Whether cognitive representations are better conceived as language-based, symbolic representations or perceptually related, analog representations is a subject of debate. If cognitive processes parallel perceptual processes, then fundamental psychophysical laws should hold for each. To test this, we analyzed both behavioral and neuronal representations of numerosity in the prefrontal cortex of rhesus monkeys. The data were best described by a nonlinearly compressed scaling of numerical information, as postulated by the Weber-Fechner law or Stevens' law for psychophysical/sensory magnitudes. This nonlinear compression was observed on the neural level during the acquisition phase of the task and maintained through the memory phase with no further compression. These results suggest that certain cognitive and perceptual/sensory representations share the same fundamental mechanisms and neural coding schemes.