A Study On The Mathematical Thought Of Marx's Political Economics And Its Development

The adoption of mathematical analysis method to analyze economic phenomena,demonstrate economic laws,and infer conclusions or theorems has become the essential tool of economic research.Xi Jinping attaches great importance to the development of mathematics,gives a high evaluation of Marx's mathematical research,as well as has repeatedly emphasized the significance of modern mathematical tools for analyzing economic problems.At the symposium on the work of philosophy and social sciences,Xi Jinping argued that“We can also use the useful knowledge systems accumulated in modern social sciences,i.e.,model deductions,quantitative analysis and other effective methods,and moreover,we should have a good command of them.”In the“Speech at the Conference Commemorating the 200th Anniversary of Marx's Birth”,Xi Jinping mentioned that Marx wrote a huge number of notes on subjects such as mathematics,and he quoted Engels'words which read that Marx had unique discoveries in the field of mathematics;in the paper“Continuously open up the new realm of contemporary Chinese Marxist political economy”,Xi affirmed that Thomas Piketty's had used full and accurate data to prove the degree of inequality in the United States and other Western countries in the book“Capital in the Twenty-First Century”,the conclusion of which was worth thinking about.From the perspective of reality,the mathematical analysis of Marxist political economy is obviously inadequate,and Xi Jinping has indicated the direction of the development of mathematical analysis of Marxist political economy for“continuously open up the new realm of contemporary Chinese Marxist political economy”.Firstly,since Marx has conducted abundant research on mathematics,mathematical analysis is an important part of Marxist political economy methodology system and the mathematical logic is one of the intrinsic properties of Marxist political economy.Marx studied math attempting to deep into the political economics.With the aid of mathematical method,Marx made the main theory of political economy abstract,and with the help of mathematical logic,he promoted the construction of political economy theory.The process was determined by the fundamental attribute,i.e.,the unity of“quantity”and“quality”,and the property of mathematics as the main research objects of the political economy.Marx was proficient in mathematics and his advanced route to mathematics was in line with the general law of the cognition.His veering from idealism to materialism marked the basic premise to study mathematics.It was Marx who firstly studied mathematics with historical materialism and with dialectical materialism,and then he promoted the unity of materialist dialectics and political economy practice in the study of advanced mathematics.Marx made outstanding contributions to the development of advanced mathematics.He promoted the development of advanced mathematics,proposed the dialectical relationship between“infinitesimal quantity”and“0”,created the 0/0 derivation method,and systematically sorted out the characteristics and shortcomings of“mysterious calculus”,“rational calculus”and“pure algebraic calculus”,keenly discovered the link from algebra to differential calculus,creatively proposed the key theories,dialectical methods and general formulas of Marx's calculus,and revealed the essence of calculus,which broke through the key leap theory from elementary mathematics to advanced mathematics.Secondly,Marx's theories,i.e.,labor theory of value,theory of surplus value,reproduction theory,transition issues,and average profit,production price,land rent theory,etc.,contain rich mathematical ideas,embodying the characteristics of rigor,simplicity,and reasonability.Accordingly,the expression of classical mathematical analysis and the study of the development logic of mathematical analysis have obvious assumptions of the times,problem limitations,and ideological differences,which can further reconstruct mathematical expressions for assumptions,measurement units,and formula models.First,Marx's definition and calculation for the quantity of commodity value and labor productivity contains the idea of“Law of Large Numbers”,using the mathematical nature of the law of average values to explain the scientific nature of the law of value.In the process of discovering surplus value,Marx was keenly aware of the fact that the“intangible added value”embodied in the currency conversion to capital process could only be realized when the existence of special commodities established the equivalent logic of circulation.Following mathematical logic,Marx discovered the fundamental carrier for capitalists to extract surplus value,which embodied the mathematical“price scissors”and the mathematical thought of transmission;Marx's ways of explaining the simple reproduction,expansion and regeneration problem,and transformation problem were all based on the inherent mathematical meanings given to“quality”and“quantity”,and must maintain a certain proportional relationship,which promoted the development of theoretical logic from a mathematical perspective.Furthermore,the classical mathematical analysis of Marx's political economy was realized by elementary mathematical formulas,literal logic and examples.The mathematical expressions of Marx's labor theory of value,classical surplus value theory,reproduction theory,and transformation problems all reflected rigor,simplicity,and reasonability.Based on the basic viewpoints of Marx's political economy and the basic premise assumptions of the era to which Marx belonged,the author tried to build the“mathematical model of the total production volume of value and use value”included in the classic labor theory of value,and the“mathematical model of value and labor productivity and its changes”,“the mathematical model between departmental productivity and the change of value”,“the mathematical model of the change of enterprise labor productivity and the change of value”,“the mathematical model of the relationship between the change of labor productivity of an individual enterprise and the change of the value of the enterprise unit labor time”etc.;tried to establish the“Marxian absolute surplus value production model”,“relative surplus value production model”,and“excess surplus value production model”included in the classic theory of surplus value;and also tried to establish the“classical simple reproduction”and“classic expanded reproduction”,“classical value transformation problem”,“average profit and average price”,“commercial capital”,“land rent”and other theoretical mathematical models.In addition,seeing from how scholars at home and abroad dialectically explore the development logic and path system of Marx's labor theory of value,surplus value theory,reproduction theory,and transition issues,we find Western scholars seem to have enriched the analytical content of Marxist political economics mathematical expression,though,still expose the ideological prejudice against the development of Marx's political economy as western scholars tend to overemphasize the importance of mathematical tools and often make the mistake of“mathematical logic is greater than theoretical logic”;while the research of domestic scholars basically focuses on the review of western scholars'research and on the mathematical construction of classical theory,which still lack a more systematic and comprehensive innovation.Last but not least,the modern reconstruction of the mathematical analysis of Marx's political economy must be based on the new laws,new changes,and new phenomena that have emerged in the economic and social development process,so as to further reconstruct the modern assumptions,measurement units,and formula expression systems.Under the premise of basic concepts and methods of Marxist political economy,it is in line with contemporary economic and social development to promote the construction of mathematical models.Finally,the scientific development of Marxist political economy,based on the basic positions,perspectives and methods of Marxism,calls for a correct view of the mathematical analysis of Marx's political economy and a dialectical analysis of the evolution logic of the mathematical analysis of Marxist political economy in foreign countries.In addition,the development of Marxist political economy,starting from the perspective of the essential attributes of Marxist political economy and the needs of the times,innovates the research on the productivity and production relations of Marxist political economy,continuously improves the scientificity and explanatory power of the mathematical analysis of Marxist political economy,and forms the basic principles,effective path and method systems in order to advance the Marxist political economy in 21^st century scientifically.