The professor had made a fatal error, which could hardly have been avoided even if it had been foreseen. Being a mathematical genius, he had for years scorned the applied mathematics of his time and had evolved a new and revolutionary system from the realm of pure mathematics. Consequently, his symbols, although relatively simple, were intelligible only to himself and Bourget. Indeed, the conclusion which he had reached by the new method could not have been deduced or even expressed by ordinary mathematical symbols. It was, therefore, hardly surprising that a mathematician of the old school should utterly fail to grasp the meaning of the calculation. Professional pride, however, would not permit this fact to be recognized, and so like many another innovator, Montesquieux was to pay dearly for his temerity.