Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an image of a handwritten digit from another, can it also distinguish an "image of a sample" (such as a scatter plot) generated under a given statistical model from one generated outside that model? Motivated by this idea, we propose a novel procedure called deep-testing, which approaches the classical inferential problem of hypothesis testing through deep learning. More specifically, the test statistic is a classification map learned by a deep neural network from simulated data satisfying the null and alternative hypotheses, leveraging its strong discriminating power to construct a highly powerful test. As a proof of concept, we apply deep-testing to the problem of independence testing, arguably one of the most important problems in statistics. In a large-scale simulation study, deep-testing achieves the highest overall power against nineteen competing methods across a broad range of complex dependence structures, confirming the viability of the proposed approach.