"All abstract speculations, all knowledge which is dry, however useful it may be, must be abandoned to the laborious and solid mind of man.... For this reason women will never learn geometry." In these words Immanuel Kant, more than a century ago, gave expression to an opinion that had obtained since the earliest times respecting the incapacity of the female mind for abstract science, and notably for mathematics. Women, it was averred, could readily assimilate what is concrete, but, like children, they have a natural repugnance for everything which is abstract. They are competent to discuss details and to deal with particulars, but become hopelessly lost when they attempt to generalize or deal with universals. De Lamennais shares Kant's opinion concerning woman's intellectual inferiority and does not hesitate to express himself on the subject in the most unequivocal manner. "I have never," he writes, "met a woman who was competent to follow a course of reasoning the half of a quarter of an hour--_un demi quart d'heure_. She has qualities which are wanting in us, qualities of a particular, inexpressible charm; but, in the matter of reason, logic, the power to connect ideas, to enchain principles of knowledge and perceive their relationships, woman, even the most highly gifted, rarely attains to the height of a man of mediocre capacity." But it is not only in the past that such views found acceptance. They prevail even to-day to almost the same extent as during the ages of long ago. How far they have any foundation in fact can best be determined by a brief survey of what woman has achieved in the domain of mathematics. Athenaeus, a Greek writer who flourished about A.D. 200, tells us in his _Deipnosophistae_ of several Greek women who excelled in mathematics, as well as philosophy, but details are wanting as to their attainments in this branch of knowledge. If, however, we may judge from the number of women--particularly among the hetaerae--who became eminent in the various schools of philosophy, especially during the pre-Christian era, we must conclude that many of them were well versed in geometry and astronomy as well as in the general science of numbers. Menagius declares that he found no fewer than sixty-five women philosophers mentioned in the writings of the ancients[108]; and, judging from what we know of the character of the studies pursued in certain of the philosophical schools, especially those of Plato[109] and Pythagoras, and the enthusiasm which women manifested in every department of knowledge, there can be no doubt that they achieved the same measure of success in mathematics as in philosophy and literature.[110]