Mathematical Modeling: Problems and Prospects

The article examines the problems and prospects of mathematical modeling as a tool for scientific inquiry and decision-making. It is shown that models of complex systems, whether ecological, economic, or social, face difficulties with parameter identification, incomplete data, and computational complexity. The main approaches are analyzed, including differential equations, agent-based modeling, and machine learning methods, together with their limitations. Particular attention is paid to model validation and to the correct transfer of results from controlled conditions to real processes. Using a model of information diffusion in a social network as an example, the paper demonstrates how combining analytical and numerical methods makes it possible to assess the sensitivity of a solution to input parameters. The prospects of the field are discussed, including the integration of hybrid models, the use of digital twins, and greater transparency of algorithms. The author concludes that the value of a model depends not only on its accuracy but also on its ability to produce testable predictions and well-grounded recommendations for practice.