Hypatia was the daughter of the mathematician Theon of Alexandria (c. 335 – c. 405 AD). According to classical historian Edward J. Watts, Theon was the head of a school called the "Mouseion", which was named in emulation of the Hellenistic Mouseion, whose membership had ceased in the 260s AD. Theon's school was exclusive, highly prestigious, and doctrinally conservative. Theon rejected the teachings of Iamblichus and may have taken pride in teaching a pure, Plotinian Neoplatonism. Although he was widely seen as a great mathematician at the time, Theon's mathematical work has been deemed by modern standards as essentially "minor", "trivial", and "completely unoriginal". His primary achievement was the production of a new edition of Euclid's Elements, in which he corrected scribal errors that had been made over the course of nearly 700 years of copying. Theon's edition of Euclid's Elements became the most widely-used edition of the textbook for centuries and almost totally supplanted all other editions.
Nothing is known about Hypatia's mother, who is never mentioned in any of the extant sources. Theon dedicates his commentary on Book IV of Ptolemy's Almagest to an individual named Epiphanius, addressing him as "my dear son", indicating that he may have been Hypatia's brother, but the Greek word Theon uses (teknon) does not always mean "son" in the biological sense and was often used merely to signal strong feelings of paternal connection. Hypatia's exact year of birth is still under debate, with suggested dates ranging from 350 to 370 AD. Many scholars have followed Richard Hoche in inferring that Hypatia was born around 370. According to a description of Hypatia from the lost work Life of Isidore by the Neoplatonist historian Damascius (c. 458 – c. 538), preserved in the entry for her in the Suda, a tenth-century Byzantine encyclopedia, Hypatia flourished during the reign of Arcadius. Hoche reasoned that Damascius's description of her physical beauty would imply that she was at most 30 at that time, and the year 370 was 30 years prior to the midpoint of Arcadius's reign. In contrast, theories that she was born as early as 350 are based on the wording of the chronicler John Malalas (c. 491 – 578), who calls her old at the time of her death in 415. Robert Penella argues that both theories are weakly based, and that her birth date should be left unspecified.
Hypatia was a Neoplatonist, but, like her father, she rejected the teachings of Iamblichus and instead embraced the original Neoplatonism formulated by Plotinus. The Alexandrian school was renowned at the time for its philosophy and Alexandria was regarded as second only to Athens as the philosophical capital of the Greco-Roman world. Hypatia taught students from all over the Mediterranean. According to Damascius, she lectured on the writings of Plato and Aristotle. He also states that she walked through Alexandria in a tribon, a kind of cloak associated with philosophers, giving impromptu public lectures.
Original Greek text of one of Synesius
's seven extant letters to Hypatia from a 1553 printed edition
According to Watts, two main varieties of Neoplatonism were taught in Alexandria during the late fourth century. The first was the overtly pagan religious Neoplatonism taught at the Serapeum, which was greatly influenced by the teachings of Iamblichus. The second variety was the more moderate and less polemical variety championed by Hypatia and her father Theon, which was based on the teachings of Plotinus. Although Hypatia herself was a pagan, she was tolerant of Christians. In fact, every one of her known students was Christian. One of her most prominent pupils was Synesius of Cyrene, who went on to become a bishop of Ptolemais (now in eastern Libya) in 410. Afterward, he continued to exchange letters with Hypatia and his extant letters are the main sources of information about her career. Seven letters by Synesius to Hypatia have survived, but none from her addressed to him are extant. In a letter written in around 395 to his friend Herculianus, Synesius describes Hypatia as "... a person so renowned, her reputation seemed literally incredible. We have seen and heard for ourselves she who honorably presides over the mysteries of philosophy."
The Christian historian Socrates of Constantinople, a contemporary of Hypatia, describes her in his Ecclesiastical History:
There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner which she had acquired in consequence of the cultivation of her mind, she not infrequently appeared in public in the presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more.
Philostorgius, another Christian historian, who was also a contemporary of Hypatia, states that she excelled her father in mathematics and the lexicographer Hesychius of Alexandria records that, like her father, she was also an extraordinarily talented astronomer. Damascius writes that Hypatia was "exceedingly beautiful and fair of form", but nothing else is known regarding her physical appearance and no ancient depictions of her have survived. Damascius states that Hypatia remained a lifelong virgin and that, when one of the men who came to her lectures tried to court her, she tried to sooth his lust by playing the lyre.[b] When he refused to abandon his pursuit, she rejected him outright, displaying her bloody menstrual rags and declaring "This is what you really love, my young man, but you do not love beauty for its own sake." Damascius further relates that the young man was so traumatized that he abandoned his desires for her immediately.
Michael A. B. Deakin, a historian of mathematics, argues that Hypatia's menstruation was proof of her celibacy, since, in ancient times, menarche generally occurred much later than in developed countries today and around the time a woman reached marriageable age, and, since no reliable methods of birth control existed, menstruation would have actually been a relatively rare occurrence for any woman who was not devoted to a life of celibacy. Charlotte Booth, a British Egyptologist, rejects this assertion as unfounded, stating that Pharaonic texts make reference to amenorrhea, the unusual absence of menstruation in a woman of the proper age, and that Egyptian homes from the Hellenistic Period onwards had rooms under the stairs called "women's spaces" that were specially designated for women to stay while they were menstruating. Both of these would be inexplicable if menstruation was indeed "rare". Furthermore, Booth asserts that Deakin's claim is flawed, since menstruation starts at around the same time regardless of whether it was in ancient Egypt or in the modern world, and what has changed is simply the marriageable age. Therefore, Booth regards Hypatia's menstruation, not as evidence of her celibacy, but rather of her "femininity and even fertility."