The article discusses the tasks and models of choice, the diagnosis of the conditions of a person and a group of people, forecasting and interpretation in mathematical psychology. The basic concepts and examples of practical tasks in this area are given. The authors note that mathematical psychology is not only mathematical statistics, but more general - an imitation of consciousness, in which neural networks are the most effective means. The apparatus for simulating consciousness is the apparatus of the foundations of mathematics and mathematical psychology. The results of the work show that mathematical methods are actively used to solve applied problems of psychology. Due to the fact that the described tasks are poorly formalized, they have to use an image recognition apparatus and neural networks. The authors of the article show the use of Boolean functions and committee constructions in the problem of collective choice. It is noted that mathematics in psychology can successfully solve the utilitarian problems of diagnosis, prediction and classification. The results obtained as a result of using the mathematical apparatus are the material for further study of psychological phenomena and the development of a specific technique in a given situation.