The study captures and summarizes the experience of teaching philosophy at non-specialized faculties of universities and institutes. The broad non-humanities student population turns out to be the social cross-section and the group by which one can study society in its specific humanitarian perspective. The youth student audience reacts most quickly and as specifically as possible to the changes and processes taking place in the country. The authors analyze three time stages of philosophy teaching over the past few decades in Russian higher education. The first stage begins with the time of Perestroika and covers the first half of the 1990s; it is characterized by the introduction of ‘new philosophies’ into the stable Marxist canon of education. The second stage is connected with the spread of the values of postmodernism and universal tolerance in various spheres of culture, including the rather conservative sphere of higher education. We are currently experiencing the third stage, which began with the widespread adoption of smart phones and the integration of neural network to universities. Each of these stages is characterized by key problems and nodal points that the teacher faced and is currently working with in the classroom. The research substantiates the thesis about the specific form of teaching philosophy to the youth audience of a Russian university. This work, understood and implemented as a mission, a specific service, corresponds to those historical forms of existence and dissemination of philosophy that have accompanied it since its inception. The missionary potential of a teacher’s work in time of a crisis in the humanities be it at the level of schooling or higher education does not decrease or becomes easier, but instead increases and becomes more complicated every year. However, according to the authors of the study, without this potential, philosophy loses its salvific and life-giving role in the formation and upbringing of the young student generation in Russia.