Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence.
In this sense, 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 is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. In this sense, mathematics belongs to formal science, not natural science. All mathematical objects are artificially defined in essence. They do not exist in nature, but only in human thinking and ideas.
Therefore, the correctness of mathematical propositions can not be tested by repeated experiments, observations or measurements, like physics, chemistry and other natural sciences whose purpose is to study natural phenomena, but can be directly proved by strict logical reasoning. Once the conclusion is proved by logical reasoning, then the conclusion is correct.
Axiomatic method of mathematics is essentially the direct application of logical method in mathematics. In an axiomatic system, all propositions are linked by strict logic.
Starting from the original concept directly adopted without definition, other derived concepts are gradually established with the help of logical definitions; Starting from the axiom based on unproven direct adoption, with the help of logical deduction, a further conclusion, namely theorem, is gradually drawn; Then all the concepts and theorems are combined into a whole with internal logical connection, that is, an axiomatic system is formed.