Typographical conventions in mathematical formulae

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Typographical conventions in mathematical formulae provide uniformity over numerous mathematical articles and books and help to read mathematical texts.

Mathematical notation includes letters from various alphabets, as well as a set of special mathematical symbols. Letters in various fonts often have specific, fixed meanings in particular areas of mathematics. A mathematical article or a theorem typically starts from the definitions of the introduced symbols, as, e.g., in: "Let G(V, E) be a graph with the vertex set V and edge set E...". Theoretically it is admissible to write "Let X(a, q) be a graph with the vertex set a and edge set q..."; however, this would decrease readability, since the reader has to consciously memorize these unusual notations in a limited context. In fact, there is the "mathematization" joke that teaches how to write incomprehensible articles by abusing and misusing mathematical notation; in particular it thrives upon using standard symbols in a nonstandard way without explicitly defining them.

Usage of subscripts and superscripts is also one of important conventions. In the early days of computers with limited graphical capabilities for text sub/superscripts were represented with the help of additional notation. In particular, $n 2$ could be written as n^2 or n**2 (the latter borrowed from FORTRAN) and $n 2$ could be written as n_2.

[edit] General rules in American mathematical typography

The rules of mathematical typography differ from country to country; thus, American mathematical journals and books will tend to use slightly different conventions from those of European journals.

One advantage of mathematical notation is its modularity — it is possible to write extremely complicated formulae involving multiple levels of super- or subscripting, and multiple levels of fraction bars. However, it is considered poor style to set up a formula in such a way as to leave more than one level; for example,

$AX = \Omega_{e^x} + \begin{matrix}\frac{a}{b+\frac{c}{d}}\end{matrix}$

might productively be rewritten as

$AX = \Omega_{\,\exp(x)} + \begin{matrix}\frac{a}{b+(c/d)}\end{matrix}$

Incidentally, the above formula demonstrates the American rule that italic type is typically used for Latin letters, and upright type for Greek letters. Upright type is also standard for digits and punctuation. Bold Latin capital letters usually represent matrices, and bold lowercase letters are often used for vectors.

Certain important constructs are written in blackboard-bold letters. Some examples are the natural numbers $\mathbb{N}$ , the integers $\mathbb{Z}$ , the rational numbers $\mathbb{Q}$ , the real numbers $\mathbb{R}$ , etc.