What is mathematics?
Mathematics is a subject that studies concepts such as quantity, structure, change, space and information. 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.