OpenAI's unreleased model solved 10 open math problems for $2,000

Ten problems, $2,000, and a name

On August 1, OpenAI published a 249-page document and gave its next model family a name. Sébastien Bubeck, who runs math research there, opened his post with a sentence that means nothing to most of us and a great deal to a few hundred people: @SebastienBubeck wrote "yes, nonsofic groups exist," calling it one of many new results proved by Astra, OpenAI's next major model. Ten of those results were released, each one "complete with lean certificates and CoT walkthroughs."

In plain terms, an unreleased OpenAI model produced new mathematics on ten problems that had gone essentially nowhere for at least a decade. The list includes the first explicit construction of a non-sofic group, a question left open since 1999, a disproof of Connes's rigidity conjecture, and the first improvement to a general high-dimensional sphere-packing bound since 1978.

Then Greg Brockman posted the number that made everyone else look up. @gdb said the ten advances came from an internal version of Astra at "a total cost of about $2000 at Sol API prices." Two thousand dollars, for work that had resisted the best people in the field for decades.

Why this one landed differently

Last October an OpenAI researcher announced that GPT-5 had solved a batch of open Erdős problems. It had not. The model had turned up existing papers that already solved them, and the claim fell apart in public. One of the mathematicians who corrected the record was Thomas Bloom, who maintains the Erdős problems database.

This time Bloom's reaction ran the other way. @thomasfbloom posted "Big news!" and rated the result above OpenAI's unit distance counterexample from earlier this year, adding that "in terms of constructions, this is big."

What changed between October and now is not OpenAI's marketing. Every result shipped with a Lean 4 certificate published on GitHub under an open license. Lean is a proof assistant: it walks an argument one step at a time and refuses to accept a gap. So nobody has to trust OpenAI's summary, or Bubeck, or the press coverage. You download the files and run the checker yourself.

That is an unusual way for an AI lab to make a claim. Most arrive as a benchmark chart you have no way to reproduce.

My honest read

Impressive, and smaller than some of the headlines. Astra has not been released, so nobody outside OpenAI can run the model that did this. None of the ten results have been through peer review, and mathematicians still have to confirm that the formal statements match the problems everyone believed were open. The $2,000 covers the API cost of the runs that worked, which is not the cost of the research program that produced them. OpenAI also chose which ten to publish, so we are not seeing the failures.

The checkable part is what I would actually pay attention to. Everything else is a press release with better vocabulary.

What this has to do with your business

Nothing about your invoicing changes because a model constructed a non-sofic group. The part that transfers is how the claim was made believable.

Every software vendor you talk to right now has an AI pitch attached. It will cut your response time. It will save your office manager hours every week. Almost none of those promises come with anything you can check against your own records, which means you are being asked to buy on vibes and a slide.

The question the math community just got answered is the one to borrow: show me the certificate. What number inside my business will be different in 60 days, where does that number live, and how do I look at it myself without taking your word for anything?

A vendor who cannot answer that is selling you a chart.

That is roughly how our free process audit works. We map how work actually moves through your shop or office, tell you where automation pays and where it honestly does not, and name the number that should move if it works. No software to buy and no pitch at the end.

Bloom did not change his mind because OpenAI wrote a better announcement. He changed it because they handed him files he could run himself.