Some facets of knowledge management in mathematics

Knowledge management in mathematics has a long history. The development of Jahrbuch über die Fortschritte der Mathematik in 1868 saw the first systematic analysis of the content of a comprehensive set of mathematical publications which would be termed today the core of mathematical knowledge. The leading reviewing services in mathematics – formerly the reviewing journals Zentralblatt für Mathematik which followed the Jahrbuch, and Mathematical Reviews, which are today the databases ZBMATH and MathSciNet – have introduced and popularized several notions and tools for analysing the content of mathematical knowledge, for example a classification system for mathematics (the Mathematical Subject Classification – MSC), keywords for the most relevant terms of a publication, and abstracts and reviews for short descriptions of the content of publications.
In the electronic age, the challenges of knowledge management have dramatically increased.
New types of knowledge have been developed (for example, software), information is linked together, and the World Wide Web has become the universal archive – by far the biggest archive ever, and a storage medium for all kinds of information. It is therefore necessary to improve the existing methods and tools for retrieval and knowledge management.
In our contribution, our intentions and ideas for a redesign of the MSC will be presented.The MSC is a complex hierarchical classification scheme for mathematics and areas of application of mathematics. It was developed in the 1970s and is periodically updated by the editorial offices of ZBMATH and MathSciNet in cooperation with the mathematical community. (For more information see the MSC master site at http://www.msc2010.org.)
The MSC has some deficits hampering its use: too many classes (more than 5,500) which make it confusing for the user, missing strong definitions of the classes, and as a consequence a broad overlapping and redundancy of the classes (the MSC is only rudimentarily a faceted classification). As a first step we mapped the present version of the MSC into a machine-understandable XML version basing it on the Simple Knowledge Organization System (SKOS) and Resource Description Framework (RDF). The SKOS version will enable automatic processing of the information in the databases mentioned above, for example a cross-linking of the database entries with library catalogues, but it will also offer new retrieval functionalities for the human user.
In a second step, we will enhance the MSC by semantic annotation and redesign of its structure, for example by characterizing the MSC classes with a controlled vocabulary. In our presentation we will present a first SKOS version of the MSC and discuss its use in the future.