Abstract: Kazhdan's Property (T) for a group G is a representation-theoretic form of rigidity; it is defined by the vanishing of the first cohomology of G with coefficients in any unitary G-module. Property (T) for G=Sp(n,1) was established by Kostant in 1969. Until recently, all known proofs of this fact involved hard computations either on representation theory or on special functions. In 2002, Gromov had the idea to connect property (T) for G with the growth of harmonic maps on the associated riemannian symmetric space, allowing for the first geometric proof of Kostant's result. I will explain the proof based on these ideas.