A book by the famous physicist about modern approaches to the study of brain activity, mental processes, etc. The fundamentals of the mathematical apparatus are outlined - from classical theory (Gödel's theorem) to the latest achievements related to quantum computing. The book consists of two parts: the first part discusses the thesis about the incomputability of consciousness, the second part examines issues of physics and biology necessary to understand the functioning of the real brain. For a wide range of readers interested in science.