OpenAI's Astra Model Solves Decade-Old Math Problems with Lean 4 Proofs

OpenAI has announced that an internal version of its next major model, Astra, successfully solved ten mathematical problems that had seen no progress on their main results for at least a decade. The company claims to have spent less than $2,000 per problem at GPT-5.6 Sol token prices. The solutions are accompanied by Lean 4 formalizations in the openai/ten-proofs repository, a paper describing the solutions, and an LLM-generated PDF that reconstructs the proof process from unpublished reasoning traces. This level of transparency is notable, though the prompts used were not disclosed. The announcement follows a similar effort by Anthropic, which used Claude with Mythos Preview to discover cryptographic weaknesses, spending $100,000 on tokens. Mathematicians online have reacted with a collective sense of a 'Deep Blue moment.' The work echoes Terence Tao's concept of 'big mathematics,' as described in IEEE Spectrum in June, which envisions large-scale, decentralized collaborations between humans and machines, with AI handling technical grunt work and humans focusing on creative aspects. The post was made by Simon Willison on 1st August 2026.