Does your writing have a noticeable style? Is there something characteristic about your use of vocabulary, punctuation, voice, and the many other ingredients of written composition?
Style is likely not foremost on your mind when you are writing a paper. Refining and verifying the technical content and completing the paper are usually of higher priority.
Although the format of an academic paper is quite rigid and confining, there is still plenty of scope for writing it your own way. A trivial example is the explanation of a paper’s organization, which usually appears at the end of the introduction. Many authors write, “The contents of this paper are as follows,” or “The rest of this paper is organized as follows.” But there are ways to avoid these clichéd phrases. For example, one can write, “We begin, in the next section, by …” The ensuing sentences are typically of the form, “In section 2 we investigate …” — you could rewrite these more compellingly to sound less like a table of contents.
Cartoon created by mathematician John de Pillis
How you cite other work is also very much a matter of style. Compare
Jones’s analysis was extended in , .
Smith extended Jones’s analysis to semisimple eigenvalues , and Walker subsequently treated the general case of defective eigenvalues .
The second version adds a human interest element and saves the reader from having to turn to the bibliography to determine the gist of the extensions.
Especially for those of you starting out in academic writing, it is good exercise to identify authors whose style you like and analyze what it is about their writing that attracts you. Donald Knuth’s writing has always inspired me, and I learned a lot from his book on mathematical writing . As with all of us, Knuth’s writing style has evolved over time. In one of the volumes collecting his papers on particular subjects, he writes, “I first wrote nearly all of these chapters long before the copy editors of TAOCP [The Art of Computer Programming] taught me how to write better sentences. I cannot be happy now with stylistic errors that I would no longer tolerate in the writing of my students, so I have tried to remove them, together with all the technical errors that have come to my attention” .
Software for checking style goes back at least as far as Unix utilities of the 1970s. At their crudest, these tools compute readability indices or check for commonly used “waffle words.” Microsoft Word reviews both grammar and spelling as you type. I am not aware of many tools that integrate with other editors, though a variety of web-based services are available. It seems reasonable to expect that future artificial intelligence-based tools will offer useful analysis of one’s text.
A different aspect of style is the house style of journals. Most reputable journals have a prescribed submission style for uniformity. Copy editors edit for this style and correct grammatical and formatting errors in manuscripts. SIAM is well known for the quality of its copy editing. Less well known is the SIAM Style Manual, which is freely available. SIAM style is not too prescriptive and largely follows standard guidelines, such as those in the Chicago Manual of Style, though with more detail on how to format mathematics. Although primarily aimed at documenting SIAM style for copy editors, the SIAM Style Manual is also an informative read for authors. You might as well try to adhere to the style guidelines if you are writing for a SIAM journal, as this will minimize the copy editing changes made to your manuscript. What’s more, simply thinking about style issues may help you improve your paper’s readability.
Less experienced authors who submit to SIAM may benefit from improved wording provided by SIAM copy editors — as many of us have over the years, and as Knuth did from the TAOCP copy editors. Likewise, my articles always benefit from improvements suggested by SIAM News copy editors, who apply SIAM News’s own house style.
Another aspect of style concerns the LaTeX style file used to produce SIAM papers. This has evolved over the years, with a major modernization in 2016.
The most recent version is dated December 17, 2017, and is thoroughly documented. It comes with a BibTeX style file siamplain.bst that formats your bibliography in SIAM style, and will include DOIs if they are present in the BibTeX database. By using siamplain.bst, you can produce a neatly formatted, DOI-linked bibliography and save a great deal of copy-editing time.
 Knuth, D.E. (2003). Selected Papers on Computer Languages. Stanford, CA: Center for the Study of Language and Information.
 Knuth, D.E., Larrabee, T., & Roberts, P.M. (1989). Mathematical Writing. Washington, D.C.: Mathematical Association of America.
||Nicholas Higham is the Richardson Professor of Applied Mathematics at The University of Manchester. He is the current president of SIAM.