 
Summary: Digitisation, Representation and Formalisation
Digital Libraries of Mathematics
A. A. Adams
School of Systems Engineering, The University of Reading.
A.A.Adams@Rdg.ac.uk
Abstract. One of the main tasks of the mathematical knowledge management com
munity 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, digi
tally 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 glob
ally. Represented material is digital material in which there is some structure (usually
syntactic in nature) which maps to the mathematics contained in the digitised infor
mation. 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 man
aging that information, we must ensure that these resources are applied to digitise,
form representations of or formalise, existing and new mathematical information in
