How to write a good mathematical paper?

Question

I hesitate to ask this question. However I read many advices from math.stackexchange, and I couldn't find anything similar.

A good time always goes too fast! Two years are fled. In the third year of PHD, my major is general topology and I'm facing with graduation from PHD. I do enjoy research, however the pressure to publish makes me be agitated and not quite, for I haven't publish any paper. I find, sometimes, doing research and to publish are contradictory.

Here is my question: How to write a good mathematical paper? Could anybody give me some suggestions?

Thanks ahead.

Answer 1

As someone who is currently working on my first mathematical paper, I've found this guide from MIT to be very helpful. It covers both writing a clear and precise paper in general as well as the specific challenges presented by a mathematical paper. It's also fun to read! For example, the author likes to illustrate common mistakes within the text. One of my favorites is:

Don’t string adjectives together, especially if they are really nouns. Many high quality pure mathematics original research journal article sentences illustrate this problem.

Answer 2

There are some notes on Mathematical Writing from a course taught by Knuth. They are quite extensive; I've only read the first few pages and those were already quite helpful to me, but there are also notes from guest lectures by various people, e.g. Wilf and Halmos.

Answer 3

You say you haven't published a paper yet. Then perhaps this would be useful to you: How to Write Your First Paper by Steven G. Krantz (Notices of the AMS, December 2007, pp. 1507-1511).