This paper presents our work in progress on the Planetary system, along with a critical evaluation of the project relative to its stated goals and the goals of one of its main \clients", PlanetMath.org. 3 PlanetMath.org (2001-ongoing), http://planetmath.org 4 The Planetary System (2010-ongoing), http://trac.mathweb.org/planetary 5 http://kwarc.info
The metaphor or analogy implied by the title of this paper is that PlanetMath3 is like an operating system for mathematics, and Planetary4 is like a kernel for this system (think GNU/Linux). This analogy is both apt and sloppy.
In particular, PlanetMath is not a complete mathematics \userland". Indeed,
it is best known for its mathematics encyclopedia which contains over 9000
entries, and de nes around 16000 concepts (see [
In 2010, the present rst author was beginning a Ph. D. project on \Semantic Adaptivity and Social Networking in Personal Learning Environments" that aimed to extend PlanetMath so that encyclopedia entries were \connected to exercises and applications, preliminary materials, and resources for further learning", and to develop software that would track individual performance and provide personalized advice based on aggregated data.
Due to the extensive (and intensive) nature of software modi cations that
would be required to do this well, he welcomed the possibility to collaborate
with Michael Kohlhase and his team at KWARC5 on a complete re-build of
Noosphere, using contemporary web frameworks, and integrating the \KWARC
stack" of semantic technologies into PlanetMath. This led to an early prototype
of the Planetary system being named a nalist in Elsevier's Executable Papers
Challenge [
The rest of this paper will descibe our technical achievements to date, discuss
the immediate road ahead, and re ect on Planetary's potential, particularly from
the point of view of its use on PlanetMath. (The reader is referred to [
As indicated above, one of our main goals behind rebuilding PlanetMath's software was to be able to more easily bring new developers into the project. Another was to integrate new technologies.
After our rst round of prototyping, Drupal 7 emerged as a good candidate solution for both of these issues. It is a popular system, with a wide variety of contributed modules { and it also supports a healthy marketplace for professional services. So far, the Planetary team has 14 contributors (most of them computer science students at Jacobs University, Bremen), with the current second author focusing on developing Drupal support for features and work ow similar to those found on PlanetMath.
We have found that there are some modules that can be installed and used
directly, with minimal con guration (e.g. privatemsg, for the exchange of private
messages between users) { others needed to be custom-built (e.g. support for
corrections, essentially a custom form of bug report used to maintain accuracy and
quality in PlanetMath's encyclopedia). Some others, like the userpoints module
can be installed and used with minor tweaks. All in all, we depend on around 25
existing contributed modules, and have written a comparable number of custom
modules. For a few legacy features, we took things in a new direction:
1. For mathematics rendering, we are using LATEXML6. Full support for MathML
lays the foundation for many other future services. (For example, our
Executable Paper demo integrated JOBAD, a Javascript tool for interacting
with mathematical documents while reading.)
2. In place of, or alongside, the legacy autolinking service, we have a new
interactive (\semi-automated") autolinker, which should provide greater precision
for links { and, again, open the door to a range of new interactive services
during the document-authoring/editing process [
and demo an integration between Drupal, LATEXML, and the Virtuoso triple store, which, again, will be useful in a range of future applications (e.g. we will be able to generate RDFa that can then be used to maintain backlinks, for example from an image to all of the articles that include that image).
There are some other features that have been developed for Planetary that are in use in other installation environments (namely, Michael Kohlhase's Computer Science courses), that are not yet integrated into our work on PlanetMath: speci cally, an integration with SVN via TNTBase7, which provides the ability to edit math on the web without ever opening a web browser, and a new books module, which provides support for lengthy documents. These features may eventually make their way into PlanetMath, but they can already serve to illustrate part of our goal in Planetary: to make a system that is useful in many di erent math-on-the-web contexts, with various features available in the various environments that need them.
One of our core aims in this regard is to make Planetary install \out of the box"; we are currently in the process of using Drupal's pro le project to package up our work and support this. In future, this should be very helpful both for users and developers. 3
As we can seen in Figure 1, the latest version of Planetary captures many of the same interactions as the legacy version of the site, although the two sites are certainly not identical.
In the short months leading up to CICM in July, we aim to nalize the handful of features that remain unimplemented or partly implemented, and be ready to enter a \beta" with the new platform (i.e., ready to make it the software you see when you browse to PlanetMath.org). From a project management point of view, we have passed our last \milestone" and can now focus on feature-driven development. Our path to deployment on planetmath.org looks like this: { May 4th: nal module tweaking and building for features like requests, private messages, scoring, notices, and the object orphanage. { May 11th: any nal \alpha" features (e.g. nish integrating Etherpad), and a rst round of optimizations. { May 18th: A public \alpha" launch. { June: Add any \beta" features that we need, in consultation with the PlanetMath user community. { July: Final improvements readying the site for a switch over to the \beta".
4 Fig. 1. The current PlanetMath webpage under Noosphere 1.5, and the new \beta" version.
The question we take up in this section is: is the Planetary system meeting the aims of its developers, and the needs of its user community? What could it do to improve?
Clearly, releasing the system on PlanetMath, and providing links the code8 and installation instructions9 should improve things dramatically. The new PlanetMath will render LATEX blazingly fast, have better links, and a range of new features that address long-standing user concerns and also some nice surprises.
But our aspirations have in fact been much bigger { and switching to Planetary should play a big part in bringing them closer. Speci cally: { It is relatively easy to make new content types in Drupal, and we are introducing \problem" and \solution" node types, and allowing people to attach them to encyclopedia articles, and discuss problems with attached \questions" and solutions with attached \reviews". { Our aim will be to develop some semantically aware activity tracking and \heads up" information for people using this system (see Figure 2). It is within reach to provide \related problems" using the MSC classi cation, but further analysis of theory dependencies (or approximations to the same) should allow us to give links to \simpler related problems", automating a key Polya heuristic. Even without sophisticated tools, our hope is that a new generation of students will feel more encouraged to participate when problems and solutions become \ rst class" objects in the system. { Our hypothesis is that the introduction of problems and solutions will provide a vital quality check, and enhancement. In short: encyclopedia articles that do not have attached exercises (or applications) should not necessarily be presumed to be useful. At the same time, exercises that do not have attached solutions may be too hard, i.e., the relevant subjects in the encyclopedia may not be su ciently developed.
While we are not there yet, this is an example of the sort of thing we expect this technology together with the \encyclopedic approach", puts tantalizingly close to within reach.
Note that PlanetMath, unlike, say, Wikipedia, is not constrained to be either \just a wiki" or \just an encyclopedia" { so, interactive problem sets and/or peer tutoring are welcome in PlanetMath, though they might not t so cleanly within the existing Wikimedia family. Rather, the encyclopedic approach envisioned here connects interactions to a carefully curated and systematic knowledge base { in contrast with, for example, the StackExchange sites, at least in their current implementation.
In any event, the perspective developed above should brings up some big questions: in brief, what happens to mathematics teaching when students have access to a universal solutions manual for their mathematics course work? We may be able to measure whether lecture/homework/test is as e ective for learning, as, say, participating in applied research projects.
Still, the hazard here would be to imagine that this can all happen overnight. It has taken PlanetMath 10 years to de ne 16000 terms, how much time will it take to provide a good exposition of those terms (always assuming that we do nd users who want to participate in this process)?
Furthermore, as we have learned in the last few years, programming Drupal is not equally easy for everyone, documentation is not always clear (or available), and development work is generally a slow process (even with skilled programmers onboard). If the potentially revolutionizing changes (sketched above for mathematics education, but relevant also to research) of math on the web are to be realized, most aspects of this project will have to scale up a lot { and hopefully coding will be less of a bottleneck. 5
We have described the Planetary system, and discussed its relevance to PlanetMath's continued project of building \a central repository for mathematical knowledge on the web, with a pedagogical slant." We expect the phase of work we will complete this summer to fully renovate and modernize PlanetMath. But once we have readied and deployed an extensible { and re-deployable { core, in a sense, our main work will just be beginning.
For example, we recall the meaning of \planet" from the blogosphere, i.e. planet-as-aggregator. Thinking in this way, PlanetMath might best ful ll its promise not just with a great new platform, but by successfully integrating content from other math on the web projects. This sort of aggregation service has yet to be realized, but forms a highly interesting direction for future work.
Indeed, if we are going to do anything about the \$500 million pricetag" for building a math-capable AI10, we either have to bring about greater e ciencies, or spread the cost out over a relatively large number of people. Without making promises about just when this will be accomplished, we assert that we have, with PlanetMath and now Planetary, taken some vital steps in this direction.