This is a philosophical question, whether mathematics exists independent of intelligence discovering it.
It exists in the same sense that every story exists whether or not it's been written because the Library of Babel contains it.
It exists in the same sense that every story exists whether or not it's been written because the Library of Babel contains it.
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.
I’m sure Russell’s Paradox would have something to say about that.
One might also consider alternative axiomatizations of mathematics with statements that cannot be expressed in ZF set theory, and vice versa. To say that all of these things exist is to really stretch the definition of existence far beyond the ordinary sense of the word.