Growth cones are the main motile structures located at the tip of neurites and are composed of a lamellipodium from which thin filopodia emerge. In this article, we analyzed the kinetics and dynamics of growth cones with the aim to understand two major issues: first, the strategy used by filopodia and lamellipodia during their exploration and navigation; second, what kind of mechanical problems neurons need to solve during their operation. In the developing nervous system and in the adult brain, neurons constantly need to solve mechanical problems. Growth cones must decide how to explore the environment and in which direction to grow; they also need to establish the appropriate contacts, to avoid obstacles and to determine how much force to exert. Here, we show that in sparse cultures, filopodia grow and retract following statistical patterns, nearly optimal for an efficient exploration of the environment. In a dense culture, filopodia exploration is still present although significantly reduced. Analysis on 1271, 6432, and 185 pairs of filopodia of DRG, PC12 and Hippocampal neurons respectively showed that the correlation coefficient |rho| of the growth of more than 50% of filopodia pairs was >0.15. From a computational point of view, filopodia and lamellipodia motion can be described by a random process in which errors are corrected by efficient feedback loops. This article argues that neurons not only process sensory signals, but also solve mechanical problems throughout their entire lifespan, from the early stages of embryogenesis to adulthood.