The intellectual intimacy between them could never be perfect. If Comte entered entirely into Saint-Simon’s ideas, (without adopting them all, however), in return there was an aspect in Comte’s thought which Saint-Simon scarcely discerned through the lack of a sufficiently strong scientific education. It is enough to see how he speaks of the law of universal attraction. Comte must have been scandalised by it. So, at the very moment when he submits with most enthusiasm and youthful confidence to Saint-Simon’s influence he does not neglect his special mathematical studies. “My labours,” he writes to Valat on the 28th of September, 1819, “are and will be in two orders, scientific and political. I should set little value upon the scientific studies, did I not continually think of their utility to the human race. As well then amuse myself in deciphering very complicated puzzles. I have a supreme aversion for scientific labours whose utility, either direct or remote, I do not see. But I also confess, in spite of all my philanthropy, that I should put far less eagerness into political labours, if they did not stimulate the intellect, if they did not bring my brain strongly into play, in a word: if they were not difficult.”[2] A year later, in sending a parcel of political tracts to his friend, in which he distinguishes what is in his own manner and what is from Saint-Simon, he says that he is besides very eagerly occupied with mathematical work. He wants to take part in the competition opened by the Institut; and his ambition is soon to enter the _Academie des Sciences_. From 1822, in the celebrated pamphlet entitled _Plan des travaux scientifiques nécessaires pour réorganiser la société_, the synthesis between the two orders of labours is accomplished in Comte’s mind, thanks to the double discovery of the classification of the sciences and of the great law of social dynamics. We know that this work was, if not the principal reason, at least the occasion of the rupture between Comte and Saint-Simon. It is the moment which Comte himself considers to have been decisive in the history of his mind. The whole of his future doctrine was essentially contained in this pamphlet. The preface added by Saint-Simon shows that he did not understand its full bearings. Comte is henceforth his own master. At length he has found what for several years he had been seeking without being clearly conscious of it; and the rest of his life is now consecrated to the work which he has conceived and of which he has just outlined the plan. Since he has established a philosophical hierarchy of the sciences, whose summit is crowned by social physics, he has no further occasion to ask how he can conciliate his scientific labours with his political studies.