OpenAI's Astra model cracks 10 decade-old math problems for just $2,000

OpenAI just dropped a bombshell on the mathematics world, and it’s not a preprint—it’s a proof of concept. The company’s next major model, an internal version called Astra, generated solutions to ten open problems that have stumped mathematicians for at least a decade, and in most cases, far longer. The sheer breadth is what grabs you: the results span from high-dimensional sphere packing and coding theory to a disproof of Connes’s rigidity conjecture and a resolution of Erdős problem 183 on multicolor Ramsey numbers. The total compute cost to find these solutions? Roughly $2,000 at current API rates.

This isn’t a theoretical exercise. For each problem, the model produced a mathematical argument that human researchers then prepared into a manuscript. Afterward, the model formalized its own reasoning into a Lean certificate, a rigorous proof-checking language. This creates a verifiable paper trail, sidestepping the black-box criticism that often plagues AI-generated research. The company is releasing the model’s narrated thinking process for each solution, offering a rare window into how a machine arrives at novel mathematical insight.

OpenAI is clearly sensitive to the brewing controversy over AI’s role in academic discovery. The announcement directly addresses the Leiden declaration on AI and Mathematics, whose signers are wary of the technology’s impact. The company draws a sharp line: the mathematical arguments were generated by the system, while the humans took responsibility for preparing the manuscripts and verifying correctness. Claiming human authorship for a machine-generated proof, they argue, would be a misrepresentation. It’s a candid admission that sidesteps a messy authorship fight by simply crediting the tool.

This push follows the company’s recent launch of ChatGPT for Academic Researchers, which gives 100,000 scientists free access to its best models. A previous AI-generated disproof of the Erdős unit-distance conjecture already sparked a flurry of follow-up papers. The real test now is whether the broader mathematical community will engage with these ten dense, highly specialized results—or dismiss them as computational parlor tricks. A $2,000 solution to a problem like the closest vector problem, which underpins post-quantum cryptography, is the kind of thing that demands a serious look, not just a shrug.