In a mathematical theoretical system, starting from as few original concepts as possible and a set of unproven axioms, the axiomatic method is to use the law of pure logical reasoning to build the system into a deductive system. It comes into being with the development of mathematics and logic.

Around the 6th century BC, Thales, a Greek mathematician, began to prove geometric propositions, which opened up the deductive scientific direction of geometry as proof. In the 4th century BC, eudoxus of Pythagoras School established a deductive method based on axioms when dealing with incommensurable measures. Zhi Nuo of Ionian School used reduction to absurdity in his argument. Plato expounded many logical principles. Aristotle systematically summed up the axiomatic method in his book Analysis, and pointed out the logical structure and requirements of deductive proof, thus laying the foundation for the axiomatic method.

At the turn of the 3rd and 4th century BC, the Greek mathematician Euclid applied the axiomatic deduction method of formal logic to geometry on the basis of summarizing the geometric knowledge accumulated by predecessors, and completed the handed down work "The Elements of Geometry" by using a series of basic concepts and axioms he abstracted, which marked the birth of axiomatic method in the field of mathematics. Because of the complicated expression and content of the fifth postulate in the Elements of Geometry, people doubt the necessity of this postulate itself. In 2000, people tried to give a proof of the fifth postulate, but all the attempts failed. /kloc-in the 9th century, Lobachevsky, a young Russian mathematician, learned lessons from the failures of his predecessors, raised questions from the opposite side, gave a new axiom system, and founded non-Euclidean geometry. This is the further development of axiomatic method.

1899, the German mathematician Hilbert wrote a book "Fundamentals of Geometry" on the basis of predecessors' work, which solved the shortcomings of Euclidean geometry, perfected the axiomatic method of geometry and created a brand-new formal axiomatic method. In order to avoid the paradox in mathematics, Hilbert thought that we should try to prove the non-contradiction of mathematics absolutely, which led him to engage in the research of proof theory, so Hilbert pushed the axiomatic method to a new stage, that is, the stage of pure form development, and produced the pure form axiomatic method.

Axiomatization of geometry has become a model of other disciplines and branches. Axiomatic systems of various theories have appeared one after another, such as axiomatization of theoretical mechanics, axiomatization of relativity, axiomatization of mathematical logic, axiomatization of probability theory and so on. At the same time, the pure form axiomatic method promotes the research of mathematical foundation and broadens the prospect for the wide application of computers.