mathematics, n

1. Originally: (a collective term for) geometry, arithmetic, and certain physical sciences involving geometrical reasoning, such as astronomy and optics; spec. the disciplines of the quadrivium collectively. In later use: the science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis; mathematical operations or calculations.

Colloq. abbreviated maths, (N. Amer.) math.

When the modern subject is studied as an abstract deductive science in its own right, it is often referred to more fully as pure mathematics (see PURE a. 2d); when applied to the modelling of physical objects and processes (e.g. in astronomy, various branches of physics, engineering, etc.) and random processes (in probability), and to the handling of data, its full name is applied mathematics (see APPLIED a.), or (in early use) mixed mathematics (see MIXED a.2 5).

In early use always construed as a plural, and usually preceded by the. In modern use regarded as a mass noun, except when used of calculations.

2. The mathematical considerations or principles relating to a specified phenomenon, process, etc.

(excerpted from Oxford English Dictionary Online)