In this talk we present three pairs of extreme opinions about remote teaching: "pedagogy should drive technology" vs. "technology should drive pedagogy", "you can't build a community without everyone in the same place" vs. "you can't have synchronicity while being fair and equitable", and "asynchronous teaching means making lots of videos" vs. "there is already a video on every concept I might want to teach". For each of these pairs of statements, we will provide practical suggestions for pedagogical approaches, resources, tools, and course components for striking the balance in between. We will also provide a list of resources for teaching technical material, specifically statistics and data science, but applicable to most mathematical sciences.