I suspect that to the ancient Greeks, math and natural science were not yet separate disciplines. "Geometry" means something like measuring the world. They had to be aware of the relationship between their math and the ability to function as a minimally technological society, surveying land, navigating, and so forth. As I understand it, they believed that math was telling them something deep about reality.

I think turning math into a purely abstract game came later, and we owe our fun to the discipline's more humble origins.