The sphere packing problem has various applications. Firstly, it extends quite simply into other dimensions (in two dimensions it becomes the circle packing problem). It is also analogous to the problem of constructing optimal codes (see "Coding theory: the first 50 years" elsewhere in this issue). A proof of the conjecture may also help physicists to understand the structure of crystals, something that Harriot himself urged Kepler to consider in his work on optics.