Liber Mathematicae: A Web-Based Documentation and Collaboration Project for Mathematics

Traditionally, mathematical knowledge is published in printed media such as books or journals. Withthe advent of the Internet, a new method of publication became available. To date, however, most onlinemathematical publications do not employ the full capabilities ofthe medium. For example, the arXiv preprintserver [1] hosts documents in Adobe’s Portable Document Format (PDF), a format designed to transmitprint documents between computers and maintain the formatting. Wikipedia [6], on the other hand, presentsdocuments in-browser, but does not have support for presenting mathematics in scalable or copyable ways,since all mathematics is presented as images, not text.The languages of the World Wide Web, namely HTML and XHTML, are derived from StandardizedGeneralized Markup Language(SGML), originally, and Extensible Markup Language(XML), more recently.Unfortunately, (X)HTMLhas no provisions for displaying mathematics, a problem which the World WideWeb Consortium (W3C) solved with the MathML markup language. Like XHTML, MathML is a markuplanguage with “programs” stored as human-readable, plain-text ﬁles, formatted by a web browser or specialviewer. As such, and as a standardized language, MathML is uniquely able to serve as a platform by whichmathematics can be presented – primarily on the Web – but also processed by computer programs. Inparticular, computer algebra systems or tools for processing and disseminating text-based information suchas search engines can handle mathematical content written in MathML. In an article in the Notices of theAMS from May 2005, Miner[4] explained in detail such features and the importance of MathML for thecummunication of mathematical content in the future.The real power of XML technology is that it allows to transcend a current “consumer culture” withinthe community of mathematicians, in which a few people produce content which is then consumed by manyothers, and reach what Fischer[2] calls a “culture of participation” in which knowledge is created, shared,and acted upon by all parties. This goal can be achieved by encoding mathematics in browser-readable andeasily-editable documents in MathML, instead of in read-only documents like PDF.The Liber Mathematicae project [3] looks to bring the open source model of software development tomathematics publishing by employing cutting edge XML technology, high-quality mathematics fonts forthe Web from the STIX Fonts project [5] (see also [7]), and relational database technology to allow for asophisticated version control and review process for the submitted mathematical content. We have developeda web site, where members of the mathematical community can not only view articles but can additionallyparticipate in the creative process by contributing corrections, suggest improvements, or by expanding onthe original content. In contrast to traditional mathematics journals, the main goals of Liber Mathematicaeare to have articles which are expandable, correctable and dynamic, with tools for collaborative writingand open access to the entire mathematics community. Moreover due to their online nature, articles onLiber Mathematicae may contain more than static text and images and may in fact hold animations, livecomputational demonstrations, and so forth, and may use hyperlinking to strongly cross-reference otherarticles. An additional goal is to create a logical dependance tree for all mathematical theorems on LiberMathematicae. We hope that with this new environment for communicating mathematical knowledge, theopenness and cooperation will help to increase both the pace and quality of new mathematical research.References