User:Barto/Sandbox/mw

The need for a new format
Roughly speaking, mathematical (see also below) resources can be divided into the following categories, according to the style in which they are written:


 * Textbooks, lecture notes, minicourses, ... The typical resources used in high-school or at university. Whether physical objects or online resources, some characteristics are the following: They focus on a specific subject, are written in an explanatory style and serve to learn this subject in detail up to a certain level, determined by the authors. The structure is linear. They tend to have a specific target audience and assume some foreknowledge. Proofs are often not fully detailed or even left as an exercise to the reader, because it would otherwise become unwieldy, or the reader would lose track. This is where the difficulty of the material originates. For the same reason, it cannot present everything in the most general form, together with all connections to other parts of mathematics. This type of resources is covered by Wikiversity and Wikibooks, as well as other OpenCourseWare projects.
 * Encyclopedias. The overview style, presenting a mathematical concept, often accompanied by a rigorous definition, together with lots of properties and connections, which could not be found in a single textbook-style resource. Occasionally a proof is given, but it cannot be too detailed for various reasons: pages would become filled with borderline interesting information and details (that can be found elsewhere), and notability policies such as WP:notability. In most cases one is referred to literature. This type of information is adequately covered by Wikipedia, nLab, MathWorld, Encyclopedia of Mathematics, PlanetMath and so on.
 * Forums, blogs and articles, whose style and content floats somewhere between the encyclopedic style and textbook-style, leaning towards the latter.

and...


 * Databases. To be interpreted broadly. Presenting dictionary-like information of varying level of detail, typically very efficient in conveying information, this knowledge-type is in the process of being covered by ProofWiki and subject-specific databases such as OEIS, Groupprops and related wiki's, π-base, LMFDB and so on. (Not all of them are wiki's.)

Mission statement
(draft) The mission of ProofWiki is to create a free [...], by working existing mathematical literature and dispersed bits and gems into a heavily connected whole that reflects the axiomatic nature of mathematics.

Values
Accessibility. In both senses of the word. ProofWiki makes existing literature freely accessible, albeit by presenting it in a new form. --> links -> one thing per page

Rigor:

Vision
The intention is that anybody, with no prior knowledge or experience, should be able to select a random page and be able to understand it completely.

Content

 * 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.

ProofWiki is not an encyclopedia

 * 1) Enclyclopedia: with wikipedia, nlab, PlanetMath, Mathworld, Enclopedia of Mathematics, there are plenty of those. roofWiki has a different purpose. Inspiration to flesh this out at Wiktionary:wt:What_Wiktionary_is_not

ProofWiki is not one big course or learning project

 * 1) Learning project or a collection of courses. 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.) ProofWiki goes far beyond what can be achieved with a textbook.

Don't get confused: just because mathematics is a subject that happens to be taught at universities, doesn't mean that this project's goals are the same as those of Wikiversity!

ProofWiki is not a book

 * 1) 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.

In particular, it is not an Exercise book. Although, in a way, we do include exercises, except they're called "Theorem" or "Example", the solution is called "Proof" and is given right away, and a hint translates as a "Proof Outline". In particular, ProofWiki contains solutions to the exercises of those books that have been incorporated.

ProofWiki is not a library
Unlike Wikisource, ProofWiki creates new content by reworking multiple existing sources into one structure.

ProofWiki is not a formal language project
ProofWiki has nothing to do with proof assistants and is not a formal language project like Mizar system, Metamath or QED manifesto. Such projects and their viability are discussed at MathOverflow. ProofWiki uses organic languages (currently only English) and can be read by humans.

ProofWiki is a database, 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 sciences
Parts of connected sciences like computer science or physics are welcome, as long as they fit in the axiomatic model of ProofWiki. There are already some examples of such pages.

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.