Why does aluminium oxide dissolve in molten cryolite?

Cryolite does not dissolve aluminium oxide, but lowers its melting point.

Mixtures usually have lower melting points than pure substances so a mixture of cryolite and bauxite melts at a lower temperature than either pure substance. The electrolysis process is actually run at temperatures slightly below the melting point of pure cryolite. Nevertheless as bauxite is repeatedly added to the electrolysis cell it is fair to describe the process as aluminium oxide dissolving in molten cryolite. Both are ionic materials so will dissolve in each other as the ions will held together by electrostatic forces, just as in the pure materials.