The self-ionization of water was first proposed in 1884 by Svante Arrhenius as part of the theory of ionic dissociation which he proposed to explain the conductivity of electrolytes including water. Arrhenius wrote the self-ionization as . At that time, nothing was yet known of atomic structure or subatomic particles, so he had no reason to consider the formation of an  ion from a hydrogen atom on electrolysis as any less likely than, say, the formation of a  ion from a sodium atom.
In 1923 Johannes Nicolaus Brønsted and Martin Lowry proposed that the self-ionization of water actually involves two water molecules: . By this time the electron and the nucleus had been discovered and Rutherford had shown that a nucleus is very much smaller than an atom. This would include a bare ion  which would correspond to a proton with zero electrons. Brønsted and Lowry proposed that this ion does not exist free in solution, but always attaches itself to a water (or other solvent) molecule to form the hydronium ion  (or other protonated solvent).
Later spectroscopic evidence has shown that many protons are actually hydrated by more than one water molecule. The most descriptive notation for the hydrated ion is , where aq (for aqueous) indicates an indefinite or variable number of water molecules. However the notations  and  are still also used extensively because of their historical importance. This article mostly represents the hydrated proton as , corresponding to hydration by a single water molecule.