There is thus a succession of 'partial resolvents' or an embedding of 'groups' which make the solution follow from the very conditions of the problem: the fact that an equation cannot be solved algebraically, for example, is no longer discovered as a result of empirical research or by trial and error, but as a result of the characteristics of the groups and partial resolvents which constitute the synthesis of the problem and its conditions (an equation is solvable only by algebraic means in other words, by radicals, when the partial resolvents are binomial equations and the indices of the groups are prime numbers).