Abstract: Can a surface group act properly on a product of trees? We examine three distinct approaches to constructing such actions, and ultimately decide that none of them hold much promise. We provide a large amount of computational evidence against these approaches, and instead suggest a strong negation. Central to this analysis is a novel variation on a classical machine learning algorithm which is particularly well-suited for group theory. We describe how this resolves some long-standing computational questions about groups. Finally, we’ll gesture at how this points towards a much larger research program.