One of the founding principles of human cognitive neuroscience is the so-called universality assumption, the postulate that neurocognitive mechanisms do not show major differences among individuals. Without negating the importance of the universality assumption for the development of cognitive neuroscience, or the importance of single-case studies, here we aim at stressing the potential dangers of interpreting the pattern of performance of single patients as conclusive evidence concerning the architecture of the intact neurocognitive system. We take example from the case of Leonardo Botallo, an Italian surgeon of the Renaissance period, who claimed to have discovered a new anatomical structure of the adult human heart. Unfortunately, Botallo's discovery was erroneous, because what he saw in the few samples he examined was in fact the anomalous persistence of a fetal structure. Botallo's error is a reminder of the necessity to always strive for replication, despite the major hindrance of a publication system heavily biased towards novelty. In the present paper, we briefly discuss variations and anomalies in human brain anatomy and introduce the issue of variability in cognitive neuroscience. We then review some examples of the impact on cognition of individual variations in (1) brain structure, (2) brain functional organization and (3) brain damage. We finally discuss the importance and limits of single case studies in the neuroimaging era, outline potential ways to deal with individual variability, and draw some general conclusions.