Illustration of mathematics can be thought of as a dual to modelling, instead of trying to create a mathematical model of a physical process we create a physical model of a mathematical idea. In both cases we can never have the certainty that the two systems line up perfectly, but can check some of the basic principals. For example if we assume that a flat piece of paper is a Euclidean plane, the compass makes a circle and a straight edge is indeed straight then these bridge between the drawings we make and the proofs of geometry. In this conference we hope to investigate the link between illustration and concept and ask how we can ensure that the interaction is rigorous within reason for the context.