We simplify the double curl in a couple of steps using Einstein summation. ( ∇ ∇ × × ∇ ∇ × × E ) i = ϵ ϵ i j k ϵ ϵ k l m ∂ ∂ j ∂ ∂ l E m = ( δ δ i l δ δ j m − − δ δ i m δ δ j l ) ∂ ∂ j ∂ ∂ l E m = ∂ ∂ i ( ∂ ∂ j E j ) − − ∂ ∂ j ∂ ∂ j E i