I intend to share some advice I have received during my scientific writing journal, which I have found helpful. The content comes from many sources: books, podcasts, professors, colleagues, students, and friends.
If you are in the position of starting a document, my preliminary advice is to listen carefully to others’ suggestions. Writing is a communication skill; communication simply means ‘to make common’. Hence, you want to pay attention if your readers understand your text to perfect the art. For this reason, my number zero advice is to be open to feedback. It should be your job to make the text clear and concise.
Advice for writing in English:
Use the active voice as much as possible. I wrote this sentence rather than this sentence was written by me.
Scan the text: is the sentence accurate? Is the sentence clear? Can you simplify it by rearranging or deleting words?
Prefer positive statements over negative ones. Say this is rather than this is not.
Mathematic displayed equations should be punctuated.
The custom is to write science/math using the first person plural ‘we’; for example, we now proof Lemma 1.
Advice for writing scientific documents:
a. Ask who your audience is.
b. Discuss the structure. Be mindful of the order of ideas.
- Separate content into sections, and chapters, e.g., introduction, preliminaries, methods, simulations, results, and conclusions.
- List what you will need to explain.
- Determine the logical order of the things that you need to introduce.
- Write definitions, lemmas, theorems, examples, and remarks.
c. Edit your text. Writing is a challenging task, then get involved in the process: write, read, delete, rewrite, read, rewrite, read, etc. (see 2.)
d. Within a chapter or a section, say things only once. Plan the text structure to make sure you don’t repeat ideas.
e. Write the introduction and conclusion last.
f. The introduction should clearly state the motivation of your work, the main goal, the tools you use to conduct your project and briefly, the main conclusion. Be aware that the person reading the introduction is not an expert, and you should guide her carefully into the take-away message.
g. The conclusion should state the main result; at this point, the reader should already have gained (some) expertise in the topic of your project.
Gopen, G.D., & Swan, J.A. (1990). The Science of Scientific Writing. American Scientist, 78, 550-558. Krantz, S. G. (2017). A primer of mathematical writing, 243, American Mathematical Soc.