Abstract: TBA

Abstract: The index theorem of Atiyah and Singer is a milestone of modern mathematics. This result which computes the virtual dimension of the space of solutions of an elliptic operator in topological terms, has its roots in classical results like Gauss-Bonnet and Riemann-Roch theorems. I shall trace some of these roots, going back all the way to a statement in Euclid's Elements! Any proof of the index theorem involves some heavy doses of analysis as well as geometry and topology. I shall briefly indicate the original cobordism proof, and then will focus on a more modern heat equation proof and its ramifications.