Mathematics (although the plural form is typically used to refer to the study and science) is the science that studies patterns in the structures of abstract bodies and the relationships established between them.
Despite having multiple uses in other sciences and disciplines (most notably in physics) and dealing with relationships that may seem evident, mathematics first postulates, then deduces and proves.
Mathematics is not an experimental science, but rather a formal science; mathematicians typically define and investigate abstract structures and concepts for reasons purely internal to mathematics, as such structures can provide a useful tool for frequent calculations.
The main disciplines encompassed by mathematics arose from the need to perform calculations in commerce, to understand the relationships between numbers, to measure land, and to predict astronomical events.
These four needs can be related to the subdivision of mathematics into the study of quantity, structure, space, and change—namely, arithmetic, algebra, geometry, and mathematical analysis.
There are also subdivisions dedicated to exploring links between mathematics and other fields: logic, the foundations of set theory, or the empirical mathematics of other sciences (applied mathematics) and, more recently, mathematics dedicated to the rigorous study of uncertainty.
