---
id: "2023-12-14-funsearch-cap-sets"
url: "https://postcutoff.com/e/2023-12-14-funsearch-cap-sets/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2023-12-14"
date_precision: day
category: science
importance: 4
confidence: high
status: [Result confirmed]
verification: Peer-reviewed
sources: 3
editor: human editor
human_review: null
version: "2026-10-04"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2023-12-14-funsearch-cap-sets/

# FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open maths

FunSearch (Nature, Dec 2023) paired a code LLM with an automated evaluator in an evolutionary loop. It found a cap set of size 512 in dimension 8 (previous best 496) and better lower bounds on the asymptotic cap-set capacity. It also found bin-packing heuristics beating first-fit and best-fit.

## 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.

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): in its training data
- Claude Opus 5.5 (training cutoff June 2026): in its training data
- Gemini 4 Hydrogen (training cutoff March 2026): in its training data
- Grok 4.7 (training cutoff May 2026): in its training data

## Sources

1. [Mathematical discoveries from program search with large language models (Nature)](https://www.nature.com/articles/s41586-023-06924-6) (nature.com, paper)
2. [GitHub: google-deepmind/funsearch](https://github.com/google-deepmind/funsearch) (github.com, code)
3. [Ernest Davis: comment on FunSearch](https://cs.nyu.edu/~davise/papers/FunSearchComment.pdf) (cs.nyu.edu, discussion)

## Changes

- 2026-09-29 (filed): Created

## Related

- 2025-05-14: [AlphaEvolve: Gemini-powered agent discovers new algorithms](https://postcutoff.com/e/2025-05-14-alphaevolve/index.md)