Is usually terrible. Possibly because writing is just plain hard, harder in your second language (and scientists are rarely writing in their mother language), and possibly because even highly skilled textbook authors want to create demand for lectures where they explain in person what they obfuscated in books.
I am especially interested in good mathematical style, but academic style in general could be good to know.
J.S. Milne, tips for authors.
If you write clearly, then your readers may understand your mathematics and conclude that it isn’t profound. Worse, a referee may find your errors. Here are some tips for avoiding these awful possibilities.
Shaun Lehmann, the vagueness problem in academic writing:
[It is..] likely that your writing was suffering from ‘vagueness’ – a constant problem in English. English-speaking readers (especially in an academic context) will only do a very small amount of work to figure out what you mean before they respond with confusion. […] A useful technique is to learn to read your work through the eyes of a kind of caricature of the low-context communication mode. You need to imagine a reader who is highly intelligent and logical, but who has no common sense and will fail to interpret any multiple meaning in the way you had intended.
I call my version of this the Commander Data Meditation […]
There is also some nice stuff there about “high and low context languages”:
In a high context language you can take a lot for granted and don’t have to explain yourself. You may also see cultural communication styles like this referred to as listener/reader responsible. As it happens, some of the most common first languages of students writing in English are derived from high-context environments: hinese, Korean, Japanese, Indonesian, Thai, Arabic, and to some extent Spanish and French.
On the other hand, a low-context culture relies much more so on the content of the message. Low context languages developed in situations where people living next to each other were different – such as in trading ports and countries that have been repeatedly colonised – such as England was for thousands of years. Waves of invaders: Romans, Vikings, the Normans disrupted the close bonds of society and this meant people had to work hard to understand each other.
In a low context language the recipient of the communication brings very little to the table in terms of securing understanding. The onus is on you to make yourself understood.
It’s an interesting idea, although they claim Indonesian is a “high-context language”, (this seems reasonable to me as a student of Indonesian), and yet it has a highly colonial history as a lingua franca between ethnic groups and empires in the last few centuries, so the thesis about high context cultures and how they arise is fishy if it is a real datum toward that hypothesis.
- Knuth, D. E., Larrabee, T. L., & Roberts, P. M.(1989) Mathematical Writing. . [Washington, D.C.]: Mathematical Association of America
- Lamport, L. (1995) How to Write a Proof. The American Mathematical Monthly, 102(7), 600–608. DOI.
- Lamport, L. (2012) How to write a 21st century proof. Journal of Fixed Point Theory and Applications, 11(1), 43–63. DOI.