The classical dogma of localizationism implicitly resulted in the principle of a similar brain functional anatomy between individuals, as for example the pars opercularis of the left “dominant” hemisphere corresponding to the speech area. This fixed “single brain” model led neurosurgeons to define a set of “eloquent” areas, for which injury would induce severe and persistent neurological worsening, making their surgical resections impossible. Therefore, numerous patients with a cerebral lesion justifying surgery were a priori not selected for resection and lost a chance to be treated. In fact, advances in brain mapping showed a considerable inter-individual variability explained by a networking organization of the brain, in which one function is not underpinned by one specific region, but by interactions between dynamic large-scale delocalized sub-circuits. Indeed, using non-invasive neuroimaging, a variability of both structural and functional anatomy was demonstrated in healthy volunteers. Moreover, intraoperative electrical stimulation mapping of cortex and white matter tracts in awake patients who underwent surgery for tumor or epilepsy also showed an important anatomo-functional variability. However, a remarkable observation is that this variability is huge at the cortical level, while it is very low at the subcortical level. Based upon these intrasurgical findings, the goal of this review is to propose a two-level model of inter-individual variability (high cortical variation, low subcortical variation), breaking with the traditional rigid workframe, and making neurosurgery in traditionally presumed “eloquent” areas feasible without permanent deficits, on condition nonetheless to preserve the “invariant common core” of the brain.