Let M be a compact negatively curved manifold.  Based on the correspondence between classical and quantum mechanics, one might expect Laplace eigenfunctions of high energy on M to behave chaotically, spreading out evenly and not having large peaks anywhere.  I will describe how one can use number theory to find counterexamples to this expectation, by constructing eigenfunctions with large peaks.  My talk will be based on joint work with Farrell Brumley.