In the sentence

The great historical heroes of applied mathematics include Archimedes, Newton, Euler, and Gauss.

the comma before the “and” is known as a serial comma. Whether or not to include it is a matter of style.

The serial comma is also known as the Oxford comma, because Oxford University Press style rules require it to be present. The Chicago Manual of Style (CMS) requires the serial comma, as does SIAM, which follows the CMS recommendations and explicitly states, in the SIAM Style Manual, “Use the serial comma before the and or or in lists of three or more items.”

Other organizations, such as the New York Times, The Economist, and the University of Oxford, require that the serial comma is used only when necessary to avoid ambiguity. Consider the sentence

Three important techniques in the design of algorithms are bisection, divide and conquer, and recursion.

If the serial comma is omitted the final phrase becomes “are bisection, divide and conquer and recursion”, which will be confusing to anyone who does not know that “divide and conquer” is a technique.

Conversely, the serial comma is sometimes incorrect when it might appear to be optional. In the sentence

The results show that, unlike Algorithm 1, Algorithm 2 and the SVD-based algorithm exhibit forward stable behaviour in all the experiments.

a serial comma must not be put after “Algorithm 2” because the three algorithms do not form a list, so the sentence does not make sense with that extra comma.

Examples such as the last two, where the serial comma either must be used or must not be used, irrespective of style, are relatively infrequent, but they do arise from time to time.

For the last year or two I have been using the serial comma in my papers and books, partly because it is the style of the relevant publishers. In particular, I became accustomed to its use in The Princeton Companion to Applied Mathematics. But I also like the simplicity of the serial comma: I do not have to stop to think whether to use it every time I write a list. For informal writing, such as on this blog, I have not made up my mind which style to use. I think the serial comma would look fussy in the tagline at the top right corner of this page.

In the chapter “Commas the Serial Killer” in his book Making a Point: The Pernickity Story of English Punctuation, David Crystal notes that originally the use of the serial comma was standard, and it was only in the early twentieth century that it started to be avoided, “as part of the trend towards punctuation minimalism”. Interestingly, Crystal uses the serial comma in his book even though the style of his publisher (Profile Books) is to avoid it.

There is a large amount of material on the internet about the serial comma, of which the short post The Oxford, Comma has some good examples of where it is needed, and Wikipedia has a good entry. There is a song “Oxford Comma” by the American rock band Vampire Weekend (thanks to Sam Clark for pointing this out); a video is here, but beware the expletive in the first line of the song. The “comma queen” Mary Norris has produced an excellent video about the serial comma. The serial comma even has its own Twitter account, @IAmOxfordComma.

FREE OXFORD COMMAS, please take one: ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

— Oxford Comma (@IAmOxfordComma) November 16, 2015

What better way to support the Oxford comma than by giving up some of your 140 characters for it in a Tweet!