Hypatia is the earliest female mathematician who is known by name today, and the only female mathematician of antiquity to make significant contributions to mathematics. Hypatia was born either around the year 355 or the year 370 in Alexandria, now part of Egypt. She was the daughter of Theon (ca. 335–ca. 405), a mathematician and philosopher who instructed her in these topics.
By the late fourth century, there was no longer much original mathematics being done in Alexandria. However, Hypatia and her father were the top mathematicians of their time. Probably Hypatia's greatest lasting contribution to mathematics was collaborating with her father on a new version of Euclid's Elements that became the basis for all later editions of that work. This is significant because Elements is (with the exception of sacred scripture) the most-read book of all time. Theon and Hypatia standardized the presentation, elaborated on excessively-brief arguments, fixed errors (some of which weren't really errors, though) and made a few small additions, such as the part of proposition 33 in book VI that deals with sectors of circles. Hypatia also collaborated with her father on other works such as an eleven-part commentary on Ptolemy's Almagest. Hypatia also wrote several commentaries, now all lost, on the works of Diophantus, Appollonius, and Ptolemy.
Around the year 400, she became the head of the Neoplatonist school in Alexandria, where she lectured in mathematics and in Neoplatonist philosophy. She is said to have been an excellent lecturer and her lectures were well-attended.
Like many places in the Roman Empire at that time, Alexandria in the fifth century was home to frequent political disorder. Hypatia had been accused, perhaps wrongly, of disrupting the friendship between Orestes, prefect of Alexandria, and Cyril (now St. Cyril), bishop of Alexandria. As well, she was a prominent pagan and, while some Christians (the most notable being Synesius of Cyrene prior to 410) had attended her lectures, other Christians saw her as a threat. In 415, a Christian mob seized her in the streets of Alexandria, dragged her into a church, and brutally murdered her, tearing her body to pieces.
Some people have taken her death to mark the end of mathematics in antiquity, and after her death there are no significant mathematicians to come out of Alexandria. However, some mathematics continued to be practiced at Athens, at Plato's Academy (with Proclus, who was active later in the fifth century, being the best-known mathematician there), for over a century until the Academy was closed by Emperor Justinian in 529.
See also Hypatia's biography at the University of St. Andrews.
Sources used (see bibliography page for titles corresponding to numbers): 38.