Typographical conventions for mathematics

In the scientific manuscripts I edit, certain deviations from the generally accepted typographical conventions for mathematical text crop up frequently enough that I thought I would discuss a few of them in this post. First, let’s look at some of the basic conventions:

• Single-letter symbols for variables, physical quantities, and physical constants are set in italic type: for example, V for volume and h for Planck’s constant.
• Multiletter variable symbols, mathematical constants, trigonometric functions, mathematical operators, numerals, punctuation, and fences are set in roman type: for example, cmc for critical micelle concentration, π, sin, and Δ (difference), δ (small difference), and d (infinitesimal difference).
• Superscripts and subscripts that are themselves symbols for variables or physical quantities are set in italic type, whereas superscripts and subscripts that are abbreviations are set in roman type: compare, for example, Cp for heat capacity at constant pressure and Ki for inhibition constant.
• Mathematical operators functioning as verbs or conjunctions are set with a space on each side (e.g., n = 25 and 6.022 × 1023), except when they are used in subscripts or superscripts (e.g., an+1). One exception is the slash (/), which is usually set without spaces: x/(y – z).
• Mathematical symbols used as adjectives are set without a space between the symbol and the number: for example, a pH of <5.
• Functions set in Roman type should be preceded and followed by a space unless the argument is enclosed in fences: compare, for example, sin θ and ln(2x).

Let’s look at some sample equations illustrating the departures from convention that I see most frequently. How many can you find in the following equation?

Ni / N0 = exp (–ΔEvib / kBT)

where Ni is the number of molecules in vibrational state i, N0 is the number of molecules in the lowest vibrational state, ΔEvib is the energy difference between the two vibrational states, kB is the Boltzmann constant, and T is absolute temperature. Here’s my revision:

Ni/N0 = exp(–ΔEvib/kBT)

I deleted the spaces around the slashes and the space after “exp,” and I used roman type for the subscripted numeral “0,” for the subscripted abbreviations “vib” and “B” (for “vibrational” and “Boltzmann,” respectively), and the Δ symbol. Note, however, that I retained the italics for the subscripted “i ” because it’s a variable. Here’s another example. The ozone depletion potential of chemical i, (ODPi) is given by

ODPi = kiτi/krτr

where ki and kr are the rate constants for the reactions of chemical i and a reference chemical with O2, and τi and τr are the atmospheric lifetimes of chemical i and the reference chemical. And the revised version:

ODPi = kiτi/krτr

Multiletter variables such as ODPi should not be italicized; nor should the subscripted “r,” which stands for “reference.” Whether or not you italicize Greek-letter variable symbols such as τ (as opposed to Greek-letter constants, e.g., π) will depend on what style guide you are following. Scientific Style and Format suggests that they should be italicized, as does IUPAC. In contrast, The ACS Style Guide, although it does not provide any explicit guidance, shows Greek-letter variables in roman type.

For more information on typography for mathematical copy, have a look at the following references:

Coghill, Anne M., and Lorrin R. Garson, eds. The ACS Style Guide: Effective Communication of Scientific Information. 3rd ed. Washington DC: American Chemical Society, 2006. pp. 210–223.

Council of Science Editors. Scientific Style and Format: The CSE Manual for Authors, Editors, and Publishers. 7th ed. Reston, VA: Council of Science Editors, 2006. pp 158–167.

IUPAC. “On the use of italic and roman fonts for symbols and scientific text.” http://old.iupac.org/standing/idcns/italic-roman_dec99.pdf. Accessed July 20, 2012.

IUPAC. Quantities, Units, and Symbols in Physical Chemistry. Prepared by Ian Mills, Tomislav Cvitaš, Klauss Homann, Nikola Kallay, and Kozo Kuchitsu. 2nd ed. Oxford: Blackwell Science, 1993. Available at http://old.iupac.org/publications/books/gbook/green_book_2ed.pdf. Accessed July 20, 2012.

Swanson, Ellen. Mathematics into Type. Updated edition. Providence, RI: American Mathematical Society, 1999.