Cognition in the Formal Modes: Research Mathematics and the SOLO Taxonomy

Mathematics researchers put considerable cognitive effort into trying to expand the body of mathematical knowledge. In so doing, is their cognitive behaviour different from those who work on more standard mathematical problems? This paper attempts to examine some aspects of mathematical cognition at the highest level of formal functioning. It illustrates how the structure of a mathematician's output--and, to a certain extent, its cognitive complexity--can be characterised by the SOLO taxonomy. A number of cognitive and philosophical issues concerning mathematical functioning at the research level will also be discussed.