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Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational tool for computation and tabulation of quantities, it has blossomed into an extremely rich and diverse set of tools, terminologies, and approaches which range from the purely abstract to the utilitarian.
Bertrand Russell 
once whimsically defined mathematics as, ``The subject in which we never
know what we are talking about nor whether what we are saying is true'' (Bergamini 1969).
The term ``mathematics'' is often shortened to ``math'' in informal American speech and, consistent with the British penchant for adding superfluous letters, ``maths'' in British English.
See also Metamathematics
References
Bergamini, D. Mathematics. New York: Time-Life Books, p. 9, 1969.