In this paper, we propose a novel method to estimate the electrical angular velocity, the electrical angle, and the currents of the permanent magnet synchronous motor. A recurrent neural network learning algorithm is first developed to estimate the states of the permanent magnet synchronous motor. Then, an event-triggered state observer is designed for the recurrent neural network. This state observer robustly estimates state variables of the permanent magnet synchronous motor. A sufficient condition in terms of a convex optimization problem for the existence of the event-triggered state observer is established. In contrast with the abundance of state estimation methods based on time-triggered state observers where the measurements are always continuously available, the ones in this paper are updated when an event-triggered condition holds. Therefore, it lessens the stress on communication resources while can still maintain an estimation performance. Simulation results are provided to demonstrate the merit of the proposed method.