Bridges between contemporary mathematics and theoretical physics are difficult to find, difficult to follow once found, and tend to become vaporous midway across. A potential exception is the so-called “Mathai-Quillen Formalism”. Mathai and Quillen discovered that a certain SO(V)-equivariant cohomology class provides a machine for the mass production of representatives of the Euler class for any finite-dimensional, oriented vector bundle with typical fiber V. These representatives depend on the choice of both a connection and a section and so their integrals mediate between the Gauss-Bonnet-Chern and Poincare-Hopf descriptions of the Euler number. Exploiting the flexibility available in the choice of the section, Atiyah and Jeffrey formally applied the Mathai-Quillen results to a certain infinite-dimensional vector bundle associated with the Donaldson invariants, thereby reproducing the Lagrangian of the Topological Quantum Field Theory constructed by Witten in which these invariants appear as expectation values (and in which he later discovered the Seiberg-Witten invariants). Physicists have since taken over the idea to produce a wide range of TQFTs of “cohomological type”. This talk will describe the finite-dimensional background in some detail and, if time permits, sketch the infinite-dimensional context relevant to Donaldson-Witten Theory.