Six mathematical problems for economics and management research in the big data era

Mathematics, as a fundamental tool for quantitative analysis, characterizes the functional relationships among variables and underpins the development of core analytical tools in economics and management science, such as optimization theory, game theory, statistical theory, and systems theory. At the same time, many real-world problems in economic and management research provide new material for mathematical inquiry, thereby stimulating the development of new mathematical theories. As societal complexity and data structures evolve, the relationships between variables exhibit characteristics such as non-convexity and nonlinearity, breaking the assumptions underlying some existing mathematical theories. For example, many mathematical problems encountered in economics and management are nonconvex, nondifferentiable, or involve high-dimensional and intractable optimization or statistical models, necessitating the development of new mathematical theories and methods. In this paper, we approach the topic from the perspectives of optimization theory, game theory, and statistical theory, analyze the current research bottlenecks, and propose six mathematical problems. The goal is to attract more mathematicians to engage in this line of research, to advance relevant mathematical theories, and to provide more effective methods for the development of economics and management science.