New User Guide

New User Guide

1 Before You Begin

We are working to make PlanetMath into a consistent, correct, andcomprehensive, free mathematical resource.

When we say “free”, we are refering to freedom, not price.The PlanetMath encyclopedia is released under the GNU FreeDocumentation License (FDL). Using this license for your work means thatother people around the world will be able to copy and modify yourcontributions in ways you hadn’t necessarily imagined.

In order to be an effective PlanetMath contributor, you should beaware of the responsibilities you take on when contributing.

One important responsibility is to only contribute your own writing,or other texts that you know you have a legal right to add. The lastsection of this document is about copyright, and it is important thatyou understand the issues presented there. The other sections of thisdocument will help you understand the way the site works, and how towrite good entries.

One thing to bear in mind is that while we want our work to beconsistent and correct, it is not expected that you get things perfectthe first time. On the contrary, writing a correct and complete entryis an iterative process. We caution you against expecting to beprecisely and exhaustively correct on your first (or second, or third)attempt! You should not be afraid of receiving corrections andsuggestions from others, and in fact you should expect them.

Do not expect to retain “ownership” of your entries if you will nothave time to maintain them. There are plenty of people who will bewilling to adopt abandoned entries. If you do not respond tocorrections in a timely fashion, your entries will eventually beconsidered to have been abandoned, and they can then be adopted bysomeone else(for details seesection “The Adoption System” inNoosphere’s Authority Model).

Part of the benefit of PlanetMath is the collaborative nature of theproject: math enthusiasts from all over the world want to share whatthey know, and learn through sharing and discussion. If you do notexpect to learn and think you know it all beforehand, PlanetMath isprobably not for you.

2 Metadata

Metadata is a word meaning “data about data”. For ourpurposes, this means information about the main (LaTeX) content ofyour entry. Much of this document is about metadata for PlanetMathentries. This includes titles, synonyms, defines (sub-definitions),type, keywords, and classification.

To make your entry properly fit in with the rest of PlanetMath, it isimportant that you understand how to best write its metadata. This isnot complicated, but perhaps not obvious to beginners, so read on tosee how.

2.1 Naming Your entry

There are a few entry naming conventions that have evolved so farwhich go a long way towards making PlanetMath a cohesive andconsistent resource. Some of these are purely issues of style, butmany have to do with the dynamics of linking between objects. Note thatthey also apply to other “concept labels” — synonyms and defines.

Here are the rules for naming your PlanetMath entries:

2.1.1 Capitalize for indexing

It is convention to capitalize your title as you would want it to appear in an index or list. Generally, this means that only proper nouns and adjectives derived from proper nouns are capitalized.

2.1.2 Do not use articles

Do not start entry titles with “the”, “a”, or “an”. Articles addno useful information to your entry names.

Examples.

the binomial theorem

Wrong, should be “binomial theorem”.

the bridges of Koenigsburg

Wrong, should be “bridges of Koenigsburg”.

a proof of the binomial theorem

Wrong, should be “proof of thebinomial theorem”, or “proof of binomial theorem”, or “binomialtheorem, proof of”.

Not only do we not want (for instance) a ton of entries appearingunder ”T/the …” in the encyclopedia’s index, we also do not want”the” to be hyperlinked in the body of the entries. (The same goesfor other articles.)

2.1.3 Do not put subjects or sub-disciplines in titles

For homonyms (ambiguous terms like “algebra”, “domain”, or“complex”), it often seems appropriate to append a parenthesized“subject hint”. For example, one might think the smart thing to dois name an entry “diagonalization (Cantor)” to avoid conflation withthe linear algebra sense of “diagonalization”. However, the way thisshould officially be handled is to assign an appropriate subjectclassification to your “diagonalization” object.

Adding a parenthesized “subject hint” to your title is acceptableprovided the plain title is at least given as a synonym (and the entryis still properly classified.) You might want to do this with theencyclopedia index listing in mind (that is, it might be nice to see“diagonalization (linear algebra)” in the index.)

Example.

diagonalization (linear algebra)

Usually wrong, should be“diagonalization”, and classified somewhere in MSC area 15 (linearand multilinear algebra)

2.2 Classification

You had a hint already of one reason why classification is important:homonyms abound. There are a large number of terms in mathematics thatare ambiguous: you cannot tell from the term itself which concept isbeing referred to, and you need some sort of context (or semantichint.) Classification serves this purpose well. In addition,classification allows entries to be browsed by subject, through asubject classification hierarchy.

For classification, currently PlanetMath only supports MSC, the AMSMathematical Subject Classification scheme. MSC is very widely usedand is more or less exhaustive over known mathematics – you probablywill never run into an entry that can’t be classified with MSC (atleast to one level in the hierarchy.)

The MSC takes some getting used to. In order to make things easier, wehave set up a local copyof the MSC which is hierarchically browseable and searchable, whichis accessible from the menu.

2.3 Types

There are a number of types which are available for describing whatthe mathematical form of your entry is. These are:

• Definition

• Theorem

• Conjecture

• Axiom

• Topic

• Biography

• Algorithm

• Data structure

• Proof

• Result

• Example

• Derivation

• Corollary

• Application

The entries in italics are meant to be attached to other entries. Theydo not show up in the encyclopedia index, so placing an entry underone of these categories has important practical as well asphilosophical ramifications.

An example of why types matter: a definition should not have proof,since definitions have no truth value – but it may have aderivation. Hence, you cannot attach a proof to a definition(actually, you can, but it is discouraged.)

A theorem may have a proof, and in fact it should be provided for afull acceptance of the theorem as a theorem. Hence, PlanetMath makesit easy for a proof to be attached to a theorem (and only a theorem.)As before, you actually can attach a theorem to anything, but doing sois less convenient and is discouraged.

Examples are meant to be used everywhere. They allow some of the loadto be taken off the primary entry author, by allowing the community ofusers to pedagogically enrich existing entries.

The “Conjecture” type might be a little confusing to some. In termsof how the system treats conjectures, they are the same astheorems. That is, they are meant to have proofs attached to them, aswell as results or corollaries. This makes sense, since a conjectureis basically treated as a yet-unproven theorem. However, when onelooks at a topic like the Taniyama-Shimura conjecture (which has nowbeen proven), its hard to decide which type is moreappropriate. Proven conjectures may still be better left asconjectures by convention. The opposite situation is a conjecturewhich is considered a theorem before its time – like Fermat’s lasttheorem. Yet another situation might occur when it turns out aconjecture (like the Continuum Hypothesis) is unprovable (can only beused as an axiom). There is no single answer for these situations, yousimply must take into account practical considerations (for instance,that conjectures won’t show up in “unproven theorems”) andconvention on a case-by-case basis. Don’t worry too much, however,about picking the absolute best type the first time around in such anambiguous situation.

2.4 Synonyms and Definitions

PlanetMath provides a “synonym” field for entries. The obviousthings to put in here are alternate names for your entry. Thenot-so-obvious thing is that you should also be thinking of linkingwhen you do this. That is, you should list all aliases for your entrythat someone else might invoke in other entries, to faciliateautomatic linking.

You do not, however, need to make extra synonyms for variants ofpluralization, possessiveness, or transmogrifying “Blah, proof of”into “proof of Blah”. These are done automatically byPlanetMath.

Examples.

title: Euler’s totient function, synonym:Euler totient function. Wrong – the synonym is just thenonpossessive of the title; leave that for the software to handle!

title: Cauchy-Schwarz inequality, synonym: Kantorovich’s inequality.Correct – both names are used to refer to the same thing.

title: monotonic, synonyms: monotone,monotonically. Correct – we want all occurrences of “monotonic”,“monotone” and “monotonically” to link to the same object.

title: vector valued function, synonyms: vector-valued,vector-valued function, vector valued. Correct – we have to take careof variants in hyphenation as well as the particular set of words.

In addition, there is a “defines” field which provides for“sub-definitions” of your entry. This facility allows you to definesome set of new concepts all at once in a single entry (for example,it might be better to define “edge” and “vertex” within a“graph” entry, instead of separately). Each of these“sub-definition” handles will be treated appropriate by PlanetMath’sautomatic linking when they are invoked in other entries (they willget hyperlinked, whereas multiple synonyms to the same entry willnot.)

Previously it was the case that “synonyms” were used to list these“sub-definition” concept handles. This is no longer the case. Thetwo types of handles have different ramifications for linking, anddeserve to be separated.

Examples.

• An entry for “graph” may also define “vertices” and“edges” and hence have “vertices, edges” as the “defines”field.

• An entry for “Zermelo-Fraenkel axioms” may also list assub-definitions each individual axiom, i.e. defines=“axiom of emptyset, axiom of infinity, …”

• An entry for “Taniyama-Shimura conjecture” might also havesynonyms “Taniyama-Shimura-Weil conjecture”, “Taniyama-Shimuratheorem”, and “Taniyama-Shimura-Weil theorem”, and hence listthese as synonyms. These would not be listed in the “defines”field – if two of these terms are invoked from the same entry, theyshould not both be linked, which will be the case if they are listedas synonyms.

It is important to note that there is no general rule for the exact“granularity” of entries – things that “stand on their own”should be their own entry, but this is hardly a rigorous metric(however, if you choose to combine things that could be separateentries, you should provide a “defines” list for sub-definitions.)Use your best judgement, and you’ll probably hear from others ifthere’s disagreement.

3 Corrections

What you should file corrections for:

Mathematical Errors

These may be as simple as a typo or asserious as a completely erroneous proof.

Typographical errors and grammatical errors

PlanetMath shouldbe as “professional” as any published book or encyclopedia (infact, there is little excuse for the quality of PlanetMath not toexceed fixed media for the set of “stable” entries.) As such,please point out even the smallest of mistakes, if they truly aremistakes.

Comprehensiveness

If more can be added, it probably shouldbe. This includes showing relatedness to other branches ofmathematics, and possibly applications. It includes alternatederivations, additional results and properties, and differentmethods of visualization or approaches to explanation. You don’thave to write a book – that would of course defeat the purpose ofan encyclopedia. But the idea is to mention all of the importantinsights so that the reader knows what to look for if they’d like tostudy the idea in more detail.

Comprehensibility

Formal and concise statements tend to beuseful for reference purposes, but they are not very useful forlearning what one does not already know. More extensiveexplanations, visualizations, and examples are very powerful toolsfor teaching, and they should play a large part in nearly allentries.

Alternative conventions

This is a tough one for most. Oftentimes there are conventions which vary from country to country,region to region, school to school, or even class to class. Think ofPlanetMath in a global context when you write and critique entries,and it should become apparent that probably most alternatives shouldat least be mentioned, before a particular choice is made for usage.

Interconnectedness

By this we mean provisions for makingPlanetMath as interlinked as possible. This includes tweakingmentions of concepts so that they trigger linking to a PlanetMathentry, or conversely, adding synonyms to entries or tweaking titlesto conform with the way they are mentioned in entries. It includesadding explicit “related” (See also) links to other things in theencyclopedia when they should be there. Also important is reportingto an object owner when a link goes to the “wrong” entry, or thereis a link where there should not be, and reporting the lack of asubject classification (which serves as a hint to automaticlinking).

Likewise, you should expect to receive corrections when your entriesare lacking in any of these areas.

Corrections don’t always go smoothly. Often you feel a correction wasjustified, but the author rejects it. The first thing to do in thissituation is find out if there was a misunderstanding: you can postmessages to the correction and discuss it. You can try filing anothercorrection wording things differently. When it becomes clear theauthor is not going to do things your way, we suggest the approachfrom the next section. Under no circumstances will the staffof PlanetMath mediate disagreements about corrections.

4 Alternate Entries

You should always run a search before writing an entry to see ifsomeone else has already covered the same material. However, even ifthe ideas have already been discussed, there may still be reason foryou to write an alternate entry. Alternate entries are justified when:

• you have a radically different treatment of the subject. Thiscould be another educational level (as in introductoryvs. advanced), or another method (as in a proof, which can have tensof alternatives).

• the author of the entry is discarding corrections. In this casethe object will not eventually be orphaned for pending corrections,so you cannot force modifications to it (do not complain tothe staff in this case; we won’t force the other author to doanything).

We would prefer uniformity and cohesion on PlanetMath, but there is anatural limit to how far this can be stretched with so many differentminds. The lack of scarcity (i.e. limited space) on PlanetMath alsogives it an advantage over traditional media, allowing us to avoidstandardization and provide extra value in yet another way.

5 Copyright

While mathematical concepts can not be owned, their expression issubject to the strictest protection under copyright law. Furthermore,one cannot convey mathematical information without expressing itsomehow. There is much more to “expression” than simply anauthor’s choice of words and, accordingly, direct copying is only oneof many sorts of copyright infringements.

Below, we present some guidelines for writing entries that may helpyou avoid exposing yourself or PlanetMath.org to legal problems.

• Bear in mind that a text does not need to have a copyrightnotice attached to it in order to be copyrighted. Moreover,copyright protection has nothing to do with whether the work ispublished or unpublished, whether a work is still in print, orwhether the publisher charges for copies of the work. In fact, thesimple act of writing something down automatically confers copyrightprotection to the author. In particular, this means that classnotes and handouts, webpages, and newsgroup postings are all legallyprotected.

• If you see the exposition of a certain mathematical topic onsomeone’s homepage and think it would make a great addition toPlanetMath, you should do nothing unless you can first obtain thecopyright holder’s permission, in writing, to publish a copy of thework on PlanetMath. Likewise, you may not post a copy of notes thatwere handed out in a class, or even notes that you took on a spokenlecture, without first obtaining written permission. Asking forpermission is also an opportunity to tell others about PlanetMathand the FDL. However, if you do not receive the author’s permissionto publish under FDL terms, you cannot post the work! If you doreceive the copyright holder’s permission to use the work,include their permissions statement as an attachment.

• When dealing with published material, especially if it is still inprint, keep in mind that authors sign contracts with their publisherswhich typically restrict the author’s rights. Therefore, even if theauthor of a book or an article in a journal gives you permission touse his work, it may be and likely will be necessary to also obtain thepublisher’s permission.

• Copying from FDL’ed works is fine, but it requires us to followa special protocol – if you would like to copy from an FDL work,please post in the forum, so a site administrator can review thework’s license and then take the necessary steps.

• Copying from public domain works is also fine. Mathematicalworks that are in the public domain are mostly those whosecopyrights have expired, but also works that have been transfered tothe public domain by their authors, as well publications of the USgovernment. As a rule of thumb, works published in the ninteteenthcentury and earlier are in the public domain, but unless you canfind proof to the contrary, twentieth century works are likely to beoff-limits. It is of course wise to give a citation so that otherscan easily check the assignment (or expiry) of copyright forthemselves – and perhaps also find additional useful material fromthe same source.

• As a rule of thumb, if you cannot provide at least a sketch of agiven topic without referring to a source, you are probably not yetqualified to write an entry about that topic. Not only is thispolicy prudent from the legal standpoint, it also makes sense from thepoint of view of mathematical content. If you rely too heavily on agiven source, you run the risk of perpetuating whatever mistakes andoversights may be present there. Furthermore, unless you have afairly deep understanding of a given topic, you might misunderstandanother author’s use of a particular technical term, or forget tostate assumptions which this other author stated in an earlierchapter. A document written from your own understanding will be muchmore useful than one that purports to present facts that youyourself do not understand. You needn’t be a world expert to writea useful entry – simply trying to state your own questions clearlywill be much more helpful to everyone involved than it would be foryou to try to mimic someone else’s exposition.

• Cite all sources, including any web pages, lectures, or personalcommunications that have informed your work. If possible, summarizethe relationship your article bears to the source or sources youused. Which parts of the article derive from which sources? Whichparts are original?

• Keep in mind the fact that, as the copyright office says,“Acknowledging the source of the copyrighted material does notsubstitute for obtaining permission.” To be sure, documenting theprocess you used while writing an article, and which sources youlooked at, could help prove that you did not infringe on anyoneelse’s copyright – but whether or not you cite a particular work isnot a factor in determining whether your work infringes on thatwork’s copyright.

• Embellish your articles with examples, illustrations, proofs,and other extensions either of your own devising or drawn, bit bybit, from a variety of sources – make your exposition truly yourown. No one part of your article should be too close to anythingdrawn from any one source. In addition, neither the overallstructure of your article nor any part of its structure should betoo close to the structure or any non-trivial part of the structure ofany one source.

• Bear in mind that the particular choice of words that an authoruses is not the only thing that copyright protects: copyrightprotects expression in general, and even the particular selection offacts or ideas that an author chooses to talk about is protected.

• However, copyright does not protect individual facts, ideas,concepts – so write about all these things! But always do it inyour own words, and do not rely too heavily on one source. Evensomething as simple as a theorem statement or a non-trivial equationshould be put in your own words, and expressed in a way that isconsistent with other usage on PlanetMath.

PlanetMath staff will not protect entry authors from theconsequences of any copyright infringement, and rather will doeverything in their power to protect the site from the irresponsible(though perhaps well-intentioned) actions of persons who seek tocontribute things they do not have the right to.

We do encourage you to find content written by others that you havebeen given permission use as part of PlanetMath. As mentioned above,a special protocol must be followed in order for us to use works thathave been released under the GNU FDL. In particular, if you areadding material from a GNU FDL source that hasn’t already been listedon PlanetMath’s History page, an appropriate item will have to beadded there; thus, if you are planning to upload all or part of anFDL’ed source, or a modified version thereof, you should get in touchwith the site administrators first.

When it comes to deciding whether some particular use of a copyrightedsource is permissible, the distinction betwen a derivative workand transformative use needs to be kept in mind. While thereis no space here to go into details and study examples, at least abrief description should suffice to make the reader aware of the legalprinciples that are in play here, and the fact that there is animportant distinction between the two kinds of use.

A derivative work is one whose content has been derived from analready existing work. Examples include translations, abrigements, oradaptations. Even though a derivative work can contain a substantialchanges or additions of new material and other original contributions,a derivative work cannot be prepared without the permission of theowner of the copyright of the original work on which it is based. (Infact, minor changes and additions to an existing work do not evenqualify as derivative work, but rather as outright copying.) The FDLgives users permission to publish derivative works, so long as thederivative works are released under the terms of the FDL. In general,non-FDL’ed copyrighted works offer no such permission to their users.

In contrast, transformative use of copyrighted materialconsists of putting the material to a different use or function thanthat originally intended by the author of the original work. This ispermitted as a fair use of copyrighted material but one needs to becareful not to take any more of the material than is necessary forthis new purpose. In deciding whether a certain usage is suitably“transformative”, one consideration is whether or not the new workaffects the marketability of the old work, or whether it in factsatisfies a purpose for which the original work was designed.

One needs to remember that in deciding a copyright infringement case,courts will consider how much material may have been used withoutpermission. Thus, it may be OK to have a single short entry that israther close to the small section of an original work from which itderives; however, it is a more serious matter if a whole series ofshort entries are all based on the same source.

For further discussion of copyright issues or questions, please usethe forums.

5.1 An Important Note On Using MathWorld

In addition to the copyright guidelines above, a few more words needto be added concerning MathWorld.

In short, we strongly suggest not using MathWorld at all inthe process of researching an entry, and furthermore we suggest notlinking to it in your articles.

The owners of the copyright on the MathWorld content have a proventrack record of aggressively defending their copyright. It is simplynot worth the risk, even when you feel sure you’d only be making fairuse of things you found there. Not only will this policy help usavoid potential legal snares, it will help to solidify in the mindsof readers the difference between the two sites.