The surface tension of the air-water interface increases upon addition of inorganic salts, implying a negative surface excess of ionic species. Most acids, however, induce a decrease in surface tension, indicating a positive surface excess of hydrated protons. In combination with the apparent negative charge at pure air-water interfaces derived from electrokinetic experiments, this experimental observation has been a source of intense debate since the mid-19th century. Herein, we calculate surface tensions and ionic surface propensities at air-water interfaces from classical, thermodynamically consistent molecular dynamics simulations. The surface tensions of NaOH, HCl, and NaCl solutions show outstanding quantitative agreement with experiment. Of the studied ions, only H O adsorbs to the air-water interface. The adsorption is explained by the deep potential well caused by the orientation of the H O dipole in the interfacial electric field, which is confirmed by ab initio simulations.