On the one hand, from the development of mathematics itself, that is, the development of pure mathematics, this paper discusses how mathematics has prepared a powerful tool to describe its laws for other disciplines, so that pure mathematics has an extremely important and extensive application in the application field; On the other hand, the universality of mathematical application is discussed through the process that various non-mathematical fields need to constantly apply mathematics, constantly put forward new research questions and give mathematics new mathematical research ideas, and promote the emergence of new mathematical theoretical systems and new branches of mathematics.