One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on
digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task,
arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between
digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing
mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible
and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic
in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both
the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information
to which access is desired, and the limited resources available for managing that information, we must ensure that these resources
are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as
to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal
issues which surround the practical tasks.
This work is supported by EU Grant MKMNet IST-2001-37057 and UK EPSRC Grant GR/S10919