There was a great school of mathematics in ancient Greece. They pursue spiritual creation, study purely abstract mathematics, proceed from axioms and use logical deduction to form a strict academic system. An outstanding representative is Euclid's Elements of Geometry. They are all definitions, theorems, proofs and inferences, and they don't care about their uses. It embodies a new stage of scientific development after the division of labor between manual labor and mental labor: it creates a pure and rigorous scientific system, but it is far from real life.
Since then, mathematics has developed in two directions. On the one hand, it is pure mathematics. For example, Goldbach conjecture, Fermat's last theorem and other world-famous issues have become the focus of attention of the world. Once a breakthrough is made, it can be regarded as a major event in the history of human thought. As for non-Euclidean geometry, topology, abstract group theory, etc. Although you can't see the direct relationship with reality at first, as long as you have good mathematical knowledge, you will often find practical application in a few years. The fiber bundle theory studied by Chen Shengshen in the 1940s became a mathematical tool of gauge field discovered by Yang Zhenning and others in physics in the 1970s. The unity of this world is unbelievable.
On the other hand, applied mathematics has developed rapidly. After all, the real world is the source of mathematics development. /kloc-since the 0/7th century, social development and production demand have been the main driving forces for the development of mathematics. Newton invented calculus to meet the needs of physics. Conversely, Tycho Brahe discovered Neptune by mathematical methods. The steam engine promoted the development of kinematics and thermodynamics, and pushed the mathematical analysis to a new peak. The basic laws of electromagnetism are written in differential equations. Until the 20th century, the manufacture and navigation of jet planes and spaceships, medical equipment scanned by CT, and battle plans for organizing large-scale wars were all mathematical techniques in essence.
In modern times, mathematics is not only a tool to solve problems, but also an important part of the culture of the times. Some mathematical concepts and languages have penetrated into daily life, and some mathematical principles have become necessary knowledge for people, such as area, volume, symmetry, percentage, average value, proportion, angle, etc., and have become common nouns in social life. Such as population growth rate, production statistics chart, stock trend chart and so on, constantly appear in newspapers, television and other mass information media; However, savings, bonds, insurance, area and volume calculation (estimation) and shopping decision-making have become unavoidable practical problems. Then the future citizens-students must have the mathematical literacy to solve practical application problems, which requires the application problems to be presented in the process of mathematics education and teaching.
There has been a tradition of practice in ancient mathematics in China, and it is not a new problem to attach importance to the application of mathematics in mathematics teaching. In primary schools, the application of mathematics is the focus and difficulty of teaching, and no one has ever disagreed. In junior high school, after learning plane geometry, the taste of mathematics tends to be abstract, logical reasoning is constantly strengthened, and the application of mathematics gradually fades out. However, mathematical applications have not disappeared, such as concentration problems, travel problems, and the relationship between parallelogram and iron gate is always mentioned. Just misled by some wrong ideas, people don't pay much attention to it.
Once in high school, the situation became more and more serious. Mathematics has always been the main course in middle schools. Why do you have to learn so much math? It is generally believed that mathematics is a "sieve of ability" and "gymnastics of thought", and it is nothing more than "need for further study" and "fit for thought". As for what's the use, I'm sorry, don't ask. Because of the Great Leap Forward and the Cultural Revolution, the mathematical knowledge system was destroyed. Once it was brought bad, it focused on the requirements of pure mathematics. For some time, advocating the application of mathematics has been called "pragmatism" and "short-sighted behavior". It seems that mathematics is getting farther and farther away from real life. The pure mathematical reasoning of "pinching the head and burning the tail" has become the only choice. Therefore, the design and teaching of mathematical application problems has become an urgent task.