Research on automated reasoning systems based on a number of paradigms that support human activity in formalized text processing began in the late 1950s – early 1960s, when computer performance and memory space became sufficient for programming of complex intelligent processes. The so-called evidential paradigm was among them and it can be viewed as a way for integrating all reasonable paradigms oriented to the development of computer languages for representing formalized texts in the form most suitable for a user, formalization and development of the evidence of a computer-made proof step, creation of the information environment having influence on a current evidence of a machine proof step, and an active human-machine interaction. This work contains a brief description of the evidential paradigm and its implementation in the form of intelligent systems intended for the symbolic and deductive processing of mathematical texts focusing main attention on their features and peculiarities.