Abstract: This heuristic `physical proof' is due to E. Witten from 1980's and motivated the later rigorous heat equation proofs. I shall first review the Feynman path integral formalism for supersymmetric quantum mechanics. This formalism will next be applied to the Hamiltonian defined by the Dirac operator of a spin manifold, and after some non-trivial manipulations within the path integral, will lead to a proof of the index formula.I shall recall all needed background material from physics and geometry.