Introduction to mathematics:

Mathematics [English: Mathematics, from ancient Greece μ? θξμα(máthēma)； Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information. Mathematics is a general means for human beings to strictly describe and deduce abstract structures and patterns of things, and can be applied to any problems in the real world.

All mathematical objects are artificially defined in essence. Mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics. Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.

The definition of mathematics:

Aristotle defined mathematics as "quantitative mathematics", which lasted until18th century. /kloc-since the 0/9th century, mathematical research has become more and more rigorous, and it has begun to involve abstract topics such as group theory and projection geometry that have no clear relationship with quantity and measurement. Mathematicians and philosophers have begun to put forward various new definitions. Some of these definitions emphasize the deductive nature of many mathematics.

Some emphasize its abstraction, while others emphasize some topics in mathematics. Even among professionals, the definition of mathematics has not been reached. Whether mathematics is an art or a science has not even been decided. Many professional mathematicians are not interested in the definition of mathematics or think it is undefined. Some just said, "Mathematics is done by mathematicians."

The three main mathematical definitions are called logicians, intuitionists and formalists, each of which reflects a different school of philosophical thought. Everyone has serious problems, no one generally accepts it, and no reconciliation seems feasible.

Mathematical structure:

Many mathematical objects, such as numbers, functions, geometry, etc., reflect the internal structure of continuous operation or the relationships defined therein. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations. In addition, similar things often happen in different structures, which is further abstract.

Then it is possible to describe the state of a class of structures with axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.