How to write a good mathematical paper?

Solution 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.

Solution 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.

Solution 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).

Solution 4:

I would like to add the above mentioned Paul Halmos work on How to Write Mathematics.

In too short (taken from the MAA):

1. Say something. To have something to say is by far the most important ingredient of good exposition.
2. Speak to someone. Ask yourself who it is that you want to reach.
3. Organize. Arrange the material so as to minimize the resistance and maximize the insight of the reader.
4. Use consistent notation. The letters (or symbols) that you use to denote the concepts that you’ll discuss are worthy of thought and careful design.
5. Write in spirals. Write the first section, write the second section, rewrite the first section, rewrite the second section, write the third section, rewrite the first section, rewrite the second section, rewrite the third section, write the fourth section, and so on. (Annotation: 1,2,1,2,3,1,2,3,4,...)
6. Watch your language. Good English style implies correct grammar, correct choice of words, correct punctuation, and common sense.
7. Be honest. Smooth the reader’s way, anticipating difficulties and forestalling them. Aim for clarity, not pedantry; understanding, not fuss.
8. Remove the irrelevant. Irrelevant assumptions, incorrect emphasis, or even the absence of correct emphasis can wreak havoc.
9. Use words correctly. Think about and use with care the small words of common sense and intuitive logic, and the specifically mathematical words (technical terms) that can have a profound effect on mathematical meaning.
10. Resist symbols. The best notation is no notation; whenever it is possible to avoid the use of a complicated alphabetic apparatus, avoid it.

I would like to add

11. "If you work eight hours to save five minutes of the reader's time, you have saved over 80 man-hours for each 1000 readers, and your name will be deservedly blessed down the corridors of many mathematics buildings." p. 134

and emphasize that at least the former holds for every scientific writing.

Solution 5:

http://padic.mathstat.uottawa.ca/~mnevins/latex/sample.pdf, here is a good short and simple guide. other is the following: www2.kenyon.edu/Depts/Math/Aydin/.../Report.doc, which goes to the main aspects of the body of a math report.

Hope to be useful. Greetings.