Hypatia of Alexandria

You almost expect to hear: "she was a fine philosopher -- for a woman" when hearing about ancient female prodigies. After all, our predecessors' opportunities, especially if they were "respectable" women, were nearly non-existent.
This week's woman, however, defies all such qualifiers.

Hypatia was, simply, the last great Alexandrian mathematician and philosopher. By writing a commentary on The Conics of Apollonius of Perga which divided cones into sections by a plane, Hypatia made geometry intelligible to her students and ultimately transmissible. Since men thronged to hear her ideas on philosophy, she taught neoplatonic ideas to pagans and Christians alike, including Synesius of Cyrene, who helped refine the doctrine of the Trinity.
Hypatia's fame eclipsed her father, Theon, who taught mathematics at the (http://www.perseus.tufts.edu/GreekScience/Students/Ellen/Museum.html) museum, and is known as the source for our text of Euclid's Elements. Theon taught his daughter and may have sent her to Italy and Athens for advanced instruction. Unfortunately, little of his daughter's writing survives. Since unlike her father, she didn't have a teaching position, we don't know where or when she taught.

There may have been another eclipsed man in her life, a philospher, too, and her husband, Isidorus; yet Hypatia is known for her chastity, virtue, and beauty as much as for her ideas in an era of Belfast-style conflict between pagans and Christians. These were formative years for Christian theology, but it still serves as a humbling reminder that it was the non-Christian, Platonic, rationalist Hypatia who convinced a would be paramour to maintain his celibacy in one of two much repeated anecdotes:

She was so beautiful and shapely that one of her students fell in love with her and was unable to control himself and openly showed her a sign of his infatuation. Uninformed reports had Hypatia curing him of his affliction with the help of music. The truth is that the story about music is corrupt. Actually, she gathered rags that had been stained during her period and showed them to him as a sign of her unclean descent and said, "This is what you love, young man, and it isn't beautiful!" He was so affected by shame and amazement at the ugly sight that he experienced a change of heart and went away a better man.
From (http://www.cosmopolis.com/alexandria/hypatia-bio-suda.html) Damascius' Life of Hypatia

Some of them, therefore, hurried away by a fierce and bigoted zeal, whose ringleader was a reader named Peter, waylaid her returning home, and dragging her from her carriage, they took her to the church called Caesareum, where they completely stripped her, and then murdered her with tiles.* After tearing her body in pieces, they took her mangled limbs to a place called Cinaron, and there burnt them.
From (http://www.cosmopolis.com/alexandria/hypatia-bio-socrates.html) The Life of Hypatia, by Socrates Scholasticus