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This page (currently under development) is to serve a summary of past discussions on proofs in Wikipedia. It describes the opinions of some of the editors in the WikiProject Mathematics community on our best practices for articles that include, or are about, mathematical proofs. For discussion, see Wikipedia talk:WikiProject Mathematics/Proofs.
In this page, the word "Proof" refers to the gardenvariety proof of the working pure mathematician. There are separate issues related to the inclusion of "derivations" and other heuristics.
Proofs are often discussed in Wikipedia's mathematics articles, just as axioms, definitions, theorems, and lemmas are. Because much of the published professional literature of mathematics consists of the details of proofs, it would be very difficult to write in any depth about mathematics without including at least some proofs or proof sketches. It does not follow, however, that the bulk of coverage of mathematics on Wikipedia should consist of detailed proofs in the style professional mathematicians use.
Wikipedia articles are not intended to replace the textbooks and advanced monographs that a serious student must use to acquire a detailed understanding of topics. It can be helpful to think of Wikipedia's mathematics articles as akin to survey articles in mathematics journals. Our articles contain a mixture of introductory information, context, definitions, results, pictures, and some discussion of proofs. These articles generally serve their purpose best when they provide a brief, but significant, survey of a topic, along with pointers to the literature. At the same time, our best articles provide a useful reference for readers familiar with a field who wish to look up particular facts. The role of proofs, which may be short but correct arguments or sketches of longer arguments serving more as a map of complete proofs, is to support the "survey" and "reference" ambitions.
Unlike textbooks, Wikipedia does not strive to provide an axiomatic introduction to mathematics. Thus it is not necessary for a Wikipedia article to prove every fact that is mentioned. Our best articles include references to good textbooks that the interested reader can consult for an axiomatic presentation of the field. On the other hand, proofs or proof sketches of a few selected facts can make the article more useful as a reference.
If a proof is not significant enough to place in its own article, but long enough that it may interrupt the flow of the article it occurs in, it may be set off in a collapsed frame, which can be opened if needed. One way to do that is with the following code:
{{Collapse toptitle=Proof of ...}}
The proof of ... proceeds as follows:
...
{{Collapse bottom}}
This generates the following:
Proof of ...


The proof of ... proceeds as follows: ... 
There are no firm guidelines for when a proof may be given a dedicated article of its own, such as " Proofs of quadratic reciprocity". It is widely accepted, however, that if a proof is made a topic of its own dedicated Wikipedia article, the proof must be significant as a proof, not merely "routine". It is a little harder to explain what that means, but the criteria for inclusion seem to involve some necessary conditions that are not very controversial. Sufficient conditions are less easy to formulate, but clearly enough they describe what interest a reader might find in such an article.
Work is needed in this area to get a better understanding
Under (2) there are several facets. What we can say about a proof may relate:
This is not an exhaustive classification, however.
Under (i) it is natural to say that Wikipedia's article on the result should contain information about the proof, but it is not automatic (under Wikipedia:Summary style) that the proof deserves its own article.
Some of the existing articles with a proof as a topic have names ending in '/Proof' or '/Proofs'. This practice has been determined to be a violation of WP:SP#Articles do not have subpages (main namespace). Currently, many articles of this type begin with the words 'Proof of ...', 'Proof that ...', or 'Proofs involving ...' as in Proof of Bertrand's postulate. When more specificity is desired, a name connected with the proof may be added as in Furstenberg's proof of the infinitude of primes.
Proofs in Wikipedia should conform as much as possible to the style guidelines given in Wikipedia:Manual of Style (mathematics). In particular, the proof should be presented in conversational prose, as if being given in a lecture at a blackboard. Unnecessary use of symbols (such as ∀ and ∃) and jargon should be avoided. Avoid phrases such as "Clearly..." and "Obviously...", though it may be helpful to replace lengthy calculations with a summary. Avoid putting Q.E.D. at the end of a proof since many readers will need to look up the meaning. Instead, the end of the proof should be marked by a section heading or the end of the article itself.
Proofs normally use the imperative heavily, for example "Let ABC be a triangle…." This is standard practice in mathematical writing and should not be confused with instruction manual material.
As a matter of practice, Wikipedia articles do not typically include fully formalized proofs as would be generated by Metamath, apart from articles that specifically deal with formal proofs and formal deduction systems. The same is true in the mathematics literature; few journals publish fully formalized proofs.
Many articles containing proofs are in Category:Articles containing proofs.
The following articles demonstrate widely accepted ways of including and writing about proofs.
The following versions of articles include or included proofs in ways that are less widely accepted.
Wikibooks is a project that lets editors collaborate on writing freelylicensed textbooks. Like Wikipedia, Wikibooks is run by the Wikimedia Foundation. Wikibooks is one option for editors who would like to work on textbookstyle treatments of mathematical topics. In addition to many books on specific subjects, the book Famous Theorems of Mathematics has a collection of theorems in many different areas. Occasionally, it is suggested that proofs that are removed from Wikipedia articles might be good source material for Wikibooks, although it is not obvious how to accomplish this easily.