FunSearch

LLM + evaluator loop: Combines a pretrained LLM that proposes candidate programs with a systematic evaluator that scores them, iteratively evolving low-scoring programs into high-scoring ones.

New math discoveries: Produces novel solutions to open problems in combinatorics, including cap-set and online bin-packing, not memorized from the training data.

Hallucination mitigation: The evaluator acts as a hard filter - only programs that actually work are kept - so LLM hallucinations don't propagate into the "discovered" knowledge.

General recipe: Positions LLM-in-the-loop search as a general tool for scientific discovery beyond math, applicable wherever candidates can be automatically scored.