Foundations of mathematical education in the digital age

This article formulates the foundations of modern mathematical education that meet the new goals and objectives of mathematical education dictated by changes in mathematics itself over the last century, by changes in its role in the modern digital world, and by changes in the world. The basic system of concepts is described, starting from which the whole modern mathematics of the finite, as well as primary mathematical education, is built. For all levels of mathematical education and for all learners, the ability to solve problems whose solutions are not known (to the student) and to do it independently with the help and support of a motivating teacher is a fundamental skill. A significant role is played by a computer mathematical experiment and the transfer of tasks with solutions having been found by the student to the computer. This article also describes the actual state of affairs in the Russian mass education system and proposes the necessary actions to implement the formulated principles of modern mathematical education in Russia. Most of the articles presented in this issue demonstrate and detail the implementation of the formulated principles.