[alexk7]

Standard mathematical notation is not inevitable and is not unique. It is on par with most programming languages for being quite random. Both programmers and mathematicians use an imperfect tool (programming language, mathematical notation) to achieve goals that may, or may not, be eternal.

[cousin_it]

That's a fair point, and math notation is famously more ambiguous than programming languages. But it seems to me that the concepts denoted by math notation (e.g. numbers, arithmetical operations, functions...) are inevitable and unique, while the concepts denoted by strings in a programming language are much fuzzier and more arbitrary (except for languages that have a denotational semantics, which are few and far between).

[agentultra]

People often speak of the axioms in maths when they describe how, "elegant," and, "consistent," it is. I'm not a mathematician but I've read Gödel's "proof" and know enough that there are no guarantees. It matters what system of axioms you use and requires the reader to recognize the limits of those axioms in defining the system of logic they they imply. Or some such.

Point being that there is no system that is complete. There are large bodies of mathematics these days that have specialized their notations and axioms to their domains. It is incredibly difficult to maintain a masterful knowledge of all of their idiosyncrasies and notations.