We present a scalable and precise verifier for recurrent neural networks, called Prover based on two novel ideas: (i) a method to compute a set of polyhedral abstractions for the non-convex and nonlinear recurrent update functions by combining sampling, optimization, and Fermat's theorem, and (ii) a gradient descent based algorithm for abstraction refinement guided by the certification problem that combines multiple abstractions for each neuron. Using Prover, we present the first study of certifying a non-trivial use case of recurrent neural networks, namely speech classification. To achieve this, we additionally develop custom abstractions for the non-linear speech preprocessing pipeline. Our evaluation shows that Prover successfully verifies several challenging recurrent models in computer vision, speech, and motion sensor data classification beyond the reach of prior work.