Large Language Models (LLMs) have proven their prowess in tackling intricate tasks, ranging from quantitative reasoning to comprehending natural language. However, an issue that hinders their extensive use in scientific research is the occurrence of confabulations or hallucinations, leading to the generation of plausible yet incorrect statements [1,2].

To overcome this challenge, researchers have introduced FunSearch, a novel approach that combines a pre-trained LLM with a systematic evaluator. This evolutionary procedure has demonstrated remarkable effectiveness in surpassing previous state-of-the-art results in significant problems, advancing the limits of LLM-based approaches [3].

One area where FunSearch has excelled is extremal combinatorics, specifically in solving the cap set problem. By applying FunSearch, researchers have discovered new constructions of large cap sets that surpass existing solutions. This breakthrough includes both finite dimensional and asymptotic cases, marking the first-ever discoveries made for well-established open problems using LLMs.

Furthermore, FunSearch's versatility is showcased through its application to an algorithmic problem known as online bin packing. Remarkably, the procedure has identified new heuristics that outperform widely used baselines. Unlike traditional computer search methods, FunSearch focuses on finding programs that describe how to solve a problem, rather than solely seeking the solution itself.

One notable advantage of FunSearch is the interpretability of the discovered programs, making them more accessible to domain experts. This interpretability fosters feedback loops between experts and FunSearch, enabling a collaborative approach to further enhance its problem-solving capabilities. Additionally, the discovered programs can be effectively deployed in real-world applications, bolstering their practical utility.

The introduction of FunSearch represents a significant milestone in harnessing the power of LLMs for scientific discoveries. By addressing the issue of confabulations and offering a systematic evaluation approach, researchers have overcome a critical barrier in the utilization of large models for complex problem-solving.

As further advancements are made, FunSearch holds the potential to revolutionize the realm of scientific discovery and problem-solving, paving the way for unprecedented breakthroughs across various disciplines.