In 1970, J. Wheeler, at Princeton, offered a 1000$ award to know whether Einstein equations in vacuum should admit or not a generic potential, that is to say if it could be possible to express a solution metric by means of a few arbitrary functions and their derivatives up to a certain order, in such a way that this metric should become a solution of Einstein equations and no others. Such a
... [Show full abstract] problem is a particular case of the following one: how to recognize when a given linear partial differential operator is expressing all the compatibility conditions of a preceding one in a differential sequence. The purpose of our lecture is to give an effective answer to this question by means of the new technique of differential duality and to apply it to Einstein equations, thus solving the above challenge negatively.