User:Barto/Sandbox/mw

Purpose

 * 1) A compendium of proofs, including minor results (as opposed to wikipedia:wp:Notability)
 * 2) A dictionary of mathematical definitions
 * 3) Makes existing literature accessible, by reworking it into the structure of ProofWiki (mention process flows). No danger for copyright issues, because things are torn apart and put together.

1 and 2 are inseparable: no theorem is possible without definitions, and some definitions require theorems.

Not

 * 1) Enclyclopedia: with wikipedia, PlanetMath, Mathworld, Enclopedia of Mathematics, there are plenty of those. (Why is there even more than one?) ProofWiki has a different purpose. Inspiration to flesh this out at Wiktionary:wt:What_Wiktionary_is_not
 * 2) Learning project. While one can learn from at, just like it is possible to learn from Wikipidia, it is not designed for it. In particular, there are no lengthy explanations, numerical examples. Nothing is repeated. No distinction according to level of the reader. (We do of course put effort in making things understandable.)
 * 3) Book. Books are linear, ProofWiki is not. So ProofWiki does something books and even Wikibooks cannot. Books typically consist of paragraphs of text. ProofWiki consists of terse sentences, almost dictionary style. See also Wikibooks:wb:What_is_Wikibooks ProofWiki has unlimited scope (within mathematics) and will never be finished, in contrast to books at Wikibooks.
 * 4) A project on formalization of mathematics, like Mizar, Metamath, QED manifesto. This and its viability are discussed at MathOverflow. ProofWiki uses organic languages (currently only English) and can be read by humans.
 * 5) Library. Unlike WikiSources, ProofWiki creates new content by reworking existing sources into a specific structure.

A dictionary
Wiktionary is a dictionary, with occasional example sentences, but it does not teach grammar or how to form sentences. In the same way, ProofWiki can be thought of as a dictionary completed with proofs, but not a learning project.

That is, roughly speaking it is the mathematical equivalent of Wiktionary. Words correspond to definitions, sentences correspond to proofs. (The analogy is of course not exact.)

Wikipedia:wp:Wikipedia is not a dictionary, in particular: "A good definition is not [...], overly broad or narrow, [...]". Narrow definitions belong at ProofWiki, much like not notable species belong at WikiSpecies.

more refs: Wikipedia:wp:Notability (numbers) (also about sequences)

Other languages
Mathematics is so universal that it translates directly into any language. Inter-language links would face no ambiguity where to link to. The question is whether other language sites are viable. Possible model: take English as the main site, and only allow translation, no independent creation of articles in other languages.