FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open maths
Result confirmed
Importance: major (4 of 5)The takeaway
FunSearch (Nature, Dec 2023) paired a code LLM with an automated evaluator in an evolutionary loop.
Status
- Claim
Result confirmed
- Our reporting
- High confidence
- Verification
- Peer-reviewed
- Importance
- Major (4 of 5)
- Last verified
- 29 September 2026
Your AI and this story
- GPT-6 AstraIn its training data
- Claude Opus 5.5In its training data
- Gemini 4 HydrogenIn its training data
- Grok 4.7In its training data
It happened before the cutoffs of all four assistants, so it can be in their training data.
Key facts
- Cap set in F_3^8 of size 512, beating the previous record of 496
- Improved lower bound on cap-set capacity via new admissible sets
- Outputs are programs, so humans can read how the construction works
- Co-author: mathematician Jordan Ellenberg
What happened
DeepMind evolved short Python programs that construct cap sets, with an LLM proposing program mutations and a scorer keeping the best.
Why it matters
It was the direct ancestor of AlphaEvolve and showed that LLMs’ mistakes don’t matter when outputs can be automatically checked.
Sources
3 sources from 3 sites. Numbers match the chips in the text.
3 sources: 2 primary, 1 reaction
Primary
- Mathematical discoveries from program search with large language models (Nature)nature.com, paper
- GitHub: google-deepmind/funsearchgithub.com, code
Reactions
- Ernest Davis: comment on FunSearchcs.nyu.edu, discussion
Changes
- Filed