OpenAI's Astra Solved Ten Decade-Old Math Problems for $2,000
An internal OpenAI model cracked ten open problems in mathematics for roughly $2,000, signaling a concrete shift in AI's role from research tool to research agent.
1. OpenAI's Astra Solved Ten Decade-Old Math Problems for $2,000
On August 1, 2026, OpenAI published results showing an internal version of Astra, its next major model, solved ten open problems in mathematics and theoretical computer science. Each problem had seen no meaningful progress for at least a decade. The problems span high-dimensional sphere packing, binary and spherical codes, non-sofic groups, Connes's rigidity conjecture, arithmetic circuit complexity, quantum parallel repetition, the closest vector problem, Ehrhart's volume conjecture, multicolor Ramsey numbers, and two Erdős extremal graph conjectures. Total compute cost: roughly $2,000 at Sol API rates. After finding solutions, the model also formalized each argument as a Lean certificate.
The competitive frame here is not about benchmarks. Google DeepMind's AlphaProof and related systems have shown AI can verify and search mathematical proofs, but the claim from OpenAI is different in kind: Astra is generating novel arguments on open problems, not checking human-written ones. That shifts the question for labs like DeepMind, Anthropic, and academic math departments from "can AI assist mathematicians" to "at what cost does AI replace the decade-long research arc." The $2,000 figure is the sharpest data point. It prices a category of mathematical labor that previously had no market rate, and it does so in a way that is directly comparable across future model versions.
OpenAI also announced ChatGPT for Academic Researchers in the same period, giving 100,000 scientists free access to its best models. That program and this publication are coordinated positioning: establish the tool, then demonstrate what the tool can do at the frontier. The next signal to watch is independent verification by the named mathematical communities, particularly on the non-sofic groups construction and the Connes disproof, both of which carry broad implications well outside their immediate subfields.
Source: Ten advances in mathematics and theoretical computer science