Explaining how intelligent systems come to embody knowledge of deductive concepts through inductive learning is a fundamental challenge of both cognitive science and artificial intelligence. We address this challenge by exploring how a deep reinforcement learning agent, occupying a setting similar to those encountered by early-stage mathematical concept learners, comes to represent ideas such as rotation and translation. We first train a Dueling Deep Q-Network on a shape sorting task requiring implicit knowledge of geometric properties, then we query this network with classification and preference selection tasks. We demonstrate that scalar reinforcement provides sufficient signal to learn representations of shape categories. After training, the model shows a preference for more symmetric shapes, which it can sort more quickly than less symmetric shapes, supporting the view symmetry preferences may be acquired from goal-directed experience.