FunSearch makes a mathematical discovery with an LLM

Google DeepMind described FunSearch, a method that paired a large language model with an automated evaluator to search for new solutions to mathematical and algorithmic problems. Rather than ask the model for an answer directly, FunSearch asked it to write a program that produced candidate solutions; the evaluator scored each program against the problem, and the best programs were fed back to the model as the basis for further variation — an evolutionary loop with the model as the source of new ideas and the evaluator as the check on them.

The team, led by Bernardino Romera-Paredes and Pushmeet Kohli, applied it to the cap set problem, a question in combinatorics about the largest set of points avoiding certain lines, and reported the largest improvement in the known bounds in two decades. Applied to bin packing — fitting items into as few containers as possible, a problem with direct data-centre relevance — it found heuristics that outperformed standard ones. The authors described the cap-set result as the first time a genuinely new discovery on an open problem in mathematics had been made using a large language model.

The design turned the model’s unreliability into a manageable property. Because every output was a program checked by an external evaluator, wrong or nonsensical suggestions were simply filtered out, and only verifiable improvements survived. That separation — an unreliable generator paired with a cheap, exact verifier — became a recurring pattern in later attempts to use models for discovery, where the check on the output matters as much as the model producing it.