The first period: the formation period of mathematics (ancient times-the sixth century BC), which is the period when human beings established the most basic mathematical concepts. Since counting, human beings have gradually established the concept of natural numbers, simple calculation methods, and recognized the most basic and simplest geometric forms. Arithmetic and geometry are not separated.
The second period: elementary mathematics period and constant mathematics period (6th century BC-AD17th century), the basic and simplest achievements in this period constitute the main content of middle school mathematics, which lasted for about two thousand years. This period gradually formed the main branches of elementary mathematics: arithmetic, geometry and algebra.
The third period: the period of variable mathematics (1early 7th century to1end of 9th century). Variable mathematics came into being in17th century, and has gone through two decisive and significant steps: the first step is the generation of analytic geometry; The second step is the creation of calculus.
The fourth period: the modern mathematics period (beginning at the end of19th century), the beginning of the modern stage of mathematics development, which is characterized by profound changes in all foundations-algebra, geometry and analysis.
Mathematics needs to be rigorous:
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.