Mathematical and scientific documents should be as clear and straightforward as possible. On this page I’m building up a list of advice on good writing.
General English writing advice
More on clear and concise sentences from Sharon Goldwater.
A slide set repeating many of the above points, and with some nice examples of rewriting sloppy prose.
If you are unsure whether you are using the correct word, a good place to check is Paul Brians’ Common Errors in English Usage.
Breaking the rules: I don’t agree with every single recommendation in the above guides. Decide for yourself what’s important, then do your best to write text that people will want to read.
Don’t make the reader work hard
At every scale of your document (chapter/section/paragraph/sentence) a clear point should be apparent. Be able to answer the question: “What is the message in this section/paper/figure/chapter?”. Ideally your answer could be pointing to a prominent part of the text. The links between each of your points should also be made explicit.
Certain words and phrases often indicate sloppy writing or thinking:
- This means: Unqualified use of the word ‘this’ is often a vague reference to the whole previous sentence or paragraph. Try making the point more precise by saying “This large variance…”, “This reduction in complexity…”, or whatever is appropriate.
- Similar to: Do not say that method X is similar to method Y, without qualification. Instead say how they relate or differ.
Give the reader concrete information. Don’t declare that a topic is interesting, or important; demonstrate the interest or importance. Don’t say that “more work needs to be done”; detail the limitations of a method and possible avenues for research. If you don’t have any information or real content to convey, don’t write anything and move on. See point 4 of a letter by C. S. Lewis.
There’s lots of good advice in those course notes (along with some things I think are overly-prescriptive). Here’s one piece that has stuck with me:
Many readers will skim over formulas on their first reading of your exposition. Therefore, your sentences should flow smoothly when all but the simplest formulas are replaced by “blah” or some other grunting noise.
A general principle: don’t make your reader parse, understand and remember your mathematical notation. Give them the main ideas in English first, so that they could almost fill in the mathematics themselves.
Some notes from an Edinburgh course on writing a literature review. Some of the advice is only for literature reviews, but most of it applies generally.
Some short advice on writing research articles by Andrew Gelman.
The story of the success of Watson and Crick’s paper on DNA contains several useful insights. These insights include: 1) write in simple short sentences; 2) don’t be afraid to repeat words; and 3) state clearly what you did.
If I or someone else has scribbled over your document, it can be useful to know some standard proofreading marks. I only use two non-obvious marks extensively: 1) I use a loop through two words to say “swap these”. 2) I often make mistakes and write “stet” to mean “sorry, ignore the scribblings here”.