Mathematics is a subject that studies concepts such as quantity, structure, change and spatial model. By using abstract and logical reasoning, the shape and motion of objects are counted, calculated, measured and observed. Mathematicians have extended these concepts in order to express new conjectures with formulas and establish strictly deduced truths from properly selected axioms and definitions.

The knowledge and application of basic mathematics will always be an indispensable part of individual and group life. The refinement of its basic concepts can be found in ancient mathematical documents of ancient Egypt, Mesopotamia and ancient India. Since then, its development has made small progress until the Renaissance in16th century, and the mathematical innovation generated by the interaction with new scientific discoveries led to the acceleration of knowledge, until today.

Today, mathematics is used in different fields of the world, including science, engineering, medicine and economics. The application of mathematics in these fields is usually called applied mathematics, and sometimes it will lead to new mathematical discoveries and the development of new disciplines. Mathematicians also study pure mathematics with no practical value, even though its application is often discovered later.

The French Bourbaki School, founded in 1930s, believes that mathematics, at least pure mathematics, is a theory to study abstract structures. Structure is a deductive system based on initial concepts and axioms. Boone School believes that there are three basic abstract structures: algebraic structure (group, ring, domain …), ordered structure (partial order, total order …) and topological structure (neighborhood, limit, connectivity, dimension …).

Mathematics is also divided into geometry, calculation and area.