Where Mathematical Symbols Come From

There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ' $+$ ' or '8' by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice. In the case of symbols that were introduced a long time ago, the original motivations remain mostly inaccessible to us. Accordingly, motivations that are discussed in the literature are only ascribed retrospectively and should be considered as post-hoc rationalizations. For more recent introductions of new symbols (e.g., in symbolic logic), however, we sometimes do have first-hand accounts by the authors that inform us of the reasons behind their notational choices. In this paper, I present a systematic overview of possible motivations for the design of mathematical symbols, which include practical (such as ease of writing and reuse of previously used symbols) as well as cognitive aspects (such as indicating relations to other symbols or to their intended meanings).