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Mathematics (English: Mathematics, from the ancient Greek μ θ η μ α (má th ē ma); Often abbreviated as math or maths]) 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.
Mathematics is produced by counting, calculating, measuring and observing the shape and motion of objects through abstract and logical reasoning. [1] Mathematics has become a part of education in many countries and regions.
It is applied in different fields, including science, engineering, medicine, economy and finance. Mathematicians also study pure mathematics, which is the substantive content of mathematics itself and does not aim at any practical application.
In ancient China, mathematics was called arithmetic, also called arithmetic, and was finally changed to mathematics. Arithmetic in ancient China was one of the six arts (called "number" in the six arts).
Mathematics originated from early human production activities. The ancient Babylonians had accumulated some mathematical knowledge, which could be applied to practical problems. Judging from mathematics itself, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof. However, we should fully affirm their contribution to mathematics.
The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical classics 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.
At present, mathematics includes many branches. 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 …), ordered structure (partial order, total order …) and topological structure (neighborhood, limit, connectivity, dimension …).
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 new mathematical disciplines. Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application. Although many jobs begin with learning pure mathematics, they may find suitable applications in the future.
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), to more modern uncertainty research (chaos and fuzzy mathematics).
As far as verticality is concerned, the exploration in each field of mathematics is getting deeper and deeper.