In this article we present the results of a discussion on the problems and prospects of artificial intelligence, held at the Chair of Mathematical Theory of Intelligent Systems on October 14, 2020. The topic of the discussion goes back to the classic works of Alan Turing “Can machines think?” and John von Neumann “The Computer and the Brain”, which emerged at the dawn of Cybernetics as a science. Since then, the discussion on the topic “Can machines think?” appeared and faded, but they did not bring much clarity in the understanding of this issue. In recent years, due to the development of the technological base of computing systems, the topic has become relevant again. Together with the scientific base developed in the theory of artificial intelligence and applications in this area, a lot of speculative works have emerged that are ready to declare any device with trivial algorithmic additions “an artificial intelligence system”. This paper attempts to separate the wheat from the chaff by presenting several points of view on this issue.