That's a different matter: how does one contract a plural - but the plural is still the same:

- Math is short for mathematics, not for mathematic, which isn't a word (try looking up 'mathematic' sometime).

- Maths is also short for mathematics.

"mathematic (n.) - late 14c. as singular noun, replaced by early 17c. by mathematics, from Latin mathematica (plural), from Greek mathematike tekhne "mathematical science," feminine singular of mathematikos (adj.) ..."

http://etymonline.com/index.php?term=mathematic

The obvious comparison is to "physics" which is short for "physical sciences" IIRC.

Was mathematics once referred to as "the mathematical arts" or something?

(A similar way to appear very uncool is to walk into a record shop and proclaim, "look at all these vinyls!")

It isn't "short for" anything. This is just a normal suffix for fields of study: Physics, mechanics, politics, statistics, optics, ethics, linguistics, and so on.

Etymologically it is a plural suffix, but in modern English it is singular.

http://dictionary.reference.com/browse/-ics

Cambridge University has a 'Centre for Mathematical Sciences', housing both the departments for pure and applied maths.

You're not contracting a plural. Mathematics is singular. "Mathematics IS a field of study", not "Mathematics are fields of studies". There aren't "3 mathematics".

A history of math vs maths: http://m.youtube.com/watch?v=SbZCECvoaTA

Etymologically mathematics is a plural, as another poster notes. There are many smaller topics involved in mathematics: geometry, trig, calculus, etc. Much in the same way as mechanics, optics, politics, acoustics, etc (as a different poster mentions).

'maths' is not plural, it's a contraction of 'mathematics'.