Monsky asked whether the Hilbert-Kunz multiplicity of a ring can ever be irrational. One may expand the question to Hilbert-Kunz multiplicities of m-primary ideals, or even more generally to finite-length modules (defined by Seibert). Using techniques arising from the algebraic geometry of vector bundles, the speaker finds an example where the Hilbert-Kunz multiplicity of a finite-length module is irrational.