This article is devoted to the questions of interaction of economics and mathematics, as well as the search for ways of complementarity of these sciences. In this article, we consider some theoretical aspects of the interaction of the two disciplines of economics and mathematics. Methods of applying mathematical models in economics are also considered. The article concludes that the mathematical apparatus lets one correctly explicate and scientifically justify the statements of economic theory. The actual application of mathematics in economic research, allowing an explanation of the past, an ability to see the future, and an evaluation of the results of the research, will require significant efforts, which at the moment in the economy are not adequate.