This is the website of the Math Seminar at the Department of Mathematics Education, Seoul National University.
Title: Evolutionary coding based AI agents for mathematics
Abstract: The rectilinear crossing number is the minimum number of edge crossings in a straight-line drawing of a graph in the plane. Despite its elementary definition, even the case of complete graphs remains poorly understood, and progress over the past several decades has relied on a blend of geometric intuition, combinatorial reasoning, and increasingly sophisticated computational methods. In this talk, I will present a progress report on an attempt to use artificial intelligence as a new exploratory tool for this classical problem. After briefly surveying the history of the rectilinear crossing number and its known constructions, I will introduce OpenEvolve, an open-source framework inspired by AlphaEvolve, which has recently been applied to the study of mathematical conjectures. I will describe the framework at a high level and explain how it can be adapted to the rectilinear crossing number. I will then discuss results from this ongoing work. OpenEvolve was able to not only rediscover known optimal constructions for small complete graphs, but also improve upon a best known construction for a larger instance. I conclude by reflecting on the potential role of AI-assisted exploration in mathematics.
Venue: Room 103, Building 10-1 (Map), Seoul National University
Host: Boram Park
Speaker: Cheolwon Heo (SUNY Korea), Kang-ju Lee (SNU), Minho Cho (KIAS)
Website: Click here
Venue: Room 207, Building 10 (Map), Seoul National University
Host: Boram Park