The mathematical software developed from the algorithm standard program was formed in the early 1970s. With the development of several major mathematical software projects, such as the NATS project in the United States, people have explored ways, methods and technologies to produce high-quality mathematical software. After long-term accumulation, a wealth of mathematical software has emerged, covering a wide range of mathematical fields. Mathematical software in some fields, such as numerical algebra and ordinary differential equations, has been improved day by day. Important progress has also been made in other fields, such as partial differential equations and integral equations. These mathematical softwares have become powerful tools for algorithm research, scientific calculation and application software development. Software that uses numerical methods to solve mathematical problems and gives solutions in discrete or other approximate forms. Numerical software products can be divided into three levels: mathematical program library, mathematical software package and mathematical software system.

Comprehensive mathematics library involves a wide range of mathematics fields. The library is mainly composed of algorithm programs, supplemented by problem-solving programs and functional modules. There are many products, but each has its own emphasis. For example, some focus on numerical algebra and statistical calculation; Some of them have strong processing functions in numerical integration, differential equations and other fields; Some are good at interpolation and approximation.

Mathematical software package is a collection of program components specially designed for a certain subject or application. The special software package is usually produced after in-depth research on the processing object, which has better adaptability and stronger processing ability. They are important resources for libraries and application software. There are many specialized mathematical software packages, such as software packages for solving a class of mathematical problems, software packages for algorithm research and software packages for teaching.

Mathematical software system is an application system for a class of mathematical problems, which has a complete control management system and user interface language system. According to the mathematical problems clarified by users, it can automatically judge the rationality and completeness of the problems, analyze the types and characteristics of the problems, choose the appropriate algorithm, or dynamically select the algorithm with the solving process, automatically handle or report the problems in the solving process, and verify the accuracy of the results. This is an advanced mathematics software, which is simple and easy to use. The mathematical derivation is completed by symbolic calculus of computer, and the solution is given in the form of mathematical expression. Such as function expansion, algebraic calculus, function derivative quadrature, algebraic equation and differential equation solution. By using the formula processing system, users can quickly and accurately deduce formulas and deal with mathematical problems.