But it was in the higher mathematics that Maria Gaetana was to win her chief title to fame in the world of learning. So successful had she been in her prosecution of this branch of science that she was, at the early age of twenty, able to enter upon her monumental work--_Le Instituzioni Analitiche_--a treatise in two large quarto volumes on the differential and integral calculus. To this difficult task she devoted ten years of arduous and uninterrupted labor. And if we may credit her biographer, she consecrated the nights as well as the days to her herculean undertaking. For frequently, after working in vain on a difficult problem during the day, she was known to bound from her bed during the night while sound asleep and, like a somnambulist, make her way through a long suite of rooms to her study, where she wrote out the solution of the problem and then returned to her bed. The following morning, on returning to her desk, she found, to her great surprise, that while asleep she had fully solved the problem which had been the subject of her meditations during the day and of her dreams during the night. Could the psychiatrist who so loves to deal with obscure mental phenomena find a more interesting case to engage his attention or one more worthy of the most careful investigation? Finally Maria Gaetana's _opus majus_ was completed and given to the public. It would be impossible to describe the sensation it produced in the learned world. Everybody talked about it; everybody admired the profound learning of the author, and acclaimed her: "Il portento del sesso, unico al Mondo"--the portent of her sex, unique in the world. By a single effort of her genius she had completely demolished that fabric of false reasoning which had so long been appealed to as proof positive of woman's intellectual inferiority, especially in the domain of abstract science. Maria Gaetana's victory was complete, and her victory was likewise a victory for her sex. She had demonstrated once for all, and beyond a quirk or quibble, that women could attain to the highest eminence in mathematics as well as in literature, that supreme excellence in any department of knowledge was not a question of sex but a question of education and opportunity, and that in things of the mind there was essentially no difference between the male and the female intellect.