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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.
306:. 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
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that a serious student must use to acquire a detailed understanding of topics. It can be helpful to think of
Knowledge (XXG)'s mathematics articles as akin to survey articles in mathematics journals. Our articles contain a mixture of introductory information, context, definitions, results, pictures,
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is a project that lets editors collaborate on writing freely-licensed textbooks. Like
Knowledge (XXG), Wikibooks is run by the Wikimedia Foundation. Wikibooks is one option for editors who would like to work on textbook-style treatments of mathematical topics. In addition to many books on specific
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Unlike textbooks, Knowledge (XXG) does not strive to provide an axiomatic introduction to mathematics. Thus it is not necessary for a
Knowledge (XXG) article to prove every fact that is mentioned. Our best articles include references to good textbooks that the interested reader can consult for an
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Proofs are often discussed in
Knowledge (XXG)'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
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applies. If the proof can be found verbatim in any standard textbook on a subject, then it is better off transwikied to a project such as
Wikibooks, Wikiversity, or ProofWiki. There is also no point in presenting a novel proof not appearing before in print, because it falls afoul of
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does not, it is a little hard to explain precisely what a "significant proof" is. One measurement might be the interest a general
Knowledge (XXG) reader might have in such an proof. We can imagine several facets that may be brought up in an AfD debate:
189:. It is likely a better style to instead use explanatory footnotes for short or abbreviated proofs, and to omit long proofs by replacing them with a citation to a good presentation of the proof. For an example of this style of presenting proofs, see
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has a collection of theorems in many different areas. Occasionally, it is suggested that proofs that are removed from
Knowledge (XXG) articles might be good source material for Wikibooks, although it is not obvious how to accomplish this easily.
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without including at least some proofs or proof sketches. It does not follow, however, that the bulk of coverage of mathematics on
Knowledge (XXG) should consist of detailed proofs in the style professional mathematicians use.
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However, even if the proof is significant, there may be little to say about the proof. The proof most likely qualifies as a sub-topic of a relevant article on the theorem or subject of the theorem. Therefore, under
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This is not an exhaustive list, but it should be clear that, given sufficient evidence for a proof being significant, it is natural that
Knowledge (XXG) should contain information about that proof.
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In this page, the word "Proof" refers to the garden-variety proof of the working pure mathematician. There are separate issues related to the inclusion of "derivations" and other heuristics.
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Internal or technical features of the proof that have implications (elementary in the technical sense, constructive or non-constructive where there is some point to knowing that)
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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.
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is an article about a particular theorem, whose proof is short but requires a technical trick. The article includes a description of this proof, as a reference for the reader.
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This page (currently under development) is to serve a summary of past discussions on proofs in
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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
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A common suggestion is that articles with a proof as a topic have names ending in '/Proof' or '/Proofs'. This practice has been determined to be a violation of
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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.
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be a triangle…." This is standard practice in mathematical writing and should not be confused with instruction manual material.
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contains a lengthy derivation of an elementary fact. Moreover, the proof is presented in a "two-column" style instead of prose.
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As a matter of practice, Knowledge (XXG) articles do not typically include fully formalized proofs as would be generated by
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community on our best practices for articles that include, or are about, mathematical proofs. For discussion, see
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Having stated that there is a "significant proof" criterion that allows inclusion under conditions that
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The following versions of articles include or included proofs in ways that are less widely accepted.
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There are no firm guidelines for when a proof may be given a dedicated article of its own, such as "
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The following articles demonstrate widely accepted ways of including and writing about proofs.
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Proofs in Knowledge (XXG) should conform as much as possible to the style guidelines given in
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Social or historical features (a proof that has generated controversy, or had influence).
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Knowledge (XXG) articles are not intended to replace the textbooks and advanced
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uses a walk-through of a proof to explain the scope of a mathematical identity.
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debates, proofs may be significant because the result is "surprising" (
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is a short survey addressing the several hundred known proofs.
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