Dark matter is a major component of the universe, about six times more abundant than ordinary visible matter. We measure the effects of its mass, but it escapes the telescopes. It has the particularity of emitting no radiation and interacting only by the action of gravity. The main purpose of this article is to try to answer what dark matter is: we conjecture that it is composed of magnetically charged neutrinos, true magnetic monopoles. But that requires a huge conceptual leap: Maxwell's laws must be inverted and the electric charge becomes a magnetic charge. Asymmetric "reversed" Maxwell's laws would provide the "dark" magnetic charge that would replace the electric charge. The very form of the Dirac equation, which imposed on ordinary matter that the particle carries an electric charge and obeys the principal properties of the electron, would impose in the dark matter that the "dark" particle obeys the main properties of a neutrino associated with a magnetic charge. The second aim of the article is to show that dark matter is derived from black holes, mainly from active supermassive black holes. This requires a second conceptual leap: the horizon of the black hole undergoes a high temperature and an intense pressure of magnetic fields which cause a blackout and a phase transition (or broken symmetry) when the matter crosses the horizon. The result is a reversal of Maxwell's laws: a magnetic charge is substituted for the electric charge, and the electric current becomes a tributary of the magnetic current. A third important conceptual leap follows: sterile magnetic neutrinos created inside the black hole would cross the horizon to the outside to constitute dark matter.