OpenAI's next major model Astra claims breakthroughs on 10 long-standing math problems
TLDR ● Covered by 3 sources
OpenAI previewed Astra, its next big model, and it just cracked 10 math problems that sat unsolved for decades. Total compute cost: about $2,000.
OpenAI didn't wait long to tease what comes after GPT-5.6. Barely five weeks after that model rolled out to the public, the company showed off an internal build of its next frontier system, called Astra, and used it to make headway on ten open problems in math and theoretical computer science. Some of these questions had been sitting untouched for ten years or more. A few, like Erdős problem 183 on multicolor Ramsey numbers, have been kicking around since the mathematician himself was alive.
What's striking isn't just that Astra found new results — it's how cheap the whole exercise was. OpenAI says the total token spend across all ten discoveries would run about $2,000 at GPT-5.6 Sol API pricing. That's a rounding error for a lab that reportedly burns through enormous GPU budgets on training runs. The company didn't throw a data center at these problems; it just pointed a model at them and let it think.
The range of topics is the other notable part. Astra tightened bounds on sphere-packing density near the Cohn–Elkies threshold, produced exponential improvements on binary and spherical code sizes, and built a construction proving non-sofic groups exist — a question group theorists have wrestled with for years. It also disproved Connes's rigidity conjecture, delivered new arithmetic circuit lower bounds for the permanent, and worked out a quantum parallel repetition theorem that extends a classical complexity idea into two-player quantum games. There's a hardness result for the closest vector problem, relevant to post-quantum cryptography, plus answers on Ehrhart's volume conjecture and two more Erdős problems in extremal graph theory.
OpenAI isn't just claiming a win here and moving on. After the model surfaced these proofs, researchers used Astra itself to write them up as manuscripts and then formalized each argument in Lean, the theorem-proving language mathematicians use to machine-verify logic step by step. The company is releasing the manuscripts, the Lean certificates, and the model's own reasoning walkthroughs so outside mathematicians can pick them apart, confirm the results hold, and build on whatever techniques Astra stumbled into along the way.
My take
I'll believe the hype once independent mathematicians have actually chewed through these Lean certificates, not before — OpenAI grading its own homework on ten notoriously hard problems is exactly the kind of claim that needs outside verification. That said, if even three or four of these hold up, it's a real signal that these models are starting to do something closer to research than autocomplete, and the $2,000 price tag should scare every math department that thought this was decades away.
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