From heart cells to fireflies to arrays of metronomes, nature is full of enormous collections of oscillators that somehow manage to synchronize themselves. The Kuramoto model is the simplest mathematical model of such self-synchronizing systems. Amazingly, it is exactly solvable (in some sense), despite being an infinite-dimensional nonlinear dynamical system with random parameters. I'll discuss what's known and unknown about this remarkable model. No background is required, beyond an undergraduate-level understanding of probability and differential equations.