# Simon Willison — Ten advances in mathematics and theoretical computer science

- Company: Simon Willison (simonwillison.net)
- Announced: 2026-08-01T20:34:49+00:00
- Category: research-paper
- Subject: Commentary
- Models affected: Astra
- Source: https://simonwillison.net/2026/Aug/1/ten-advances-in-mathematics/#atom-everything
- Record: https://forck.live/items/3013-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.

## Evidence

Verbatim from https://simonwillison.net/2026/Aug/1/ten-advances-in-mathematics/#atom-everything:

> 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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Record: https://forck.live/items/3013-ten-advances-in-mathematics-and-theoretical-computer-science
Catalogue: https://forck.live/llms.txt
Feed: https://forck.live/feed.md