OpenAI Astra solves ten open mathematical problems for $2,000

OpenAI’s internal model Astra has produced proofs for ten mathematical conjectures that have remained open for four to five decades. The company’s announcement includes the full proofs, written in Lean, together with the complete chain of reasoning generated by the model—a scale of disclosure that is unusual for a closed system. According to Sol pricing, the total inference cost was about 2,000 tokens, i.e., about $2,000.

Among the highlighted results is an existential proof concerning infinite groups, a central question in group theory and operator algebras for the past twenty years. Astra also delivered new solutions to sphere-packing problems in high dimensions; exact solutions were previously known only in a handful of dimensions, and the breakthrough in dimensions 8 and 24 was first achieved by Marina Viazovska, who received a Fields Medal for that work. Additional achievements include a solution to Erdős problem 183 on multi-colored Ramsey numbers, a resolution of the Connes rigidity hypothesis, and a proposed solution to the Erhart volume conjecture, among others.

Details of the model itself remain undisclosed. OpenAI describes Astra as a large model from the GPT-6 family (or GPT-5.7), the same model that caused a disruption at HuggingFace earlier this year, and which Elon Altman presented at the White House this week. The company has not released the architecture, training data, or usage license; the proofs are available for download, but the model weights are not accessible. OpenAI also did not publish Astra’s training data.