Granular media are ubiquitous in nature and in the industry. In order to forecast how they behave, engineers will rely on numerical simulation. In this talk, one of the most popular numerical simulation models for granular media will be presented—the Distinct Element Method. A related efficient contact detection algorithm will be presented as well, and the theoretical issues it poses will be discussed. The talk will then move from there to a number of mathematical questions in surface topology, optimization, discrete geometry, and group geometry that are, perhaps surprisingly, the same questions engineers have about their contact detection algorithms.