Combinatorial mathematics in a broad sense is discrete mathematics, and combinatorial mathematics in a narrow sense is the general name of graph theory, algebraic structure, mathematical logic and so on. But this is only the difference between different scholars. In a word, combinatorial mathematics is a science that studies discrete objects. With the development of computer science, the importance of combinatorial mathematics is increasingly prominent, because the core content of computer science is to process discrete data with algorithms.

According to the current research and development of combinatorics, it can be divided into the following five branches: classical combinatorics, combinatorial design, combinatorial order, graphs and hypergraphs, combinatorial polyhedron and optimization. Since combinatorics involves almost all branches of mathematics, it may be as impossible to establish a unified theory as mathematics itself. However, how to establish some unified theories on the basis of the above five branches or form some new branches of mathematics independently from combinatorics will be a new challenge for mathematicians in the 2 1 century.