Which one is considered correct? I say "math", however I believe I heard somewhere that "maths" is correct. Also, should it (and "mathematics") be capitalized or not?
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This is simple:
It is a common noun and should only be capitalized at the beginning of a sentence.
This is meant to be added to nohat's response but I can't seem to add comments (yet).
The words "math" and "maths" are both abbreviations of "mathematics" and are dictated by your local variation of English.