Hypatia was a working mathematician and Neoplatonic teacher, daughter of Theon of Alexandria, and she edited and commented on technical texts, Ptolemy's Almagest, Apollonius on conics, Diophantus, probably in collaboration with her father. Her own writings are lost. The best evidence for her as a person is the letters of her student Synesius of Cyrene, who became a Christian bishop and wrote to her with undiminished affection, which is itself the most useful single fact about her situation.
In March 415 she was seized from her carriage by a mob, dragged into a church, killed and her body burned. That is not disputed; it is reported by the Christian historian Socrates Scholasticus within a generation.
What it was about is where the popular account goes wrong. The standard modern treatments, Maria Dzielska's and Edward Watts's, place the killing inside a political conflict between the imperial prefect Orestes and the bishop Cyril, in a city with a long history of factional street violence. Hypatia was a prominent figure of the civic elite and a friend and adviser of Orestes; she was killed as a political actor on the losing side of a struggle over who governed Alexandria. She taught Christian students, including future bishops, and there is no evidence she was attacked for her philosophy or her mathematics.
The version in which she dies as a martyr of science at the hands of religion is an Enlightenment invention, Toland and then Gibbon and Voltaire found her useful, and it has been repeated ever since in histories of science and in film. It is worth being exact about this, because the true account is not exculpatory: a Christian mob murdered a pagan woman philosopher, in a church, with the bishop's partisans involved. It simply was not a quarrel about astronomy.