Given a nonconstant harmonic function on the unit ball in n-dimensional Euclidean space, it is a classical result that its gradient vanishes on a set of dimension at most n-2. We discuss a quantitative extension of this result, which shows that if the gradient is epsilon-small in magnitude on a set with positive (n-2+delta)-dimensional Hausdorff content, then this smallness propagates to any compact subdomain of the unit ball. This is sharp and improves the result of Logunov and Malinnikova which required the dimension of the smallness to be close to n-1. This is joint work with Josep Gallegos.