Abstract: I will discuss Mark Kac’s famous question as to what geometric information is encoded in the Laplace spectrum of a manifold. The Laplacian is a generalized second derivative and we consider its eigenvalues and eigenfunctions. We’ll see examples of spaces which have the same Laplace spectrum (isospectral) yet which are geometrically distinct (non-isometric). I’ll present a pair of isospectral spaces that I’ve constructed together with Mary Sandoval in order to examine their inaudible geometric properties. This talk should be accessible to undergraduate math majors.