From The Euclidean Geometric Axiom Model To The Hilbert’s Axiomatic Thought

In this article, through reading related books, using historical analysis, On the basis of the predecessors,the author of the paper has done a detailed study of mathematical axioms system from the Euclid era to the Hilbert era.The main work is as following:Firstly, the writer reads up Euclid’s "Elements of Geometry" in detail and makes the full and accurate textual research of its origin and transmission. The paper points out that this book determines its deduction mode in algebra area by logical method but it also has the drawback. For example, some definitions are unclear which cannot be ratiocinated in logic; some axioms are not independent, that is, the axiom system is incomplete.Secondly, the paper dissects why the non-Euclidean geometry comes and its development process. It also affirms that the ideology of Lobachevsky’s non-Euclidean geometry is consistent with Gauss J. Bolyai’s, which features the historical and practical significance of the non-Euclidean geometry.Thirdly, the paper elaborates the origin of Hilbert’s "Foundation of Geometry", excavates his idea of axiomatization and realizes that it’s a complete axiom system which it’s different from Euclid’s. Its creation most powerfully promotes the deep study of mathematics.Fourthly, the paper presents Hilbert’s transformation of the concepts and axioms in Eu-clid’s "Elements of Geometry", who eliminates the logical drawbacks of Euclid’s axiom system with his wisdom and strikes up the complete system of axiomatization.