This is a compelling way of looking at things for sure; to me it seems like you're saying math is just a language (like English) that we can use to describe the world. English is no more "right" than some other made up language, so same goes for math, and thats certainly seems true in some cases. However there are things that are intrinsic to mathematics that also seem intrinsic to existence, like prime numbers. Many things about prime numbers are 'discovered' as if they were elements of nature that need to be revealed through study. For example, the distribution of primes and the distribution of twin primes are things likely to have been discovered by an alien intelligence, assuming one exists. What would their math look like? Different for sure, but I think it's likely they still studied the primes, hypothetically.