We will now give an informal description of the language of mathematics, and highlight some of the major issues that arise to confront a theory of mathematical language. No systematic survey of this kind exists in the literature, and we will therefore for the most part construct our description ab initio. Exceptions will be drawn in certain areas where Ranta has discussed similar phenomena, especially in §2.4.
We will start by introducing a basic division of the language of mathematics into ‘textual’ and ‘symbolic’ halves (§2.1) and introducing the most important way in which the language of mathematics differs from natural languages (§2.2). We will then examine each of textual and symbolic mathematics in greater detail (§2.3 and §2.4), and finally turn to the macroscopic discourse structure of mathematical language (§2.5).