As von Neumann, the "father of electronic computers", said, "Mathematics is at the center of human intelligence". The study of mathematics has a great impetus to the development of the whole science. At the same time, the deepening of the study of mathematics as an ideological system will also promote human understanding of the causes and ways of thinking.
History and characteristics of mathematics
Mathematics is an early science, and the primitive mathematics has been tested and enriched for a long time before it formed the mathematics we see today. Mathematics was originally an empirical description of natural phenomena by human beings, and later it developed into a logical ideological system, and then it flourished and formed a huge mathematical system. In the process of continuous development of mathematics, it also shows many characteristics of mathematics: the concepts and methods of mathematics are highly abstract and the mathematical system is highly logical. These two basic characteristics determine the universality of mathematical application.
The origin of mathematics
Mathematics is a science that studies the relationship between spatial form and quantity, so the original mathematical concepts are "shape" and "number".
In the long-term production practice and life practice, people find that there are differences between things. On the one hand, their forms are different; On the other hand, the number of things with the same or similar external forms is different. Therefore, after practice and thinking, the concepts of "shape" and "number" have appeared in people's minds.
The appearance of these two mathematical concepts marks a leap in the level of human understanding, because both are highly abstract concepts. Although the external form of things is visible, when points, lines and surfaces appear as mathematical concepts, they have already existed without the shape of objective things. In real life, we can't find points without area, lines without width and surfaces without thickness, because they have become abstract concepts. The concept of "number" is abstract. Color, temperature, hardness, etc. Can be felt by sensory organs; The number of objects can not be directly perceived, but can only be realized through abstract processing of the brain. "In order to count, we must not only have objects that can be counted, but also have the ability to consider only the number of objects without considering all other characteristics of the objects." This ability is the ability of human abstract thinking.
The concept of "quantity" is significant: it is the contribution of mathematics to the whole scientific system. A science has moved from qualitative description to quantitative analysis and calculation, which is a sign that this science has developed to a relatively mature stage. The premise of realizing quantitative analysis is to apply the concept of "quantity" in mathematics and its related theorems.
In the process of mathematics, abstract concepts appeared. In fact, any science needs to abstract some concepts from nature. The difference between mathematics and other natural sciences is that the abstract depth and breadth of mathematical concepts are higher than other sciences. The initial abstraction was limited to the abstraction of mathematical concepts, and in the process of mathematical development, the abstraction of mathematical methods appeared again.