We propose a learning approach to corner detection for event-based cameras that is stable even under fast and abrupt motions. Event-based cameras offer high temporal resolution, power efficiency, and high dynamic range. However, the properties of event-based data are very different compared to standard intensity images, and simple extensions of corner detection methods designed for these images do not perform well on event-based data. We first introduce an efficient way to compute a time surface that is invariant to the speed of the objects. We then show that we can train a Random Forest to recognize events generated by a moving corner from our time surface. Random Forests are also extremely efficient, and therefore a good choice to deal with the high capture frequency of event-based cameras-our implementation processes up to 1.6Mev/s on a single CPU. Thanks to our time surface formulation and this learning approach, our method is significantly more robust to abrupt changes of direction of the corners compared to previous ones. Our method also naturally assigns a confidence score for the corners, which can be useful for postprocessing. Moreover, we introduce a high-resolution dataset suitable for quantitative evaluation and comparison of corner detection methods for event-based cameras. We call our approach SILC, for Speed Invariant Learned Corners, and compare it to the state-of-the-art with extensive experiments, showing better performance.