Google DeepMind has used a large language model called FunSearch to solve an unsolvable math problem. This is the first time a language model has been used to discover a solution to a scientific puzzle. FunSearch combines a language model called Codey with other systems to reject incorrect answers and suggest good ones. The researchers started by sketching out the problem in Python and let FunSearch fill in the blanks to suggest code that solves the problem. After several million suggestions and repetitions, FunSearch produced a correct and previously unknown solution to the cap set problem. This problem is important in mathematics and is connected to matrix multiplication. FunSearch has advantages over other tools as it can be used to find solutions to a wide range of problems and its results are easier to understand. The researchers also used FunSearch to solve the bin packing problem, which it did faster than human-devised methods. Math researchers are still exploring how to incorporate large language models into their workflow, and FunSearch provides a promising way forward.
