It wasn't meant to be complacently terse, it was meant to represent the basic tautology. Mathematics is a language as well as a way of thinking and one needs both since things are truly complicated under the hood. The language is actually our friend here, it allows people to speak clearly and have near universal understanding of what is meant. With this in mind, the correct answer to 'how do we communicate maths to non-mathematicians'(as opposed merely to teaching its importance which is advocacy) is to teach them the maths. That's how I see it anyway.

I understand the tautology. It's inherent in every field that requires specialization. And the point I'm trying to make is that the best teaching relies on ideas or analogies already familiar to the student. It's not enough to say math is a language. So is French. But to learn French, we first learn to map our native language to the new one. The analogy isn't perfect, but math often describes things in the world, and we can use those things to provide windows to the math itself.

While the language of math is a useful tool for the initiated, like all linguistic barriers it keeps out newcomers. So yes, we must teach people math, but we must do it at first, as much as possible, in a language that allows them to enter into a new way of thinking. It's about unfurling a series of ideas one at a time instead of all at once. (I don't pretend to do that perfectly, but that was the intent. My understanding is as defective as some matrices. ;)