Large language models (LLMs) have displayed an impressive ability to harness natural language to perform complex tasks. We explore whether we can leverage this ability to find and explain patterns in data. Specifically, given a pre-trained LLM and data examples, we apply interpretable autoprompting (iPrompt) to generate a natural language string explaining the data. iPrompt iteratively generates explanations with an LLM and reranks them based on their performance when used as a prompt. Experiments on a wide range of datasets, from synthetic mathematics to natural language understanding, show that iPrompt can yield meaningful insights by accurately finding dataset explanations that are human-interpretable. Moreover, iPrompt is reasonably efficient, as it does not require access to model gradients and works with relatively small models (e.g. ~6 billion parameters rather than >=100 billion). Finally, experiments with scientific datasets show the potential for iPrompt to aid in scientific discovery.