  We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations
which have finite total energy, and whose magnetic helicity is not a constant
function of time. In view of Taylor's conjecture, this proves that there exist
finite energy weak solutions to ideal MHD which cannot be attained in the
infinite conductivity and zero viscosity limit. Our proof is based on a
Nash-type convex integration scheme with intermittent building blocks adapted
to the geometry of the MHD system.
