User:Barto/Sandbox/mw

Draft.

The need for a new format

 * In this section: an overview of existing mathematical resources; identifying the gap that ProofWiki aims to fill.

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


 * 1) Textbooks, lecture notes, other course materials. (Covered by Wikiversity, Wikibooks) The typical resources used at high school and university. Some characteristics (apply to both physical and online materials):
 * 2) * Strong points: Long explanations, relevant exercises (practice makes perfect), thanks to limited scope it can afford to use simplified terminology and other conventions (but this has drawbacks, see below)
 * 3) * Limitations: Focus on a specific subject, limited target audience (specific level, assumes some foreknowledge). Structure is close to linear and not a "rooted tree" (which would be closer to reality); The linear structure implies space limitations, because being too detailed makes it hard to search for the important parts, or the reader would get lost. Thus: proofs are often not fully detailed or even left as an exercise (increasing the difficulty), it does not present everything in the most general form, or from all perspectives, together with all connections to other parts of mathematics.
 * Terminology, notational and other conventions make it hard to impossible to start reading in the middle. Or perhaps Theorem 2.6.1 is being used all the time without mention, because the reader is assumed to be used to it at that point.
 * Coverage outside WMF: various OpenCourseWare projects.
 * 1) Encyclopedias. (Covered by Wikipedia)
 * 2) * Strong points: Presents lots of perspectives, properties and connections to other concepts, that could never be found in a single single textbook-style (type 1) resource.
 * 3) * Limitations: Notability policies such as WP:notability and common sense prevent from being completely detailed: you don't want to load pages with borderline interesting information (that can be found elsewhere). For details and all proofs, one is referred to literature (type 1) instead.
 * Coverage outside WMF: nLab, MathWorld, Encyclopedia of Mathematics, PlanetMath and some more.
 * 1) Forums, blogs and articles, whose style and content floats somewhere between the encyclopaedic and textbook style.
 * 2) Databases. Two types:
 * 3) Databases of mathematical objects (of a specific type). Typically bordering encyclopedic style (for the sake of usefulness): OEIS, LMFDB, Groupprops and related wiki's, π-base and so on. (Not all of them are wiki's.)
 * 4) Databases of proofs and definitions. (ProofWiki])
 * Characteristics:
 * 1) * Strong Points: Very efficient in conveying information, nonlinear, no space limitations and can thus be very detailed, relaxed notability policies, possible to start reading at any point thanks to heavy use of links.
 * 2) * Limitations: Doesn't have what course materials and encyclopedias do: explanations, exercises, overview of properties.

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
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.