Mathematical discoveries from program search with large language models

ABSTRACT

Large language models (LLMs) have demonstrated impressive capabilities in code generation, but their ability to discover novel mathematical knowledge has been limited by hallucinations and lack of grounding. We introduce FunSearch (searching in the function space), a method that pairs a pre-trained LLM with an automated evaluator in an iterative loop. The LLM generates creative solutions in the form of computer programs, and the evaluator provides rapid feedback, ensuring only correct and highly scored programs are retained. We apply FunSearch to the cap set problem and the bin packing problem, discovering new, verifiable results that surpass previous mathematical bounds and algorithmic heuristics.