The generation of an action potential that propagates along a nerve axon has been a problem of significant interest since the early '50s. In this talk, I will discuss the FitzHugh-Nagumo model on a surface of a long, thin cylinder that represents the axonal membrane of a single neuron. This model is a system of a partial differential equation coupled with an ordinary differential equation in two dimensions (plus time). Key questions are the existence of a pulse -- a special solution that travels along the length of the axon -- and its stability under small perturbations of the initial conditions and the geometry.