CanOneHear theSound ofaTheorem?

M athematics and music have been intertwined in a long-running drama that stretches back to ancient times and has featured contributions from many great minds, including Pythagoras, Euclid, Mersenne, Descartes, Galileo, Euler, Helmholtz, and many others (see, e.g., [1]). Applications of mathematics to music continue to develop in today’s digital world, which also supports active communities of musicologists and experimental composers who examine music methodically, often using mathematical elements. In light of the recent wave ofmusico-mathematical books, blogs, journals, and even articles in the Notices, this multifaceted side of the mathematical world deserves reexamination. Although the scrutiny given here will reveal many problems posing as solutions, some promising prospects will also emerge, and positive turns in the plot may yet unfold, especially when viewed from a novel educational angle described below. From the mathematician’s perspective, besides providing a bounty of physical applications, the search for relationships between music and mathematics should serve both as a philosophical reflection pool and as a portal to an engagement of the general public with mathematics. But the view is often obstructed by the unwitting entanglement of several distinct lines of thought. It is not uncommon for commentary on music and mathematics to bounce between the physics of sound, theoretical analysis of music, and metaphorical prose. While each approach has its strengths and weaknesses, unjustified juxtapositions can serve to cloud the big picture by masquerading as implicit unifications of unresolved key issues or by