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ABSTRACT: The rectilinear crossing number of a graph is the minimum number of edge crossings in a straight-line drawing of the 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 is adapted to the rectilinear crossing number. I will then discuss results from this ongoing work. OpenEvolve was able to (re)discover constructions matching the known optimal bounds for small complete graphs, and for a larger instance it was able to produce drawings whose crossing numbers are within 99.98% of the best known upper bound. I conclude by reflecting on the potential role of AI-assisted exploration in mathematics.