Data from both neuropsychological and neuroimaging studies have implicated the left inferior parietal cortex in calculation. Comparatively less attention has been paid to the neural responses associated with the commission of calculation errors and how the processing of arithmetic errors is modulated by individual differences in mathematical competence. Do more competent individuals exhibit a different brain response to errors than less mathematically able individuals? These outstanding questions were addressed in the present functional Magnetic Resonance Imaging (fMRI) study through an investigation of which brain regions respond more to erroneously versus correctly solved arithmetic problems while a group of 24 adult participants with varying levels of mathematical competence solved problems of all four arithmetic operations. Despite high levels of accuracy, a robust main effect of accuracy (incorrect vs. correct) was observed in both medial and lateral regions of the prefrontal cortex. These regions have frequently been associated with both the detection of errors and the deployment of cognitive control following an error. Furthermore, mathematical competence was found to modulate the activation of an area in the right dorsolateral prefrontal cortex. Specifically, individuals with relatively higher mathematical competence (n = 12) were found to activate this region more for incorrectly solved trials than their less mathematically competent peers (n = 12). Taken together, these findings suggest that the commission of arithmetic errors modulates responses of prefrontal regions and, moreover, that activation of the right lateral prefrontal cortex during arithmetic errors is affected by individual differences in mathematical competence. In view of the evidence associating the lateral prefrontal cortex with the implementation of cognitive control, we suggest that individuals with relatively high mathematical competence may exhibit greater awareness of calculation mistakes and implement greater control following the commission of errors. (Contains 2 figures and 1 table.)