@Arlo - I was responding to Omicron and Archer, but really it applies to anyone who is trying to say that the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language. They, and everyone else, are of course entitled to their opinions but I, as you may have noticed, disagree to a rather large degree.

Sorry about being unclear as to who that was directed at.

Maths is a perfect self-contained system. **We represent it with an invented language** and numeracy system to model things that we perceive and concepts we've invented, **but maths itself is not invented**.

Definitely not invented, discovered. Math exists in nature and many examples can be made, like fibonacci's series in plants or nautilus. As Livewire stated above, **the way we express math was invented, but math itself was just discovered.**

As I already noted, both of those responses, along with all the other responses at least since your last one, very explicitly point out the distinction between the two things. They very pointedly do NOT claim that "the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language." In fact, at least in the past three weeks or so (I haven't bothered to read back further than that), NOBODY has made that claim.

??