DeepMind’s new large language model (LLM), dubbed FunSearch, has achieved a major milestone in AI by making a novel scientific discovery. Specifically, FunSearch figured out the solution to one of math’s most notoriously difficult unsolved problems – the cap set problem. For decades, this puzzle has confounded researchers who have only been able to find answers for small dimensions of the problem. FunSearch was able to break new ground by finding far better constructions for large-cap sets than the most well-known ones. This marks the first time an LLM has produced a new, verifiable piece of knowledge about a longstanding puzzle in the field of math.
The cap set problem essentially involves connecting dots on a paper with lines in such a way that no three dots ever form a straight line. While simple to explain, finding solutions to larger cap set problems has perplexed mathematicians. FunSearch was able to construct never-before-seen solutions for significantly larger cap set dimensions than thought possible.
While large language models have previously been used to solve known arithmetic problems, they frequently suffer from a problem called “hallucinations.” This refers to when an LLM simply makes up information and presents it as fact. Naturally, this has limited their ability to produce scientific discoveries that can be independently verified by researchers.
FunSearch overcomes this issue by fusing the LLM with an automated “fact checker” that screens solutions for accuracy. This back-and-forth between the LLM and assessor transforms the initial solutions into verified new knowledge that expands scientific understanding.
The researchers highlighted that FunSearch doesn’t just provide answers, but also generates readable computer programs that explain its reasoning in solving problems. This level of interpretability offers scientists valuable insights into the creative problem-solving process of advanced AI systems. Additionally, the researchers expressed hopes that engaging with these computer-generated explanations could spur new ideas and advancements from scientists using FunSearch.
Although FunSearch did not completely solve the cap set problem, its ability to make even a small novel discovery related to such a notoriously difficult open problem highlights the vast potential of large language models. As the researchers stated, this marks the first time an AI system has verifiably expanded scientific knowledge of a longstanding mathematical puzzle strictly through its computational analysis.
While more work is needed, this breakthrough sparks immense excitement around how large language models could accelerate discovery across the sciences. By leveraging massive datasets and computational power, FunSearch was able to uncover something unknown to even the most brilliant mathematicians of the past decades. Its innovative blend of self-checking to filter inaccuracies also provides a promising path for overcoming limitations around trust and verification.
Ultimately, this research opens the door to a future where AI and human scientists work symbiotically to push the boundaries of our collective understanding. Findings that once seemed decades away could be unlocked much sooner through these sophisticated AI systems doing the heavy lifting on hard problems. If scaled successfully across more fields, large language models could usher in a new era of rapid advancement in math, science, and even more specialized domains like physics, engineering, and economics.
Of course, care must be taken to ensure these models are aligned with ethical principles and human values as they take on expanded roles. Additionally, while FunSearch represents significant progress, researchers emphasize it has substantial room for improvement in solving cap sets robustly. Still, its ability to make even minor verifiable discoveries highlights the vast possibilities ahead in leveraging AI to expand the scientific frontier.
