The development of mathematics is nothing more than a deep understanding and accumulation of concepts, theorems and formulas, and in this process, it is accompanied by the development of ideas, thinking methods, organizations and tools. From different angles, mathematics can be divided into different stages of development, for example, from the perspectives of discipline development, thinking methods, symbol use, and mathematical talent training, we can see different stages of development of mathematics.
The variable thought began to enter mathematics, which made great changes in mathematical thinking methods and became one of the most important and basic ideas in modern mathematics. Thus, mathematics can successfully solve the problems related to movement changes put forward by engineering technology and other natural science disciplines.
The establishment of analytic geometry marks the development of mathematics, from constant stage to variable stage; The thinking method of mathematics has been greatly enriched, which provides a powerful tool for solving sports problems in natural science. The second important stage of the development of variable mathematics is the establishment of calculus, which has promoted a large number of new mathematics disciplines and directions and occupied the mainstream of mathematics development for a long time.
Calculus expands the application field of mathematical thinking method and promotes the further development of other natural science disciplines. Because the research object of natural science is the changing material world, and calculus is the mathematics of studying variables, the thinking method of calculus will inevitably become a powerful tool to study the changing law of the material world.
Applied mathematics is independent from mathematics; Mathematics has an unprecedented close relationship with other natural sciences; The invention and use of computers have expanded the research field of mathematics and made computational mathematics a new direction.