Wear is a ubiquitous phenomenon that limits the life of many engineered components with sliding interfaces through the gradual removal of material. The wear of polymers is crucial in many applications, ranging from bearings to orthopedic implants to nanolithography processes. The wear rate of polymers is strongly affected by the stress and temperature at the interface. The effects of temperature and stress are often described empirically since the wear process involves complex interactions between multiple asperities on rough surfaces over a range of length scales. Nanoscale tribology experiments at the single-asperity level have provided new insights into the underlying mechanisms of wear. Experiments on hard covalently bonded materials, including silicon and diamond, have demonstrated that wear is an atomic attrition wear process that can be modeled using stress-assisted transition state theory. Here, we examine the wear of a common polymer, polymethylmethacrylate (PMMA), at the nanoscale as a function of stress and temperature and show that the polymer wear is controlled by a combination of atomic attrition and viscoelastic relaxation. While the wear experiments are conducted at the nanoscale via atomic force microscopy, the results show that accounting for the local stress distribution at the contact interface is critical to understanding the wear behavior, an effect that was not considered in earlier studies on hard materials. Using a model that accounts for the stress distribution, we demonstrate the ability to predict the wear volume within 8%.