(1) The mathematical problem-solving method makes it possible to solve mathematical problems and acquire mathematical knowledge. Without mathematical problem-solving methods, there will be no progress in mathematics.
(2) In the process of understanding and transforming the world, human beings always set various tasks for themselves according to certain purposes. We should not only put forward the task, but also solve the problem of how to complete it. For example, our task is to cross the river, but we can't cross it without a bridge and a boat. If we don't solve the problem of the bridge and the problem of the boat, crossing the river is empty talk. The study of mathematical methods is equivalent to the problem of bridges and ships mentioned here. The research purpose of mathematical problem solving method is to solve practical problems.
(3) The research on mathematical problem-solving methods is the core of mathematical methods and the cornerstone of the development of modern mathematics. For example, the creation and development of calculus is almost an example of the creation and development of general mathematics. Infinitesimal method, Lagrange multiplier method, Lobida rule, etc. It is not only an important part of calculus knowledge, but also provides a powerful method for solving specific problems. While solving the "Seven Bridges Problem", Euler gave euler theorem's theorem, which provided a powerful method for solving similar graph theory problems and pointed out the direction for the research and development of graph theory. Another example is the contraction mapping theorem in functional analysis, which is proved by iterative method, and this iterative method has been widely used in numerical analysis, dynamic systems and many other fields. Contraction mapping theorem has also become a fixed point theorem, which is widely used to solve algebraic equations, differential equations, integral equations, mathematical economics and other equations.
(4) The research purpose of mathematical problem-solving method is to study and discuss the development law of mathematics, the thinking method of mathematics and the general law of discovery, invention and innovation in mathematics.