where A μ μ is the dynamical field variable) that give rise to the conservation of all zilches using Noether's theorem. Until recently, the answer to this question had been given only for the case of optical chirality by Philbin in 2013. This open question was also emphasized by Aghapour, Andersson and Rosquist in 2020, while these authors found the symmetries of the duality-symmetric Maxwell action underlying the conservation of all zilches. (Aghapour, Andersson and Rosquist did not find the symmetries of the standard Maxwell action, but they speculated that such symmetries should exist ). There are also earlier works studying the conservation of zilch in the context of duality-symmetric electromagnetism, but the variational character of the corresponding symmetries was not established.