The history of PlanetMath.org is discussed, tracing its inception, stabilization, and some defining challenges. Research and outreach efforts that have been conducted in the course of work on the PlanetMath project are reviewed, and the scope and reach of the resource are discussed. Recent developments are indicated briefly. Some remarks evaluating PlanetMath's trajectory and content conclude the paper.
PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible. PlanetMath’s content is created collaboratively: the main feature is the mathematics encyclopedia with entries written and reviewed by members.
cannot be easily separated from a history of the PlanetMath community and the technology behind the site, though the presentation here is not especially technical. The reader who is interested in a succinct overview of the current characteristics of the encyclopedia will find what they seek in Sections 6 (quantitative aspects) and 8 (qualitative aspects).
In the words of Eric Weisstein: “if you ever assemble a body of knowledge that you want to share with others, you don’t want to go through what I have just gone through.”6 So it came to pass that in the Fall of 2000, Nathan Egge and Aaron Krowne, at that time both undergraduates at Virginia Tech, came up with the idea for PlanetMath: a collaboratively created mathematics reference work that would have resistance to copyright threats built in, in the form of an open content license. By the summer of 2001, the basic infrastructure for creating an encyclopedia was complete, and a fledgling community had grown up around the resource.
some very different principles and practices. Whereas MathWorld’s terms of use disallow archival copies,
(and, indeed, encouraged) to copy, mirror, redistribute, print, remix, and reuse PlanetMath content for commercial or any other purpose – so long as all such works are published under the same license as
3
under the supervision of Ed Fox. In this thesis, Krowne describes how the early design and development of the site benefited from continuous feedback in the #math IRC channel on Undernet.8 He also details the key technical and community features of the site as they developed in this period:
sources.
7http://mathworld.wolfram.com/about/faq.html#history 8irc://irc.undernet.org/math 4
In 2003, the present author was enrolled as a graduate student in mathematics at the University of Texas in Austin, and in possession of a large and growing personal collection of very tersely-written definitions and proofs relevant to the department’s prelim exams.9 In fact, this work had as much to do with the tradition of computer mathematics in the air in Austin (QED, Maxima, ACL2, AM) as it had to with exams. A representative example: (lebesgue outer measure: fact: lebesgue outer measure is infimum of lebesgue outer measures of open supersets) 1: X Rn 2: L = fO Rn : O Xg 3: jXje = infO2L(fjOjeg)
the contents of the “Austin Problems in Mathematics – Cross-Index” (styled APM-x ) into the PlanetMath encyclopedia as world-editable “seed entries”. This turned out to be a first-rate disaster.10
The primary complaints from community members were: (1) the entries could not be understood without reading an accompanying FAQ; (2) a casual visitor to the PlanetMath website might get the wrong impression about the nature of the encyclopedia when looking at “apmxi” entries; and, (3) nearly 600 entries had been introduced into PlanetMath by the site’s administrator in one big batch, circumventing, at least in outward appearances, the site’s usual model of careful review and collaborative editing of entries.
not adopted by community members after a week would be deleted from the encyclopedia. This was the fate that befell most.
The event was a defining moment in the history of PlanetMath. In the first place, it was a testament to the strength of the community’s norms. Secondly, it showed that the specific affordances of computers, e.g. for mass processing of data, or for dealing with hypertextual complexity associated with alternate related treatments of a given topic, needed to be tempered to work well for the people involved. These issues would set much of the research and development agenda around PlanetMath for the following decade. 5
In 2005, several established PlanetMath contributors met in person at a Symposium on Free Culture and
the Digital Library at Emory University, where Krowne was then based. Contributed papers looked at
an adaptation of PlanetMath’s software for collaborative creation of course notes in a graduate
course on ordinary differential equations [
which looked at the drawbacks of current copyleft licenses, particularly “license lock” [
workshops: The Evolution of Mathematical Communication in the Age of Digital Libraries (Minneapolis, 2006)14, and Mathematical Knowledge Management: Sustainability, Scalability and Interoperability (Halifax, 2007)15.
nicer-looking volume17, thanks to Ross Moore’s contribution of multinclude.sty and other tweaks.18
2008). The best outcome of this was that PlanetMath’s autolinking subsystem was turned into a modular
piece of code, NNexus19, as written up in [
generated by the user community.22 Nor did the Noosphere codebase present a particularly compelling
resource for capable computer mathematics developers like Claus Zinn [
The rapid growth of math resources on the web, which is further pushed by wiki-based communities, is both a threat and an opportunity for intelligent math learning environments [...] If we could harness the collaborative authoring process and encourage and guide wiki authors to continually provide content and metadata, then intelligent services could unleash their true potential. 6
At the time of this writing, PlanetMath contains 8945 entries, dealing with 15655 concepts. 298 people have contributed an entry in the encyclopedia, and 2742 have contributed something (perhaps just one forum post).
11www.jointmathematicsmeetings.org/meetings/national/jmm/san-prog.pdf 12http://www.dessci.com/en/company/shows/jmm/mow2007.htm 13http://www.maa.org/abstracts/mf2008-program.pdf 14http://www.ima.umn.edu/2006-2007/SW12.8-9.06/ 15http://projects.cs.dal.ca/ddrive/seminars/mkm.shtml 16http://www.scribd.com/doc/9691966/, http://www.scribd.com/doc/9692058/ 17http://metameso.org/~joe/docs/book.pdf 18http://metameso.org/~joe/math/fem-2005.tar.gz 19http://code.google.com/p/nnexus/ 20http://statprob.com 21http://planetphysics.org 22http://wiki.planetmath.org/cgi-bin/wiki.pl/Feature_Requests
Out of these, an exceptional group of 24 authors have produced more than 100 encyclopedia articles apiece. Their contributions comprise 74% of the total number of articles. About 71% of this core group joined before 2004 (in the “early days” for the site).
130 users have a score of 1000 points or more, which would correspond to contributing 10 or more new encyclopedia articles, but actually, a significant fraction of this value has been contributed through things like corrections, revisions to existing objects, and posting in the forums. All told, this group has contributed 96% of the total number of articles. About 58% of this group joined before 2004.
7
A new era
University, Bremen, and led by Michael Kohlhase, with major contributions from most members of his
research group (along with the present author).25 The Planetary system is described in [
2011 will see the publication of a book chapter discussing the future use of PlanetMath as the core of
a problem-based learning system [
PlanetMath has been successful as an online community: the software stabilized early on and has
required little upkeep, while the site has continued to grow. However, there has been a danger that with
the software system running more or less on “autopilot”, new features would not be developed. With any
luck, this threat is in the process of being eliminated, heralding in the opportunity to build one or more
“new” online communities in close relationship to PlanetMath (e.g. a developer community working
on sophisticated tools for scientific communication; a learning community using the PlanetMath
encyclopedia as part of a remix-driven interactive textbook). We should do a careful evaluation of what has
worked and what could be improved for next time. There is not room in the current paper to conduct this
discussion, but framework proposed by Resnick et al. would be an excellent place to begin [
For all of its potential as a software showcase and its possible future role as a player in a larger landscape of related interlinked online communities, PlanetMath should, at least for the moment, be evaluated first and foremost as an encyclopedia. This too would be best as an ongoing task. For now, 23http://maa.org 24http://mathoverflow.net 25http://trac.mathweb.org/planetary 26http://vanillaforums.org Coverage References History Audience Clarity Pictures Accuracy Unusual Weight
ning graduate topic. PlanetMath is generally considered to have more in-depth treatment of technical issues, e.g. of proofs, than
database of references or style of presenting them (this is planned). 315 items, mostly 20th Century or later.27
but precise (e.g. from strong contributors who have have English as a second language). Other articles may be verbose and vague.
a high standard is generally maintained (see Section 4).
At the time of this writing there are 48 outstanding corrections28; more than 14080 corrections have been filed since the site began, though 2337 are classified as “addenda”, meaning that no mistake is implied, and 9182 are classified as “meta/minor”, meaning that in the entire history of PlanetMath some 2561 real errors have been found through the peer review process (and all but a few fixed!). Note that these numbers do not take into account direct changes by authors (and would tend to under-represent error fixing in world-editable articles).
edited from a lightweight laptop or netbook, weighing about 1kg.
a quick summary following the outline used by Emma Previato in her review [
Because the technology that supports the site is special-purpose, we have been able to hone in on what works best for commons-based peer production in mathematics. Features like the autolinker facilitate integration of content, and the corrections system helps avoid messy battles. There is much more work to be done, but at the close of its first decade of life, PlanetMath may be poised to become a encyclopedia in the literal classical sense of a “complete instruction”.
27http://planetmath.org/browse/objects/01Axx/ 28http://planetmath.org/?op=globalcors