Axiom is a basic proposition based on the self-evident basic facts of human reason, which has been tested by human practice for a long time and needs no further proof. If there is no hypothesis, nothing can be deduced except tautology. Axiom is the basic assumption that leads to a specific set of deductive knowledge. Axioms are self-evident, and all other assertions (theorems if we are talking about mathematics) must be proved by these basic assumptions. However, there are different interpretations of mathematical knowledge from ancient times to the present, and finally the word "axiom" has a slightly different meaning in the eyes of today's mathematicians, Aristotle and Euclid. The ancient Greeks thought that geometry was also one of several sciences, and regarded geometric theorems as equal to scientific facts. They developed and used logical reasoning as a method to avoid mistakes and used it to construct and transmit knowledge. Aristotle's post-analysis is a decisive exposition of this traditional view. The realization of axiomatization of extended data is as follows: ① Select a group of initial concepts from its numerous concepts, and introduce the rest concepts in this theory from the initial concepts through definitions, which are called derived concepts; (2) Choose a set of axioms from a series of propositions, and the other propositions are derived from axioms by applying logical rules, which are called theorems. The process of deducing theorems from axioms by applying logical rules is called proof, and every theorem is confirmed by proof. The deductive system consisting of initial concept, derived concept, axiom and theorem is called axiom system. Initial concepts and axioms are the starting points of axiomatic systems. Axiom system is divided into classical axiom system, modern axiom system or formal axiom system. The most representative classical axiom system was established by the ancient Greek mathematician Euclid in his book Elements of Geometry. The first modern axiomatic system was put forward by D. Hilbert in 1899. In the book Fundamentals of Geometry, he not only established the formal axiomatic system of Euclid geometry, but also solved some logical theoretical problems of axiomatic methods. For example, Euclid's Elements of Geometry stipulates five axioms and five postulates (from a modern point of view, postulates are also axioms), and all theorems in plane geometry can be derived from these axioms and postulates.