Evolution of mathematical modeling and analysis methods in economic theory from the 17th to the 20th century

The paper presents the evolution of mathematical modeling methods within economic theory. Particular attention is paid to mentioning scientists who have made significant contributions to mathematical modeling within economic theory, as well as presenting landmark scientific works and their contribution and influence on economic theory. The paper presents the following scientists: William Petty, François Quesnay, Antoine-Auguste Cournot, John Stuart Mill, Eilhard Alfred Mitscherlich, Charles Cobb, Paul Douglas, Knut Wecksell, Frank Ramsay, David Kas, Tjalling Charles Koopmans, John von Neumann, Oskar Morgenstern, Léon Walras, Abraham Wald, Ragnar Frisch, Vasily Vasilyevich Leontief, Leonid Vitalievich Kantorovich, Robert Solow, Viktor Valentinovich Novozhilov, Vasily Sergeyevich Nemchinov, and Edmund Phelps. In this article, the authors highlight the fundamental principles and essence of the models and studies developed by scientists. The paper presents a sequence of integrating mathematical modeling techniques and methods into economics. It is worth noting that this paper examines the prospects for integrating mathematics into economic theory using examples from ancient times. However, as the paper progresses, the authors analyze works from a different era, which is more suitable for analyzing mathematical modeling, as it was during this period (the 15th-20th centuries) that more compelling preconditions for the emergence of this phenomenon and its integration into economics were found. The paper presents a conclusion regarding the importance of integrating mathematical modeling into economics.