The roles of prefrontal and anterior cingulate cortices have been widely studied, yet little is known on how they interact to enable complex cognitive abilities. We investigated this issue in a complex yet well-defined symbolic paradigm: algebraic problem solving. In our experimental problems, the demands for retrieving arithmetic facts and maintaining intermediate problem representations were manipulated separately. An analysis of functional brain images acquired while participants were solving the problems confirmed that prefrontal regions were affected by the retrieval of arithmetic facts, but only scarcely by the need to manipulate intermediate forms of the equations, hinting at a specific role in memory retrieval. Hemodynamic activity in the dorsal cingulate, on the contrary, increased monotonically as more information processing steps had to be taken, independent of their nature. This pattern was essentially mimicked in the caudate nucleus, suggesting a related functional role in the control of cognitive actions. We also implemented a computational model within the Adaptive Control of Thought—Rational (ACT-R) cognitive architecture, which was able to reproduce both the behavioral data and the time course of the hemodynamic activity in a number of relevant regions of interest. Therefore, imaging results and computer simulation provide evidence that symbolic cognition can be explained by the functional interaction of medial structures supporting control and serial execution, and prefrontal cortices engaged in the on-line retrieval of specific relevant information.