An exploration in the space of mathematical knowledge

Abstract

Although knowledge is a central topic for MKM there is little explicit discussion on what 'knowledge' might actually be. There are specific intuitions about form and content of knowledge, about, its structure, and epistemological nature that shape the MKM systems, but a conceptual model is missing. In this paper we try to rationalize this discussion to give MKM a firmer footing, to start a discussion among MKM researchers and help relate the MKM intuitions and discourses to other communities. Starting from the observation that many concrete realizations of mathematical knowledge objects are considered equivalent, we propose a conceptual model of the space of (mathematical) knowledge objects graded by levels of abstraction and presentational explicitness and draw conclusions for MKM markup formats. © Springer-Verlag Berlin Heidelberg 2006.