%0 Journal Article %T The Hubbard Model: Some Rigorous Results and Open Problems %A Elliott Lieb %J Physics %D 1993 %I arXiv %X 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. %U http://arxiv.org/abs/cond-mat/9311033v2