Hypatia of Alexandria (c. 380 - 415) was a philosopher, mathematician, and teacher who lived in Alexandria, then a Greek city. Several works are attributed to her by later sources, including commentaries on Diophantus' Arithmetica, on Apollonius's Conics and on Ptolemy's works, but none has survived.

Letters written to her by her pupil Synesius give an idea of her intellectual milieu. She was of the Platonic school, although her adherence to the writings of Plotinus, the 3rd century follower of Plato and principal of the neo-Platonic school, is merely assumed. Hypatia's contributions to science are reputed (on scant evidence) to include the invention of the astrolabe and the hydrometer.

She was the daughter of Theon, the last fellow of the Museum of Alexandria, which was adjacent to or included in the main Library of Alexandria. Hypatia did not teach in the Museum, but received her pupils in her own private home. No images of her exist, but nineteenth century writers and artists envisioned her as an Athene-like beauty.

Hypatia was murdered in March 415 in the Alexandrian church of the Caesareum (a former pagan temple) by a mob led by a Christian magistrate named Peter. The motive seems to have been rooted in religious and political controversies.

In 391, Theophilus, the patriarch of Alexandria, had destroyed some pagan temples in the city , which may have included the Museum and certainly included the Serapeum (a temple for the worship of Serapis and "daughter library" to the Great Library).

In the same year Emperor Theodosius had published an edict prohibiting various aspects of pagan worship, whereupon (although this was part of a wider phenomenon) Christians throughout the Roman Empire embarked upon a thorough campaign to destroy or christianize pagan places of worship.

Hypatia lived during a conflict between pagans, on the one side, and Christians on the other, who were demanding the final destruction of paganism as an imperial institution; it appears that certain Christians and sympathisers of either side found it difficult to come to terms with the conflict.

Hypatia, herself a pagan, was respected by many Christians, and was even exalted by a few later Christian authors as a symbol of virtue, often being portrayed by them (and by romantic novelists) as a virgin till her death. These later portrayals (interesting as they are) are not entirely reliable, since they often contradict each other.

Some insight into the intellectual conflict of early 5th century Alexandria is given by the letters written by Synesius of Cyrene, Bishop of Ptolomais, to Hypatia, whom he loved and respected as a teacher. In one of them, he complains about people who begin to undertake philosophy after failing at some other career: "Their philosophy consists in a very simple formula, that of calling God to witness, as Plato did, whenever they deny anything or whenever they assert anything.

A shadow would surpass these men in uttering anything to the point; but their pretensions are extraordinary." In this letter, he also tells Hypatia that "the same men" had accused him of storing "unrevised copies" of books in his library. This indicates that books were rewritten to suit the prevailing Christian dogma, which may also relate to the difficulty of finding accurate contemporary information about Hypatia's life and death.

Theories about the mob violence that ended Hypatia's life range from a local, spontaneous Christian uprising tolerated by the Christian Patriarch Cyril of Alexandria over a conflict between Cyril and the more tolerant prefect Orestes; to a conspiracy supported by the Emperor himself; to a lawless, civilian "peasant stock" mob (soldiers are never mentioned) made up of superstitious Christians and non-Christians alike led by the charismatic zealot "Peter". Another point of view holds that Hypatia was part of a rebellion and her murder unfortunate, but inevitable. (In the ancient world, it was common for historians to copy from each other without further inquiry, thus making a resolution difficult.)

Although iron hooks were not used, Hypatia's death seems to match the prescribed punishment for witchcraft; the Greek term for the implements used in the killing, ostrakois, is translated as "tiles", but literally means "oystershells".

Hypatia may have been the first famous "witch" punished under Christian authority, as was noted by many church-critical authors; however, while some of the Christian invective used to justify or excuse her murder betrays a vulgar reliance on fear of black magic, the essence of Christian objections to her influence will have lain in the turbulent confluence of Christian and Platonic assertions about the nature of God and the afterlife, which achieved its most famous expression fifteen years later in Augustine's The City of God.

The Patriarch, Cyril, a sophisticated theologian who was posthumously canonised by the church, has been accused of complicity in the murder, but there is no evidence to support this; however, he does appear to have failed to condemn the act.Some authors have used Hypatia's death as a symbol of the repression of, in their terms, a reasoned paganism by an irrational religion.

Included among these was the astronomer Carl Sagan, who provided a vivid account of her death and the burning of the Library of Alexandria in his popular science book Cosmos. Earlier writers sharing that view include Voltaire and historian Edward Gibbon.

The christian English writer, Charles Kingsley, portrayed the philosopher in his historical romance, Hypatia (1860), in which she converts to Christianity at the approach of her death. A serious study by the Polish historian Maria Dzielska, Hypatia of Alexandria (1995), explains Hypatia's death as the result of a struggle between two Christian factions, the moderate Orestes - supported by Hypatia - and the more rigid Cyril.

All the above works use ancient writers as their primary sources. Dzielska, alone, makes use of surviving personal letters written by students of the philosopher.