First of all, advanced mathematics is an indispensable and important means to study economics, and its ideas are widely used in economics. As early as 100 years ago, Marx, the pioneer of human thought, used calculus to study economics and achieved good results. In addition, more than one-third of the Nobel Prize winners in economics, who have long been recognized as the highest honor in the world economy, have degrees in mathematics, and more than half of them have achieved great success in the application of mathematics, such as the great mathematician and Nobel Prize winner Leonid. Kantorovich successfully established and developed the linear programming method and applied it to economic analysis, which pushed the traditional economic problem of optimal utilization of resources from qualitative research and general quantitative analysis to the realistic measurement stage, and made original research on how enterprises scientifically organize production and how to realize optimal utilization of resources within the national economy, making outstanding contributions to the development of today's economics; And John, a famous master of game theory, a professor of mathematics and a Nobel laureate in economics? Nash's "Nash equilibrium theory" and its subsequent theories not only influenced the field of mathematics, but also changed the whole field of economics, and so on. All these show that the progress and development of economics can not be separated from advanced mathematics, which is a powerful tool to solve economic problems and plays an indispensable role in economics.

Secondly, the application of advanced mathematics in economy has strongly promoted the development of economics and greatly expanded the field of economics. Mathematics is a highly abstract theoretical discipline and a widely used tool discipline. A large number of facts have proved that applying advanced mathematics to economic problems plays an irreplaceable role in economics. It has provided a breakthrough development for the development of economics. Hua, a famous mathematician in China, once said: "The size of the universe, the size of particles, the speed of rockets, the ingenuity of painters, the change of the earth, the mystery of biology and the complexity of daily use all involve mathematics." Similarly, the application of advanced mathematics in economics has also emerged new disciplines related to economics, such as mathematical statistics, econometrics, economic cybernetics, game theory and so on. The application of system theory in economics has produced the theory of economic system analysis; The application of cybernetics in economics has produced economic cybernetics; The application of probability theory and mathematical statistics in economy produces insurance. Therefore, the application of advanced mathematics in economics has greatly expanded the field of economics.

Thirdly, the application of advanced mathematics in economy is helpful to improve the practicability of economic problems and the feasibility and scientificity of economic decision-making. As we all know, mathematics itself is deterministic and accurate, and mathematical derivation is logical and rigorous, which makes the study of economic problems using mathematical models naturally rigorous and scientific. In daily life, for a complex economic problem, perhaps a simple mathematical formula can simply express the relationship between various economic factors, which is very convenient for us to analyze the quantitative relationship between various economic variables and provide operational basis for economic decision-making, thus greatly improving the reliability and scientificity of decision-making. For example, in Keynes's national income multiplier principle, gross national product GDP=C (consumption) +I (investment) +G (government expenditure) +X (net export income). According to this formula, in today's world, we can often see that a country usually stimulates economic growth (that is, the increase of GDP) by increasing the number of any one or several factors. For example, developed countries inject a large amount of capital into financial institutions through quantitative monetary easing policies to ensure their normal operation. However, developing countries expand domestic demand through government investment, and carry out industrial stimulus and direct investment. For example, in recent years, our government's measures to stimulate the growth of gross national product and GDP are: first, a large number of 4 trillion economic stimulus, and then a series of policies to expand domestic demand, such as home appliances going to the countryside, auto appliances being replaced with old ones, and so on; On the export side, under the unfavorable export situation in China, we will increase domestic investment and domestic demand, and the central bank's interest rate will be lowered several times in succession to encourage circulation, consumption and investment. Stimulated by these policies, the gross national product (GDP) has increased substantially.