Comparison of the results from the Kamiokande neutrino-electron scattering experiment with those from the chlorine experiment and with solar models shows that the explanation of the solar-neutrino problem probably requires physics beyond the standard electroweak model with zero neutrino masses. The experimental results, including the shape of the electron-recoil energy spectrum measured by Kamiokande, are in excellent agreement with a nonadiabatic solution of the Mikheyev-Smirnov-Wulfenstein effect, yielding a neutrino mass difference of \ensuremath{\Delta}${\mathit{m}}^{2}$=1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{sin}}^{\mathrm{\ensuremath{-}}2}$${\mathrm{\ensuremath{\Theta}}}_{\mathit{V}}$ ${\mathrm{eV}}^{2}$.