How does hearing work? Can mathematics contribute to our understanding of the auditory system, and maybe even help restore hearing to those with profound hearing loss? In this talk we will give a brief introduction to the physiology of the auditory system and discuss examples of mathematical models that have been used to study how we hear and how we even restore hearing for individuals with hearing loss through the technology of cochlear implants. Mathematical topics include ordinary and partial differential equations and numerical nethods, but no prior knowledge is necessary.