There is a standard interpretation of the mathematical register, including the symbolic language, in the sense that at least most of the time most mathematicians would agree on the meaning of most statements made in the register. Students have various other interpretations of particular constructions used in the mathematical register.

- One of their tasks as students is to learn how to extract the standard interpretation from what is said and written.

- One of the tasks of instructors is to teach them how to do that.