This monograph is devoted to the topic of the interaction of philosophical and mathematical thought and represents the first attempt in Russian literature to write the philosophical history of mathematics of the 17th century. The book, using the example of analyzing the history of the emergence of new mathematical disciplines in the 17th century, shows a close connection between epistemological ideas that guide the development of mathematics and the philosophical and worldview aspirations of the new European person. We consider Descartes' analytic geometry, Leibniz differential calculus, projective geometry, Newton's infinite series, as well as probability theory.