Artificial intelligence has reached new heights in the realm of mathematics, outshining human mathematicians on longstanding, unsolved problems. The innovative AI system, FunSearch, developed by DeepMind, utilizes large language models (LLMs) to generate novel solutions to combinatorics problems, a mathematical field exploring the arrangements of finite object sets.
Published in Nature on December 14, the groundbreaking technique not only showcases FunSearch's prowess in Set-inspired problems but also hints at its potential applicability across various mathematical and computer science domains. According to Pushmeet Kohli, the head of Google DeepMind's AI for Science team, "It's not just novel, it's more effective than anything else that exists today."
FunSearch operates as a creativity engine, automatically soliciting short computer programs from a trained LLM to address specific mathematical challenges. The system then swiftly assesses generated solutions against known ones, providing constructive feedback to improve subsequent iterations. Bernardino Romera-Paredes, a DeepMind computer scientist, describes the LLM as a "creativity engine," sifting through both useful and erroneous programs.
The system's prowess was demonstrated in tackling the 'cap set problem,' an extension of the game Set. While mathematicians have previously determined solutions for various game versions, certain complexities remained unsolved. FunSearch successfully improved the lower bound for a specific scenario, showcasing its ability to go beyond established mathematical knowledge.
Importantly, FunSearch stands out by offering transparency in its collaborative approach. Users can examine and learn from the AI-generated programs, setting it apart from traditional black-box AI applications. Jordan Ellenberg, co-author and mathematician at the University of Wisconsin–Madison, sees this as an exciting avenue for new modes of human–machine collaboration, emphasizing the role of AI as a force multiplier rather than a replacement for human mathematicians.
