The dominant narratives currently offering critique of the neoliberal university suggest a professional environment that is both uncaring and unhealthy. This paper adopts a Deleuzian gaze on the rhizomatic multiplicity of teaching to identify and reinterpret key lines of flight within this assemblage -- identified as care, pedagogic health and salutogenesis. It is argued that the perspective described by the coexistence of these lines may develop a more positive ontology as a basis from which a university may be able to work towards a more productive state of healthy learning. The point at which the three lines of flight co-exist is hypothesised as a 'triple point'.