Remembering events is crucial to intelligent behavior. Flexible memory retrieval requires a cognitive map and is supported by two key brain systems: hippocampal episodic memory (EM) and prefrontal working memory (WM). Although an understanding of EM is emerging, little is understood of WM beyond simple memory retrieval. We develop a mathematical theory relating the algorithms and representations of EM and WM by unveiling a duality between storing memories in synapses versus neural activity. This results in a formalism of prefrontal WM as structured, controllable neural subspaces (activity slots) representing dynamic cognitive maps without synaptic plasticity. Using neural networks, we elucidate differences, similarities, and trade-offs between the hippocampal and prefrontal algorithms. Lastly, we show that prefrontal representations in tasks from list learning to cue-dependent recall are unified as controllable activity slots. Our results unify frontal and temporal representations of memory and offer a new understanding for dynamic prefrontal representations of WM.