  Paper: cond-mat/9311033 The Hubbard model of interacting electrons, like the
Ising model of spin-spin interactions, is the simplest possible model
displaying many ``real world'' features, but it is much more difficult to
analyze qualitatively than the Ising model. After a third of a century of
research, we are still not sure about many of its basic properties. This
mini-review will explore what is known rigorously about the model and it will
attempt to describe some open problems that are possibly within the range of
rigorous mathematical analysis.
