The massive amount of available neurodata suggests the existence of a mathematical backbone underlying the intricate oscillatory activity of the brain. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. We elucidate how and why underrated notions from geometry, topology, group theory/category theory are useful to describe neuronal issues and to provide a series of experimentally testable hypotheses. Once established that geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system, we suggest that the Monge’s theorem might contribute to our visual ability of depth perception and that the brain connectome can be tackled in terms of tunnelling nanotubes. Further, we contend that the human mind does not perceive the topological findings of visual images and that the multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of mathematical approaches like knot theory and braid groups. We show how presheaves from category theory permit to tackle the nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. The last, but not the least, we advocate that the far-flung field of soft-matter polymers/nematic colloids might shed new light on the neurulation in mammalian embryos and hypothesize that the development of the central and peripheral nervous systems might be correlated with the occurrence of local thermal changes in embryo-fetal tissues.