The article presents the state of technology of websites for designing robots with artificial intelligence. The image of a modern technical site-book as a place for the development of artificial intelligence applications is considered, the possibility of executing algorithms from the page to ensure the connection of robots with real and virtual objects is shown.

Keywords: mathematical network, technical website-book, artificial intelligence, algorithms executed on the website-book, network development of robots

The purpose of the work is to show the influence of the works of Nikolai Orem on the formation of the science of dynamics. Methods. The paper shows that the study of motion led N. Omer to the conclusion that the sum of the harmonic series, which gives an estimate of the traveled path of a uniformly tired traveler, diverges. This proved that the traveler would walk any arbitrarily long distance. The connection of the model proposed by N. Orem with the zeta function and similar paradoxical models in which the path turns out to be finite, despite the slowdown or acceleration of movement, is considered. Result. The trajectory of the wayfarer Orem is demonstrated according to the Riemann formula. Links to training servers with dynamic models animated in 3D graphics and built using the ""live book"" technology are provided.

Keywords: Orem's wayfarer, zeta function, zeros of the function, Riemann problem