Recent years have seen an explosion of new technologies for “making” shapes with unprecedented complexity: from 3D printers, to robotic folding, to soft materials that swell and buckle under changes in temperature or humidity. With each of these new technologies comes new challenges and questions about how to design objects that can be turned into real physical matter. In this talk, we will explore how modern tools for designing and manufacturing 3D shapes connect back to age-old questions from the mathematical field of differential geometry, such as how to enclose the greatest area using a fixed length of rope or guessing the shape of a bell by just listening to the way it sounds.