  The Hardy uncertainty principle says that no function is better localized
together with its Fourier transform than the Gaussian. The textbook proof of
the result, as well as one of the original proofs by Hardy, refers to the
Phragm\'en-Lindel\"of theorem. In this note we first describe the connection of
the Hardy uncertainty to the Schr\"odinger equation, and give a new proof of
Hardy's result which is based on this connection and the Liouville theorem. The
proof is related to the second proof of Hardy, which has been underservedly
forgotten. Then we survey the recent results on dynamical versions of Hardy's
theorem.
