The curse of knowledge can impede communication between experts and laymen. We propose a new task of expertise style transfer and contribute a manually annotated dataset with the goal of alleviating such cognitive biases. Solving this task not only simplifies the professional language, but also improves the accuracy and expertise level of laymen descriptions using simple words. This is a challenging task, unaddressed in previous work, as it requires the models to have expert intelligence in order to modify text with a deep understanding of domain knowledge and structures. We establish the benchmark performance of five state-of-the-art models for style transfer and text simplification. The results demonstrate a significant gap between machine and human performance. We also discuss the challenges of automatic evaluation, to provide insights into future research directions. The dataset is publicly available at https://srhthu.github.io/expertise-style-transfer/.