Simon Willison· CommentaryResearch paper

Ten advances in mathematics and theoretical computer science

OpenAI used an internal version of its next major model, Astra, to solve ten long-standing mathematical problems, spending less than $2,000 per problem at GPT-5.6 Sol token prices. They published Lean 4 formalizations in the openai/ten-proofs repository, a paper describing the solutions, and an LLM-generated PDF reconstructing the proof process.

From the source

They set "an internal version of Astra, our next major model" on finding solutions to ten mathematical problems that "have seen no progress on the main result for at least a decade". They claim to have spent less than $2,000 at GPT-5.6 Sol token prices on each one.

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01 Aug 2026 20:34 UTC

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