FunSearch separates the roles cleanly: a language model proposes program variations, and an automatic evaluator selects candidates by score to seed later prompts. The discovered programs tend to remain readable rather than disappearing into weight updates; reported runs yielded a new largest-known cap-set construction and stronger bin-packing heuristics. Compositional Intelligence gets a precise search pattern: explicit evaluation directing variation while leaving artifacts that people can inspect and reuse.
A language model proposes a program. An automatic evaluator scores it. The best programs go back into the prompt and the loop runs again. The model supplies variation and the evaluator supplies selection.
It produced a new largest known construction for the cap set problem, an open question in extremal combinatorics, and bin-packing heuristics that beat the standard ones.
The output is a readable program rather than a weight update, so a mathematician can look at the discovery and check why it works. That is the part worth copying.