The paper deals with the problem of various ways of representing concepts in specialist communication. In specialist communication in the field of mathematics we are dealing with a situation in which the concepts which are the basis of specialist knowledge are abstract. Therefore, in communication with the recipient, the problem of their representation arises. It turns out that they can be represented in a number of ways not seen outside the field of this science. In turn, the very choice of concrete representations may seem to be closely related to the communicative situation. Consequently, communication in mathematics turns out to be very complex in terms of the medium used to express content. This is because it can be represented by a word, a phrase or a metaphor, as well as by a symbol, a longer symbolic notation, or even a drawing. Such a wide range of various representations is a peculiar phenomenon in terminology, which is an important part of specialist communication, because it expands the understanding of a term as a sign, especially a linguistic one, with new, often non-literal material. The research touches upon an important problem of what unusual means a sender of a specialist text may use to present a term. The research material consists of popular representations of integrals, appearing in mathematical texts of varying levels of specialisation.