Mathematics is a discipline that studies the concepts of quantity, structure, change, space, and information, and from a certain point of view belongs to a formal science.

Mathematics arises through the use of abstraction and logical reasoning, from counting, calculation, measurement, and observation of the shape and motion of objects. Mathematics has become a part of the educational landscape in many countries and regions. It is used in a variety of fields, including science, engineering, medicine, economics, and finance. Mathematicians also study pure mathematics, which is the substance of mathematics itself, without any practical application as an objective.

Mathematics originated from the early productive activities of mankind, and the ancient Babylonians had already accumulated some mathematical knowledge from ancient times and were able to apply it to practical problems. From the point of view of mathematics itself, their mathematical knowledge is only the result of observation and experience, without comprehensive conclusions and proofs, but their contribution to mathematics should be fully recognized.

The knowledge and application of basic mathematics is an integral part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical texts from ancient Egypt, Mesopotamia and India. Since then, its development has continued in small increments. However, algebra and geometry remained separate for a long time.

Algebra is arguably the most widely accepted "mathematics". It can be said that the first mathematics that everyone is exposed to is algebra when they start learning to count as a child. As the study of "numbers", algebra is one of the most important components of mathematics. Geometry was the first branch of mathematics to be studied.

It was not until the Renaissance in the 16th century that Descartes created analytic geometry, which brought together algebra and geometry, which were then completely separate. From then on, we could finally prove theorems of geometry by calculation; we could also represent abstract algebraic equations graphically. Later, the more refined calculus was developed.

Nowadays, mathematics includes many branches. The French school of Bourbaki, founded in the 1930s, believed that mathematics, at least pure mathematics, is the study of abstract structures. Structure is a deductive system that starts with initial concepts and axioms. They believed that mathematics has three basic parent structures: algebraic structures (groups, rings, domains, lattices ......), sequential structures (partial sequences, full sequences ......), topological structures (neighborhoods, limits, connectivity, dimensionality... ...).

Mathematics is used in many different fields, including science, engineering, medicine and economics. The applications of mathematics in these fields are generally referred to as applied mathematics and sometimes lead to new mathematical discoveries and the development of entirely new mathematical disciplines. Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application as an objective. Although much work begins with the study of pure mathematics, suitable applications may be found later.

Specifically, there are subfields used to explore the connections between the core of mathematics and other fields: from logic, set theory (foundations of mathematics), to the empirical mathematics of different sciences (applied mathematics), and more recently, the study of uncertainty (chaos, fuzzy mathematics).