From the end of 19 to the beginning of the 20th century, mathematics has developed into a huge discipline, and the Department of Classical Mathematics has established a complete system: number theory, algebra, geometry and mathematical analysis. Mathematicians began to explore some basic questions, such as what is a number? What is a curve? What is integral? What is a function? ..... In addition, how to deal with these concepts and systems is also a problem. There are two classic methods. One is the old axiomatic method, but with the development of non-Euclidean geometry and various geometries, many of its shortcomings are exposed. The other is the construction method or the generation method, which often has limitations, and many problems can be solved without construction. In particular, many problems involving infinity often rely on logic, reduction to absurdity and even intuition. However, what is reliable and what is unreliable cannot be determined without analysis. The analysis and research of basic concepts have produced a series of new fields-abstract algebra, topology, functional analysis, measure theory and integral theory. The perfection of the method is to establish a new axiomatic method, which was first put forward by Hilbert in 1899 "Geometry Basis".