I suppose my post was somewhat poorly worded.

To expand/try again somewhat, uhm

First a few things that aren't maths, or that maths is not.

For one, it does not generate entirely new axioms/rules. The results often seem novel, but they are directly implied by the axioms -- a small set of things simply taken to be obvious New mathematics comes from greater insight into previous assumptions, elimination of redundant assumptions, or examination of assumptions that noone previously bothered with taking as true/false .

Another thing that maths isn't when done correctly is ambiguous. It should mean only one thing to anyone with the correct context. Two sufficiently capable mathematicians given equivalent axioms should come up with equivalent answers given the same question.

There is mathematics for dealing with vagueness and uncertainty; do not confuse this with ambiguity. Errors due to approximations can be quantified, and all sets of lower/upper bounds on answers should overlap even if different people are making different approximations. Some equations also cannot be solved (or approximated with known error) given our current knowledge.

There is also the whole field of applied mathematics (scientists, most statisticians, mathematicians who actually interact with real data etc do this) ambiguity is sometimes/often found here for various reasons (practicality, ambiguity of knowledge of what is being modelled etc) -- like anything dealing with the real world.

In short, properties of something that's maths:

The important/defining properties aren't altered by representation. Ie. it could be expressed in C++, Finnish, traditional Mathematics notation, some beads on a string, by sufficiently well defined interpretive dance, specially shaped toy blocks, or in a brain and still serve the same function.

It is not inductive (scientific/philosophical definition of inductive, not mathematical) in nature.

It is unambiguous, or is the direct application of something unambiguous.