  We introduce and illustrate a new approach to the unknotting problem via the
dynamics of vortex strings in a nonlinear partial differential equation of
reaction-diffusion type. To untangle a given knot, a Biot-Savart construction
is used to initialize the knot as a vortex string in the FitzHugh-Nagumo
equation. Remarkably, we find that the subsequent evolution preserves the
topology of the knot and can untangle an unknot into a circle. Illustrative
test case examples are presented, including the untangling of a hard unknot
known as the culprit. Our approach to the unknotting problem has two novel
features, in that it applies field theory rather than particle mechanics and
uses reaction-diffusion dynamics in place of energy minimization.
