The book outlines general ideas about systems theory, on the basis of which fundamentally new ideas about systems in mathematics are created. Summarizing the known and his own understanding of the essence of systems, the author gives them his own universal definition based on a hypothesis about the physical picture of the world. Through the prism of his own understanding of systematicity and the universal definition of systems, the author examines a number of inconvenient questions for mathematical science and gives unexpected answers to them.