The molecular characterization of the air/water interface is a key step in understanding fundamental multiphase phenomena ranging from heterogeneous chemical processes in the atmosphere to the hydration of biomolecules. The apparent simplicity of the air/water interface, however, masks an underlying complexity associated with the dynamic nature of the water hydrogen-bond network that has so far hindered an unambiguous characterization of its microscopic properties. Here, we demonstrate that the application of quantum many-body molecular dynamics, which enables spectroscopically accurate simulations of water from the gas to the condensed phase, leads to a definitive molecular-level picture of the interface region. For the first time, excellent agreement is obtained between the simulated vibrational sum frequency generation spectrum and the most recent state-of-the-art measurements, without requiring any empirical frequency shift or ad hoc scaling of the spectral intensity. A systematic dissection of the spectral features demonstrates that a rigorous representation of nuclear quantum effects as well as of many-body energy and electrostatic contributions is necessary for a quantitative reproduction of the experimental data. The unprecedented accuracy of the simulations presented here indicates that quantum many-body molecular dynamics can enable predictive studies of aqueous interfaces, which by complementing analogous experimental measurements will provide unique molecular insights into multiphase and heterogeneous processes of relevance in chemistry, biology, materials science, and environmental research.