Indeed, mathematical notation is often used (and abused) where plain language would suffice. This is so widespread, in fact, that one might think that there is

Indeed, mathematical notation is often used (and abused) where plain language would suffice. This is so widespread, in fact, that one might think that there is a conspiracy, or a contest, to come up with as unreadable a text as possible. On the other hand, the (original) purpose of mathematical notation, in its condensed form, is facilitating and, in many cases, automating reasoning and calculations on a piece of paper. (You wouldn't want do perform long division using words, believe me.) Also, the plain language may bring the possibility of an uncertainty in meaning and/or misinterpretation, so a definition or a theorem stated using notation instead often serves to minimize that possibility.