It's the only pure way to describe existence. That isn't meaningful? Mathematics is a language, first and foremost. To argue otherwise is to fundamentally misunderstand its goals, methods, and form.

You can draw all the squiggly lines on paper that you want, but it won't mean anything until someone else interpets it. You cannot prove logic that only exists in your own head, because you cannot prove yourself rational. Your very existence does not even make sense without other people perceiving you.

Languages do not require human interaction. I do not argue that there is no mathematical language.

Language without human interaction is an undefined operation, like raising zero to the zeroth power, or clapping with one hand.

Are you including interacting with oneself?

Uh, OK. Sure. Whatever

Math? No.

Math in the form of a research community which has built up centuries of work for each other to further build on? Absolutely.