Abstract

As idealized descriptions of mathematical language, there is a sense in which formal systems specify too little, and there is a sense in which they specify too much. On the one hand, formal languages fail to account for a number of features of informal mathematical language that are essential to the communicative and inferential goals of the subject. On the other hand, many of these features are independent of the choice of a formal foundation, so grounding their analysis on a particular choice of a formal system introduces unnecessary specificity. This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants and their libraries.