Getting back to the subject on whether mathematics is discovered or invented, I don't believe that classifying maths as "real maths" or "pure maths" validates the point one way or the other.
The issue is whether mathematical properties themselves are invariant.
Lets assume the Everett interpretation of QM is correct then multiple Universes exist. While prime numbers may appear to be an ad hoc invention with no physical significance, a property of prime numbers is that they form an infinite set as proven by the ancient Greeks. The question is are they an infinite set in all other Universes? If the answer is yes and the concept is applied to maths in general then one can argue that the maths is discovered. A Universe where prime numbers do not exist may simply reflect it hasn't been discovered yet
Steven