Ten advances in mathematics and theoretical computer science
Simon Willison's Weblog Simon Willison ● Covered by 9 sources
OpenAI used an internal Astra model to crack ten decade-stuck math problems, spending under $2,000 in tokens per solve. Mathematicians are having their own Deep Blue moment, and OpenAI even published Lean 4 proofs to back it up.
Based on reporting by Simon Willison's Weblog, Simon Willison — read the original for the full story.
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OpenAI is having its Anthropic moment. Just days after Anthropic disclosed it had spent $100,000 in tokens hunting for cryptographic weaknesses with Claude via Mythos Preview, OpenAI is showing off what an internal version of Astra, its next major model, can do with hard math. The company set the model loose on ten mathematical problems that had seen no progress on their main result for at least a decade. It claims each one was solved for less than $2,000 at GPT-5.6 Sol token prices.
There's an obvious gap in that framing, though. OpenAI hasn't said how many problems it threw money at without getting a solution. Ten wins is a nice number to publish. It says nothing about the denominator.
Still, the transparency on offer is more than a press release. The openai/ten-proofs repository contains Lean 4 formalizations of the results, there's an accompanying paper walking through the solutions, and OpenAI even generated an LLM-written PDF that reconstructs how each proof came together, built from reasoning traces that weren't otherwise published. That's a genuinely useful artifact for anyone trying to understand what the model actually did, even if the prompts themselves remain hidden.
The reaction from mathematicians has been described as a collective Deep Blue moment, the same jolt chess players got when a machine started beating grandmasters. It echoes something Terence Tao said back in June, when he described AI as pushing the field toward what he called big mathematics: large, decentralized collaborations where humans handle the creative leaps and machines grind through the technical work. Tao wasn't dismissive of AI, and he wasn't scared of it either. He just thinks the shape of the discipline is about to change.
What's missing from OpenAI's announcement is the same thing that's always missing from these showcases: the prompts, the failure rate, the full cost of the misses. Until that's public, this reads more like a highlight reel than a research report.
My take — AI-written commentary, not fact-checked reporting
Publishing the wins without the losses is a marketing move dressed up as science, and mathematicians cheering the Deep Blue comparison should ask how many problems got quietly abandoned along the way. Lean proofs and a reconstructed reasoning PDF are nice, but the prompts are the actual method, and withholding them keeps this from being reproducible research. Tao's big mathematics idea is probably right, but it only works if labs stop treating their process as a trade secret.
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