The shortest answer: Mathematics is abstract. Mathematics studies abstract concepts and uses abstract methods. The development of mathematics is reflected in the gradual deepening of abstraction. But if we go deeper, the essence of mathematics is not conclusive. Below I will be divided into three parts, which will briefly explain the various viewpoints mentioned in the wiki link provided by @ Taowu. General mathematics corresponds to realism mathematics and logicism mathematics in Wikipedia. Most ordinary people, researchers and many mathematicians hold these views. Under these viewpoints, mathematics is closely combined with reality, so its application is of course very extensive. On the surface, mathematics is the need of production and life. For example, geometry is used to measure land and mathematics is a tool. The representative of this view ... Marx (if he really said so). So 1+ 1 = 2, because one apple and the other apple are two apples, which is the experience and law summarized from practice. The more reliable idea is that mathematics is an immaterial and eternal objective existence and a natural law waiting to be discovered. Other mathematicians, as well as many people who study computers, think that mathematics is a part of logic and an axiomatic system. This view is still very popular in practice, and it is really powerful. But many of these paradoxes can't stand the scrutiny of the following literary mathematics. In this view, the sum of numbers is axiomatic. Literary mathematics corresponds to formalism on Wikipedia. Many mathematicians, many philosophers and myself hold this view. Formalism holds that a mathematical system is a thinking the game with certain rules, which has nothing to do with the real world. Different from previous views, this view is unprecedented abstract and open. We began to invent all kinds of abnormal rules and play all kinds of strange and inhuman games. In this view, Pythagoras theorem is correct under Euclid's geometric rules, but we can invent other non-Euclid geometry to make it incorrect; Number is an element in algebraic structure, and operation is the rule of the game. This view has brought unprecedented development to mathematics, and also led to a serious disconnect between pure mathematics and reality. Whether it is useful or not is also worth studying for formalists. Although it is not directly applied to reality, if other disciplines actively digest it, they can still find a good home. Idiot math. What I want to mention is intuition. Many people who are engaged in cognitive science and neurology will probably hold this view ... Intuitively speaking, mathematics is a human brain activity and mathematics has been experienced.