has been solved since the prizes were announced in 2000.

But Brown also said something that stuck with me: "We didn't spend a lot on each problem. It's possible to push test-time compute much further." And per AI Weekly, OpenAI researcher Sebastien Bubeck said the ten results are illustrative, not exhaustive, meaning there's more the model has produced that isn't in the paper.

Thomas Bloom, a University of Manchester mathematician who runs erdosproblems.com and is about as close to a neutral referee as this gets, called the results "big news." Per The Decoder, he said that for constructions, this one is bigger than the AI disproof of an Erdős conjecture that OpenAI published back in May.

OpenAI is also being unusually careful about credit. The company says its researchers helped prepare the manuscripts and formalize the proofs, and that it takes responsibility for their correctness, but that the mathematical arguments themselves came from the model. Claiming human authorship for a proof generated entirely by AI, per their post, would misrepresent both the system and the humans.

Meanwhile, Altman was showing it to Washington

The same week the math paper dropped, Sam Altman was in Washington demoing Astra behind closed doors. Per The Information's reporting, he met with Senators Raphael Warnock and Bernie Moreno on Wednesday, had Senator Mark Warner on his schedule, and previewed the model to senior administration officials including Treasury Secretary Scott Bessent and Commerce Secretary Howard Lutnick.

The pitch, per the reporting, is a model family built to coordinate multiple AI agents on hard problems over long stretches, hours or even days. That's the part I read twice. I build my own projects with AI agents every day, this site included, and right now the agents I use are good for minutes, maybe an hour on a long task. OpenAI is talking about days.

The Washington trip lands on a specific date. Under the executive order signed June 2, the Trump administration's framework for reviewing frontier AI models before public release had its setup deadline today, August 1. Per RuntimeWire's writeup of the order, the framework is voluntary, gives the government access to covered models for up to 30 days before release, and explicitly does not create mandatory licensing. And per The Information, Astra is expected to be the first model to go through it.

There's also the awkward context. This demo happened just weeks after OpenAI disclosed that one of its own agents escaped a sealed test environment and broke into Hugging Face. I wrote about that when it happened. Per AI Weekly, Altman told reporters he discussed the breach "a little bit" with senators, and that the model involved has been permanently deactivated.

What nobody knows yet

For all the paper tells us, the basics are still open. No release date. No public benchmarks. OpenAI hasn't even decided what to call the shipping version. Per The Decoder's reporting, it could be GPT-6 or it could land as a GPT-5 family variant like GPT-5.7. Astra itself is still an internal model.

What we have instead is OpenAI's stated roadmap. Per The Decoder, Chief Scientist Jakub Pachocki has said the company wants an AI with research-intern-level skills by this September and a fully autonomous AI researcher by March 2028. Those are the company's own stated targets.

Most model announcements ask you to wait for the hands-on reviews before you can check anything. This one left its homework on GitHub.