  We have rigorously shown that a strong Hubbard repulsion can cause
superconductivity. The model, which has a particular set of local symmetries,
manifests the phase diagram of many unconventional superconductors;
anti-ferromagnetism paramagnetism, superconductivity, and even ferromagnetism
are all observed. The key technique in the analysis is an exact non-linear
fermion transformation, which preserves the correlated motion of electrons
while removing the strong interactions. Using resolvent formalism, it is
exactly shown that two holes at the Mott point bind to form a localised Cooper
pair. As interactions are now weak, we then use BCS mean field theory to
calculate the energy, excess pairing, and superconducting gap. These results
are compared to exact diagonalisation of finite sized systems and show good
agreement. At the Mott point the system is an anti-ferromagnet, and a
superconducting phase quickly appears upon doping, and then vanishes.
