[DonHopkins]

Number theory is all about cyclical patterns, and its theorems fetishize finding cycles of discrete values with suspiciously regular behavior. Last I heard, number theory, group theory, and Fourier analysis are all math.

And yes, I will die on this singular hill: it's all one math, not a bunch of "maths". Math is one interconnected cathedral with music flowing through it, not a drawer full of unrelated trinkets. The British habit of calling it "maths" is oddly reductionist -- it makes it sound like you've got separate jars labeled "algebra", "geometry", and "spicy numbers".

[Pay08]

It's just a shortening of "mathematics". You don't call it "mathematic" do you?

[DonHopkins]

"Mathematics" is a mass noun that happens to look plural (ends in -s) but behaves singular: "Mathematics is hard" not "Mathematics are hard".

https://en.wikipedia.org/wiki/Mass_noun

>In linguistics, a mass noun, uncountable noun, non-count noun, uncount noun, or just uncountable, is a noun with the syntactic property that any part and quantity of it is treated as an undifferentiated unit, rather than as something with discrete elements. Uncountable nouns are distinguished from count nouns.

So "math" is the proper shortening of the mass noun "mathematics". What other mass nouns do you shorten by abbreviate by keeping the "s" ending?

We do not say "phys" for physics or "econs" for economics, so keeping the "s" in "maths" breaks the rule.

[Pay08]

I have heard both used before.