One of the challenges of doing mathematical art is that it seems to fit into a societal blind spot, the popular perception of both subjects appearing to have little intersection. Bridges participants know this is not at all correct, but how did it come about? More importantly how can understanding that help us all to make better mathematical art? In this talk I will discuss joint work with the late Roger Antonssen, applying the notion of Genuine Pretending (based on the work of Hans Georg Moeller) to mathematical art. I will present several examples of my own work to bring these theoretical considerations into practice, in particular how ideas from differential geometry can be both used to control digital machines to make art, and be explored themselves as the content of artwork.