Compiled by Sahar Yaghoubi
In a groundbreaking development, Google DeepMind has harnessed the power of large language models to crack a famous unsolved problem in pure mathematics. Published in the prestigious journal Nature, the researchers’ work showcases the untapped potential of these models to uncover new scientific insights and drive discoveries that were previously unattainable.
The problem in question is the cap set problem, a long-standing puzzle in mathematics that has confounded researchers for decades. The challenge involves finding the largest size of a specific type of set without three elements ever forming a straight line when plotted on a graph. While seemingly niche, the problem holds significant importance and has been described as a “favorite open question” by renowned mathematician Terence Tao.
DeepMind’s achievement lies in the development of FunSearch, a novel tool that combines a large language model called Codey with algorithms that reject incorrect or nonsensical answers and refine the model’s suggestions. By iteratively providing Codey with feedback and allowing it to refine its outputs, FunSearch was able to produce verifiable and valuable new information that did not previously exist – a remarkable feat for a large language model, which has traditionally been associated with generating plausible but factually incorrect outputs.
The implications of this breakthrough extend far beyond the cap set problem itself. FunSearch’s ability to generate code as a “recipe” for solving problems means it can potentially be applied to a wide range of mathematical and computational challenges. In fact, the researchers have already demonstrated its versatility by using it to tackle the bin packing problem, a critical optimization issue in computer science, and obtaining faster solutions than those devised by humans.
This advancement represents a significant step forward in leveraging the power of large language models for scientific discovery. Terence Tao, a renowned mathematician and Fields Medal recipient, has hailed FunSearch as a “promising paradigm” that could pave the way for incorporating these models into research workflows while mitigating their drawbacks.
As the researchers acknowledge, the reasons behind FunSearch’s success are not entirely clear, but its potential is undeniable. By combining the vast knowledge and reasoning capabilities of large language models with robust verification and refinement mechanisms, DeepMind has opened up new frontiers in the pursuit of mathematical and scientific breakthroughs.
