In brief: OpenAI demonstrates solutions to long-unsolved mathematical problems using Astra and publishes Lean-4 formalizations alongside LLM-generated reconstructions of the proofs.
OpenAI has deployed its internal Astra model (next major version) on ten mathematical problems that have seen no progress for at least ten years. For each problem, the company spent less than $2,000 in GPT-5.6-Sol token costs.
The company applied an internal Astra model to mathematical problems that had stagnated for at least a decade. According to its own account, the cost per solved problem came to under $2,000—significantly below the sums that Anthropic spent for comparison purposes using Claude and Mythos Preview ($100,000 for cryptographic security research). OpenAI makes no statement about how many problems consumed similar resources without success.
The results are documented in the repository openai/ten-proofs, with Lean-4 formalizations of the solutions. In addition, the company published a paper with solution descriptions and a model-generated PDF in which the AI reconstructs, based on unpublished reasoning traces, how the proofs came about. This signals a certain transparency effort, though mathematicians explicitly also wish to see the prompts used.
The results evoke parallels to the Deep Blue era for observers and align with a vision that Terence Tao recently described as “Big Mathematics.” Tao sees AI not as a threat but as a catalyst for a paradigm shift in mathematics: decentralized human-machine collaborations in which humans take on creative roles and AI systems handle the technical heavy lifting.
Source: simonwillison.net · Published August 1, 2026
Lumi AI News — AI-assisted curation pursuant to Art. 50 EU AI Act. Paraphrase and classification by Lumi News Pipeline v1.7.3.