1. The influence of mathematics on the research and development of modern economics With the development of economics and the deepening of research, economists gradually realize that when considering and studying problems, it is necessary to have a rigorous theoretical analysis model and conduct empirical tests through econometric analysis methods, and it is necessary to fully understand what specific conditions are needed for a conclusion to be established. Inference and analysis based solely on text description can not guarantee the standardization of the premise of the studied problem and the consistency and rigor of reasoning logic, nor can it guarantee the accuracy, verifiability and rigor of its research conclusions. In this way, taking mathematics and mathematical statistics as basic analytical tools has become one of the most important analytical tools in modern economic research. Everyone who studies and studies modern economics must master the necessary knowledge of mathematics and mathematical statistics. In modern economics, almost every field needs knowledge of mathematics, mathematical statistics and econometrics to a greater or lesser extent. Without relevant mathematical knowledge, it is difficult to accurately understand the connotation of concepts and discuss related issues, let alone the boundary conditions or constraints needed for research and conclusion. Understanding concepts is the premise of learning a subject and analyzing a problem. If you want to learn modern economics well and engage in the research of modern economics, you need to master the necessary mathematics. Second, the significance of mathematics in the application of economics If mathematics is not used in economics, economics cannot become modern economics. Many economic concepts need to be defined by mathematics, and economic behavior and economic phenomena are mainly analyzed and studied by mathematical language. Use mathematical language to express the assumptions about economic environment and personal behavior, use mathematical expressions to express the logical relationship between economic variables and economic laws, study economic problems by establishing mathematical models, and logically draw conclusions according to mathematical language. Therefore, without understanding the relevant mathematical knowledge, it is difficult to accurately understand the connotation of the concept, and it is also impossible to discuss related issues. The functions of mathematics in theoretical analysis include: (1) making the language used more precise and refined, and assuming that the expression of preconditions is clearer, which can reduce many disputes caused by unclear definitions; (2) The logic of the analysis is more rigorous, which clearly clarifies the boundary and scope of application of an economic conclusion and gives the exact conditions for the establishment of a theoretical conclusion; (3) Using mathematics is beneficial to get less intuitive results; (4) can improve or popularize the existing economic theory. Third, the limitations of the application of mathematics in economics First of all, economics is not mathematics, and mathematics is only used as a tool in economics to consider or study economic behavior and economic phenomena. Mathematics, as a tool and method, can only play its due role within a reasonable economic theoretical framework and cannot replace economics. Secondly, the development of economic theory should study and analyze the inherent nature and laws of real economic activities from its own unique research perspective. Any mathematical method used in economics cannot be separated from certain assumptions. It is not unconditionally applicable anywhere, but conditionally applicable to specific fields. Thirdly, the mathematical econometric analysis method is only one of the tools to implement economic theories and methods, not the only tool. Excessive dependence of economics on mathematics will lead to dislocation of economic research resources and simplification of economic research dimensions, which is not conducive to the development of economics. 4. Some misunderstandings about the relationship between mathematics and economy 1. Deny the role of mathematics in economics. Some economists in China think it is very important to produce economic thoughts, so they deny the role and achievements of mathematics with strong technicality. We don't deny the importance of economic thought, but without the tool of mathematics, generally speaking, we can't guarantee whether our economic thought or conclusion is rigorous or not, and whether there are any application errors. Modern economics has become a very rigorous social science discipline. Without rigorous discussion, your ideas or results will not be recognized by others. Others think that the economic problems of mathematical research are far from reality. In fact, most of the problems discussed in mathematics in economics come from the real world, which is very realistic and enlightening. 2. Economics is often too mathematical. The excessive mathematicization tendency of economics restricts people's thinking of solving problems and restricts people from seeking other effective solutions, thus hindering the research and development of economics to some extent. Economics is a science that studies the relationship between resource allocation and social economy. It has both social science attributes and natural science attributes. In order to allocate resources more reasonably and effectively, it is necessary for economics to use mathematical thinking tools.