It has to do with different conventions for abbreviation—conventions which arose haphazardly (in the typical manner of natural language evolution). Interestingly, the abbreviation “math” is older than the abbreviation “maths.” The former first appeared in 1847, whereas the latter did not turn up until 1911. The word “mathematics” originally referred to any discipline that included calculations as part of its practice. This is why the full word has an “s” at the end, but it is not—on its own—an explanation of why some people say “math” and others say “maths” (as both groups say “mathematics”).
@Dr_Lawrence Canadian English contains some of the spelling variants typically identified as American and some of the spelling variants typically identified as British. They also call association football by the name “soccer” and use “fanny” to mean “buttocks” (rather than “vulva”). The English language is not so easily divided into American versus everyone else.
Furthermore, the British have indeed added letters to existing words. “Aluminum” came before “aluminium” (though only by a matter of months), but the latter was suggested as a replacement for the former on aesthetic grounds. Usage was then inconsistent in both North America and Europe until the early 20th century when a combination of market forces and the American Chemical Society officially adopting “aluminum” made that spelling standard in North America. Meanwhile, it wasn’t until 1990 that IUPAC decided to give its blessing to “aluminium.”
And finally, “mathematics” is a collective noun, like “family” or “physics.” All of these are treated as singular for purposes of verb conjugation (“mathematics is fun,” “my family enjoys kayaking,” “my favorite thing to study is physics”), so insisting that these words are plural only carries so much force as an argument. None of this is meant to suggest that the British variants are incorrect and the American ones correct, but only that the reverse is no more true. These are differences of dialect, not clear errors like using a comma as terminal punctuation.