Dynamic neural processing unrelated to changes in sensory input or motor output is likely to be a hallmark of cognitive operations. Here we show that neural representations of space in parietal cortex are dynamic while monkeys perform a spatial cognitive operation on a static visual stimulus. We recorded neural activity in area 7a during a visual maze task in which monkeys mentally followed a path without moving their eyes. We found that the direction of the followed path could be recovered from neuronal population activity. When the monkeys covertly processed a path that turned, the population representation of path direction shifted in the direction of the turn. This neural population dynamic took place during a period of unchanging visual input and showed characteristics of both serial and parallel processing. The data suggest that the dynamic evolution of parietal neuronal activity is associated with the progression of spatial cognitive operations.