Mathematics (Mathematics or maths, whose English comes from the Greek "Má th ē ma"; Often abbreviated as "mathematics"), it is a discipline that studies concepts such as quantity, structure, change, space and information, and belongs to a formal science from a certain point of view. Mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.

In the development of human history and social life, mathematics also plays an irreplaceable role, and it is also an indispensable basic tool for studying and studying modern science and technology.

The knowledge and application of basic mathematics is 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, but algebra and geometry at that time were still in an independent state for a long time.

Algebra can be said to be the most widely accepted "mathematics". It can be said that algebra is the first mathematics that everyone has come into contact with since childhood. Algebra, as a discipline to study numbers, is also one of the most important parts of mathematics. Geometry is the earliest branch of mathematics studied by people.

Until the Renaissance in16th century, Descartes founded analytic geometry, which linked algebra and geometry which were completely separated at that time. From then on, we can finally prove the theorem of geometry by calculation. At the same time, abstract algebraic equations can be expressed graphically, and later more subtle calculus was developed.

There are many branches of mathematics at present. French Bourbaki School, founded in 1930s, thinks that mathematics, at least pure mathematics, is a theory to study abstract structures. Structure is a deductive system based on initial concepts and axioms. They think that mathematics has three basic parent structures: algebraic structure (group, ring, field, lattice …) and ordered structure (partial order, total order …).

Mathematics is applied in many different fields, including science, engineering, medicine and economics. The application of mathematics in these fields is generally called applied mathematics, which sometimes arouses new mathematical discoveries and promotes the development of a brand-new mathematics discipline. Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application. Although many works begin with the study of pure mathematics, they may find suitable applications later.

Specifically, there are sub-fields to explore the relationship between the core of mathematics and other fields: from logic and set theory (mathematical basis), to empirical mathematics in different sciences (applied mathematics), and then to more modern uncertainty research (chaos and fuzzy mathematics).

As far as verticality is concerned, the exploration in their respective mathematical fields is getting deeper and deeper.