Here's the math WikiProject's "Current activity" page, which lists each day's new articles, articles for which deletion is proposed, articles needing expert attention, articles needing references, and articles needing various other sorts of work: http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Mathematics/Current_activity

Here's the page listing "requested articles"---mathematics articles that do not yet exist: http://en.wikipedia.org/wiki/Wikipedia:Requested_articles/Mathematics

(Inexperienced or non-logged-in users are no longer allowed to create NEW articles, but they can create drafts in the user space, which can be moved by experienced users into the article space.)

**DO NOT** begin a Wikipedia article by writing "Let $\lbrace T_n\rbrace_{n=1}^\infty$ be a sequence of bounded linear operators on a Banach space $B$." That fails to even hint to the lay reader that the article is not about theology, music, chemistry, banking, politics, etc.

The title of the article should be a singular noun phrase except when there's some special reason to use the plural. One such reason is that the article is about a set of things (in something more like the layman's understanding of "set" than that of the mathematician); for example "Maxwell's equations".

One might begin by writing "In mathematics, an **oriented matroid** is . . ." Or "In algebra,..." or "In number theory,..." or "In geometry,..." or "In calculus,..." But DON'T start by saying "In functional analysis,...", or "In category theory," or "In topology,....". Again with those, the lay reader is given no reason to suspect that mathematics is what it is about. There's no need for that sort of context-setting phrase if the title of the article is "Mathematical induction" or "Algebraic equation" or "Arithmetic of $p$-adic numbers".

Usually, the word or phrase that is the title of the article should appear in or near the first sentence set in **bold**, not necessarily verbatim identical to the title (e.g. it may be plural where the title is singular).

Do not begin a biographical article by writing "John Schmon was born in Putford in 1801. His father was a polecat farmer and his mother was a quantum software designer. He attended this school and that school. His older brother died when he was 10....." The reader should be told right at the beginning what John Schmon was notable for, thus: "**John Schmon** (1801–1998) was a Nevian mathematician who discovered this theorem and that theorem and made fundamental contributions to the understanding of whatever."

Use lower case initial letters in article titles and section headings except where there is a reason to use a capital (e.g. a person's name). The first letter of a section heading is capital except in rare instances where there's a reason to use lower case. Thus a section may be called

**Applications of the theorem to population genetics**

but should NOT be called

**Applications of the Theorem To Population Genetics**

If you create a new article, it's a good idea to create redirect pages from alternative names, commonplace misspelling and miscapitalizations, commonplace misnomers, etc. Thus "Schmon's Theorem" (with a capital "T") might redirect to "Schmon's theorem" (the proper title).

One of the easiest mistakes to make in creating a new article is to leave it as an "orphan", i.e. an article to which no other articles link. If you go to the "toolbox" menu and choose "what links here" you can see which other articles link to it. In the relatively early days of Wikipedia (in 2002 or 2003), I created a new article titled "exponential growth". I then used Google to find more than 150 occurrences of "exponential growth" or "grows exponentially" or "growing exponentially" in other Wikipedia articles, and linked them to the new article. Much more recently, in 2011, I found that 60 Wikipedia articles mentioned Gerald J. Toomer, in most cases by citing one of his works, but there was no article about him. I created the links to the new article about him BEFORE creating the article about him. These are "red links": links to an article that does not exist, and are red in color, whereas links to existing articles are blue. One should create appropriate red links in anticipation of the future existence of an article even when one intends never to create it oneself. A red link invites others to click on it and then create the new article.

I've put whatever came to mind instantly into these comments. I could say a lot more if I took more time.

Most of what appears above is codified in Wikipedia's style manuals and guidance pages.

dothink mathematicians do this pretty often (some of the best known MOers are on wikipedia). – darij grinberg May 22 '13 at 13:49