There’s a whole babel of constructed languages . Klingon  is one of them. Apparetly it can be as “complete” as needed to be also a practical language for day-to-day use.
Mathematics is more of a collection of domain-specific languages  or a collection of programming languages  than a single, monolithic language.
Thinking of mathematics as a single thing out there (that there must be a “philosophy of”) shows the seduction of platonism (perhaps instilled in people by our educational system of religious schooling).
 Wikipedia: Constructed language
A planned or constructed language (sometimes called a conlang) is a language whose phonology, grammar, and vocabulary have been consciously devised for human or human-like communication, instead of having developed naturally. It is also referred to as an artificial or invented language.
 Wikipedia: Klingon language
 Wikipedia: Domain-specific language
 Wikipedia: List of programming languages by type