Our network of acquaintances determines how we get exposed to ideas, products, or cultural artworks (books, music, movies, etc.). Though this principle is part of our common sense, little is known about the specific pathways through which our peers influence our discovery processes and our experience of the new. Here, we fill this gap by investigating a data set containing the whole listening histories of a large, socially connected sample of users from the online music platform \emph{Last.fm}. We demonstrate that users exhibit highly heterogeneous discovery rates of new songs and artists and that their social neighborhood significantly influences their behavior. More explorative users tend to interact with peers more prone to explore new content. We capture this phenomenology in a modeling scheme where users are represented by random walkers exploring a graph of songs or artists and interacting with each other through their social links. Even starting from a uniform population of agents (no natural differences among the individuals), our model predicts the emergence of strong heterogeneous exploration patterns, with users clustered according to their musical tastes and propensity to explore. We contend our approach can pave the way to a quantitative approach to collective discovery processes.