Abstract The classic Mie scattering problem is revisited via an integral-equation formalism. Our approach consists in resumming the multiple-scattering Born series in terms of which the solution can be formally expressed. For small dielectric spheres, the resummation can be done exactly without invoking the full apparatus of multipoles. For a large dielectric sphere with a small refractive-index discontinuity relative to the surrounding medium, the Born series may be approximately resummed to generate correctly a description of the phenomenon of anomalous diffraction. For spheres of arbitrary size, the Born series for each excited electric or magnetic multipole has a complicated structure, but one that is shown to be exactly equivalent to the celebrated Mie results. A significant advantage over the usual differential approach is the implicit inclusion of the electromagnetic boundary conditions at the scattering surface in the integral approach, a feature that may provide valuable insights into scattering from arbitrarily shaped particles.