The proximal bundle method (PBM) is a powerful and widely used approach for minimizing nonsmooth convex functions. For smooth objectives, its best-known convergence rate has remained suboptimal. We present the first accelerated proximal bundle method to achieve the optimal O(1/sqrt(epsilon)) iteration complexity. The proposed method is conceptually simple, differing from Nesterov's accelerated gradient descent by a single line, and preserving the key structural properties of the classical PBM. As a result, we obtain an accelerated algorithm with much broader stepsize selection than what is allotted by accelerated gradient descent. The talk will include many pictures and numerical simulations to motivate algorithm design and illustrate fast convergence, respectively.