Mathematics, being a human endeavor, is fundamentally about human interaction. There's no point to doing math if there is no communicating it to other people.
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.
I would not agree with that. One can do math for personal pleasure.