Large Language Models, Mathematical Discovery and Search in the Space of Strategies - An Exploration of the Cap Set Problem

Watch a Harvard CMSA mathematics seminar where Jordan Ellenberg from UW Madison explores the intersection of large language models and mathematical discovery, focusing on the cap set problem in combinatorics. Learn about a novel approach developed with DeepMind that uses LLMs trained on code to search for programs generating large cap sets in (Z/3Z)^n, rather than directly searching for the sets themselves. Discover how this method enhances interpretability in machine learning by producing human-readable programs instead of raw vector collections. Gain insights into the successes and limitations of this innovative math-ML interface, and understand its potential impact on future mathematical practices. The presentation includes an accessible explanation of the cap set problem's significance in combinatorics and number theory, making it valuable for both mathematics enthusiasts and those interested in the applications of machine learning in mathematical research.