OpenAI has deployed an internal version of its next major model, Astra, to solve ten mathematical problems that have seen no progress on the main result for at least a decade. The company claims to have spent less than $2,000 at current GPT-5.6 Sol token prices on each one. Results are available in the openai/ten-proofs repository with Lean 4 formalizations and a paper describing the solutions. An additional LLM-generated PDF reconstructs how the proof came together based on unpublished reasoning traces. This follows Anthropic discovering cryptographic weaknesses with Claude earlier in July after spending $100,000 on tokens.
The work demonstrates a shift toward what mathematician Terence Tao describes as big mathematics. This approach envisions large-scale collaborations where humans claim creative parts and AI handles technical grunt work. The specific cost per problem highlights the efficiency of modern large language models for verification tasks. Transparency remains a key factor in how the community accepts these findings.
- Results are in the openai/ten-proofs repository
- Cost was under $2,000 per problem
- Anthropic spent $100,000 on similar research
