# New paths through mathematics.

FunSearch combined language models with program evaluation to discover mathematical constructions.

Canonical: https://brightaifuture.com/discoveries/funsearch
Format: story
Source publication: 2023-12-14
Bright publication: 2026-09-05
Substantive update: None recorded
Evidence and review: Demonstrated; confidence: unassessed; source-checked; legacy source check. Legacy source check; no named human reviewer is recorded in this projection.

## The human problem

Some combinatorial problems have vast search spaces.

## The prior constraint

Researchers develop and evaluate candidate constructions.

## AI’s actual role

Generated programs were tested, selected, and iteratively improved.

## The documented result

The study found new constructions for the cap set problem and useful packing heuristics.

## Why it may matter

Researchers gained an additional experimental tool.

## Limitations

The approach depends on an evaluator; it is not a general proof engine.

## Unresolved questions

Apply verifiable search to other suitable problems.

## Provenance and history

{
  "dates": {
    "eventDate": null,
    "publicationDate": "2023-12-14",
    "captureDate": null,
    "lastReviewedDate": "2026-09-05"
  },
  "provenance": {
    "origin": "legacy-projection",
    "externalId": "funsearch"
  },
  "revisions": [],
  "corrections": []
}

## Original sources

- [Mathematical discoveries from program search with large language models](https://www.nature.com/articles/s41586-023-06924-6)

## Continue exploring

- [Concise evidence record](https://brightaifuture.com/discoveries/funsearch)