This seems to be presenting a false dichotomy. B = (dA_z/dy - dA_y/dz)i + (dA_x/dz - dA_z/dx)j + (dA_y/dx - dA_x/dy)k and B = ∇×A are not the only ways, out of all possible strings, to encode that information. This is the power of modern programming languages. They are mathematics with much better syntax.
