First, economic research is inseparable from mathematics.
The history of science reveals the fact that all disciplines belonging to "science" are based on the practice of human social activities. The division of disciplines and the induction of their respective characteristics are all the results of "human" factors. As far as the intrinsic nature is concerned, the interaction, mutual influence and mutual penetration between disciplines are extremely obvious, not only within the natural science and social science, but also between the two disciplines.
Economics is a science that studies the allocation of social resources and socio-economic relations. Based on the measurability of resource stock and flow, in order to make resource allocation more fair and efficient, it is necessary for economics to use mathematics as a rigorous, accurate and practical thinking tool. The economic relationship formed in the process of resource allocation involves economic system, social psychology, values and other factors that are difficult to quantify. Economics, as an empirical science that focuses on speculation and qualitative analysis, cannot take mathematics as the basis or universal tool in economic research.
The role of mathematical methods in economics has been controversial in theoretical circles for at least 100 years. From "opposing the obscurantism of mathematics" to asserting that there is no science without mathematics, the views are quite different.
As a theoretical summary and abstraction of actual economic activities, economics has never left mathematics from its germination to its formation. On the one hand, the concept of number is produced in the long process of production activities. On the other hand, production activities always need different disciplines of economics, such as demography, marketing, labor and wages, price, finance, finance, accounting, etc. These disciplines are all related to counting, measurement and calculation. Without the concept of number and calculation method, it can be said that there would be no such subject.
The practice of economic activities determines that the study of economic theory is inseparable from quantity, and the application of mathematics in economics is closely related to the development of mathematics itself. Throughout the history of mathematics, it can be divided into four basic stages with qualitative differences. The first stage, the counting and arithmetic period (ending in the 5th century BC); In the second stage, elementary mathematics is a period of unchangeable mathematics (ending in17th century); The third stage, the period of variable mathematics (ending in19th century); The fourth stage, the period of modern mathematics. The outstanding characteristics of the modern mathematics period are that the branches of mathematics are constantly developing and expanding, the object and application scope of mathematics are greatly expanded, and the most common and unified concepts in mathematics are revealed with higher theoretical abstraction and generalization.
Although the concepts and conclusions of mathematics are extremely abstract, they all come from reality and can be widely used in other disciplines and social life practice, which may be the fundamental reason why mathematics not only has infinite vitality but also has great influence and attraction to all disciplines. As Engels said in Anti-Turin, the root of the possibility of applying mathematics to study the real world lies in that mathematics is extracted from the world itself and only shows the forming part of the internal relations in the world, so it can be widely used.
With the development of mathematics, the application scope of economics to mathematics is also expanding. /kloc-before the 0/9th century, elementary mathematics was mainly used in economics. From william petty's Tax Theory (1662) and Political Arithmetic (1676) to Quesnay's Economic Table (1758), the situation and changes of national wealth are described and analyzed with figures, charts and simple calculations. Since19th century, the concepts of variables and functions have been introduced into the study of economics, and the application of mathematical methods has become more common. Among them, Conrad's Research on Mathematical Principles of Wealth Theory (1838) is a book that consciously uses mathematical formulas to explain economic problems. After that, Tu Neng was based on the empirical formula of actual quantity (1850), Walras's equilibrium trading theory (1874), Harold's economic growth model (1948), Ding Bogen's 48-equation large-scale economic growth model (1939) and Lewis's "dual economy". Tobin's intermediate variable model (1958) and Solow's and Roman's economic growth models in the 1970s and 1990s. , published a large number of books on studying economic problems by mathematical methods. The common feature of these works is that they not only use general economic concepts and traditional economic methods, but also use the simplest mathematical symbols to the latest mathematical methods
From the inseparable development of economics and mathematics, we can know that mathematics can provide a unique and rigorous analysis method for economics. Like logic commonly used in qualitative analysis, mathematics is a tool to understand the world. However, the application of mathematics is meaningful only if it is combined with the profound theory of specific phenomena and the strict regulation of "quality", otherwise economic research will fall into the game of formulas and mathematics without substantive content.
Second, the deviation of using mathematical methods in economic research.
At present, the focus of debate about the application of mathematics in economic research is not whether economics should use mathematical methods, but how to use them. For the former, the practice of widely applying mathematics in economic activities and the research results of applying mathematical methods to economic theory have been answered positively, while for the latter, there are different views and opinions. It leads to serious deviation in the application of mathematical methods in economics, which affects the research effect. If it continues to develop, it may lead China's economic research astray.
The main problems in applying mathematical methods in economic research are:
1. The scope of application is too wide. The boundary of mathematical application is something that can be quantified, and the field of vision of economic research is all human economic activities and social relations. Not all economic activities and economic relations can be quantified, especially socio-economic relations, which are influenced by many social factors such as system, morality, culture and history, and these factors are almost impossible to quantify. It seems reasonable to use mathematical formulas to express the relationship between unquantifiable factors, because there is no operational relationship between them at all, and it is impossible to verify right or wrong by quantitative calculation. Although mathematics is also a language that reflects people's thinking, not all sciences can be transformed into the language of mathematics. The same is true of physics, chemistry, biology and other disciplines closely related to mathematics. Some problems may not be solved even if they are transformed into mathematical relations. However, social science, which studies human social activities, has more restrictions on the application of mathematics. Trying to dehumanize economics, even "mechanize" people in economic activities, and formalize people's activities is undoubtedly a kind of self-destruction of economic research.
It is easy for economics to indulge in the exploration of methodology and stick to microeconomic research, while ignoring and ignoring the overall problems involving macroeconomic system reform, mechanism design and social relations adjustment. As Richard Blencke said, modern economics is more and more keen on complex mathematical calculations, complacent about wonderful mathematical models and playing with mystery. The result is that economics is gradually divorced from the richness, complexity and irrationality of daily life. The trend of economic research in recent years has revealed some worrying signs in this regard.
2. The choice of mathematical model constraints is too arbitrary. Almost all theories are based on setting some premises and assumptions. For example, there are four accounting assumptions in accounting: accounting subject, going concern, accounting period and monetary measurement, while there are assumptions of "economic man" and "complete marketization" in western economics. The logical rigor of mathematical methods and the essence of calculation accuracy determine that any mathematical model is bound by several conditions, and only when these conditions are met can the mathematical model be established. The more complex the equation is, the more constraints it will be. At present, some economists completely ignore the constraints when establishing mathematical models, which is too simplistic, and the determination of constraints is very arbitrary, starting from the needs of the model itself, regardless of whether it meets the objective and practical requirements.