Sure, it is philosophical. You could even go further and say that math exists in the same sense it exists in the Library of Babel, since it's also text.

I would say that this comparison oversimplifies things. Non-math stories in Library of Babel are less practically useful and are less possible to get checked than the math texts. Wrong math can exist, but we often have ways to figure out it's wrong.

For practical purposes I would assume (maybe others can correct me) that math is treated as something you discover when you work on it as mathematician. It's a more intuitive model.