Neal Amundson's seminal contributions in chemical engineering stem from the mathematically framed elegance of his research and the consequences of rigorous analysis. However, many significant problems in chemical engineering have resisted couching in elegant formalisms, the flow of granular materials being a particularly important example. There are valuable lessons that come sharply into focus by examining the nature of the difficulties. Here, we focus on questions of framing and analysisdetermining a theoretical approach, choosing an appropriate level of description, and selecting from multiple quantitative toolsusing examples spanning vibration, mixing, surface flow, and segregation and pattern formation. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3237-3246, 2013