  Three of the four forces of Nature are described by quantum Yang-Mills
theories with remarkable precision. The fourth force, gravity, is described
classically by the Einstein-Hilbert theory. There appears to be an inherent
incompatibility between quantum mechanics and the Einstein-Hilbert theory which
prevents us from developing a consistent quantum theory of gravity. The
Einstein-Hilbert theory is therefore believed to differ greatly from Yang-Mills
theory (which does have a sensible quantum mechanical description). It is
therefore very surprising that these two theories actually share close
perturbative ties. This article focuses on these ties between Yang-Mills theory
and the Einstein-Hilbert theory. We discuss the origin of these ties and their
implications for a quantum theory of gravity.
