A central challenge in developing conceptual understanding in science is overcoming naive ideas that contradict the content of science curricula. Neuroimaging studies reveal that high school and university students activate frontal brain areas associated with inhibitory control to overcome naive ideas in science, probably because they persist despite scientific training. However, no neuroimaging study has yet explored how persistent naive ideas in science are. Here, we report brain activations of 25 scientists with a Ph.D. in physics assessing the scientific value of naive ideas in science. Results show that scientists are slower and have lower accuracy when judging the scientific value of naive ideas compared to matched control ideas. fMRI data reveals that a network of frontal brain regions is more activated when judging naive ideas. Results suggest that naive ideas are likely to persist, even after completing a Ph.D. Advanced experts may still rely on high order executive functions like inhibitory control to overcome naive ideas when the context requires it.