I don't follow. What does when the word appeared have to do with whether it's correct? People have made mistakes all throughout history.
Even if we assume that this logic is sound, your own source cites an even earlier date for the American spelling, so great job defeating your own argument.
I'm a little late to this discussion... but, really, language is decided by majority vote. Language is descriptive, not prescriptive.
And anyway, it's 'math' in US and Canada, and 'maths' everywhere else. They are both equally correct... though, one more so than the other, depending on what region you're in. For example, as an Australian I find it downright bizarre to remove the 's' when contracting Mathematics, whereas an American would find it similarly odd not to remove it.
Basically... it doesn't matter. At all. Just accept that some people spell/say it differently.
Potayto, potahto.
That said, as an outside observer, I do believe "math" to be the more correct form. "Mathematics" comes from "mathematica", which was used to refer to the philosophy of numbers as a whole. At some point in the history of English, Latin words ending in -a mutated to ending in -s. Since the 's' does not denote a plural, in my view it's a mistake to pass it on to the abbreviation. It's especially wrong to construct sentences that treat the word "maths" as an actual plural. E.g. "the maths are wrong".
Not to mention, from a purely practical point of view, "maths" makes you do stupid things with your tongue for no good reason.