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The Neoplatonian philosopher Hypatia of Alexandria, Egypt, was the first well-documented woman in mathematics. Her actual date of birth is unknown, although considered somewhen between 350 and 370 AD. She was the head of the Platonist school at Alexandria and additionally taught philosophy and astronomy.
Hypatia was taught in mathematics and astronomy by her father, who was well known for his studies at the Alexandrian School. It is unknown, where she learned philosophy, but when she was done with her basic schooling, she began teaching mathematics and astronomy as well. Her lectures became instantly famous, which was maybe due to the fact, that she was a woman or maybe its because she managed to combine her knowledge with amazing rhetorical skills. It is known that people from far away came just to be taught by her and she hosted numerous public lectures, open for everyone who wanted to hear about her research in philosophy, mathematics and astronomy. Unfortunately, many contemporary scientists disliked this behavior, thinking that philosophy should not be taught to anyone who was not adequately educated and that teachers should not just 'walk around' town and teach anything openly, especially not women. Hypatia also hosted events with only very small groups of people, who were prohibited to talk about anything that was discussed during these meetings.
Even though it is not clear, how old Hypatia exactly was when she passed away, but her life sure ended quickly. She was murdered in spring of 415 or 416, which also is not clear. The assumed motives for the crime were personal, religious and political. During the second half of the 4th century, religious fights between Christians and followers of other rituals got more frequent. The fights escalated and Cyril of Alexandria is assumed to have spread false rumors about Hypatia whom he disliked due to her religious and political believes. However, many people of Alexandria were spurred on to take revenge on the woman. She was carried into a church, brutally killed and finally burnt.
During her life time, Hypatia published next to her teaching activities several works on mathematics and astronomy, especially in the field of arithmetics and conic sections. Unfortunately, not a single publication by Hypatia was found and therefore historians have no proof that she published them up to this day. Clear is however, that her father described Hypatia's achievements in various works and that her brilliance was admired by many.
But despite the many critics during her life time and today, Hypatia was respected for her scientific achievements by numerous scientists. Also in later years, authors and scientists discussed the case of Hypatia. Voltaire once even described her as one of the earliest distributors of the thoughts of the Enlightenment and saw her murder as a proof of the church's fanaticism. Historians assume on this day that her sudden death caused a great gap concerning her fields of study and especially the role of women in science. Even Bertrand Russel's wife, Donna Russel, published a scientific work on Hypatia's history and her achievements. Based on Hypatia's life, many musical and literary works were published and performed throughout history, including novels, operas and poems.
At yovisto, you may be interested in a video lecture by Professor Maria Dzielska, who discusses Hypatia's achievements at Poland's Embassy in Washington D.C.