The first woman mathematician, regarding whose attainments we have any positive knowledge, is the celebrated Hypatia, a Neo-platonic philosopher, whose unhappy fate at the hands of an Alexandrian mob in the early part of the fifth century has given rise to many legends and romances which have contributed not a little toward obscuring the real facts of her extraordinary career. She was the daughter of Theon, who was distinguished as a mathematician and astronomer and as a professor in the school of Alexandria, which was then probably the greatest seat of learning in the world. Born about the year 375 A. D., she at an early age evinced the possession of those talents that were subsequently to render her so illustrious. So great indeed was her genius and so rapid was her progress in this branch of knowledge under the tuition of her father that she soon completely eclipsed her master in his chosen specialty. There is reason to believe--although the fact is not definitely established--that she studied for a while in Athens in the school of philosophy conducted by Plutarch the Younger and his daughter Asclepigenia. After her return from Athens, Hypatia was invited by the magistrates of Alexandria to teach mathematics and philosophy. Here in brief time her lecture room was filled by eager and enthusiastic students from all parts of the civilized world. She was also gifted with a high order of eloquence and with a voice so marvelous that it was declared to be "divine." Regarding her much vaunted beauty, nothing certain is known, as antiquity has bequeathed to us no medal or statue by which we could form an estimate of her physical grace. But, be this as it may, it is certain that she commanded the admiration and respect of all for her great learning, and that she bore the mantle of science and philosophy with so great modesty and self-confidence that she won all hearts. A letter addressed to "The Muse," or to "The Philosopher"--[Greek: Te Philosopho]--was sure to be delivered to her at once. Small wonder, then, to find a Greek poet inditing to her an epigram containing the following sentiment: "When I see thee and hear thy word I thee adore; it is the ethereal constellation of the Virgin, which I contemplate, for to the heavens thy whole life is devoted, O august Hypatia, ideal of eloquence and wisdom's immaculate star."[111] But it was as a mathematician that Hypatia most excelled. She taught not only geometry and astronomy, but also the new science of algebra, which had but a short time before been introduced by Diophantus. And, singular to relate, no further progress was made in the mathematical sciences, as taught by Hypatia, until the time of Newton, Leibnitz and Descartes,--more than twelve centuries later.