Mathematical Models of Intelligence, Axiomatization, Algebra and Paradox of Artificial Intelligence, Prospects for the Development of Intelligence

Artificial intelligence (AI) is one of the most important technologies of our time, which is actively being introduced into all spheres of human activity. But are there limits to the knowledge of human intelligence (HI) or artificial intelligence? The first (mathematical) part of the article discusses the general problems of the limits of intelligence. Mathematical models of AI and HI are given. Classification of AI is carried out. A fundamental, irremovable boundary (paradox) of AI is constructed and the path of AI limitations to overcome the paradox is indicated. Algebraic operations are introduced on the set of AI and an AI algebra is constructed. The direction of AI is formalized by introducing the axioms of AI. The boundaries of HI in their logical connection with the boundaries of AI are proposed for consideration. The second (philosophical) part of the article considers the fundamental issues of the development of the entire topic of "Artificial Intelligence" and the prospects for the relationship between AI and HI. The thesis of the inevitable end of the era of humanity and the "quiet" Apocalypse through AI is substantiated.