Hypatia (born c. 350–370 – March 415 AD) was a Neoplatonist philosopher, astronomer, and mathematician who lived in Alexandria, at that time in the province of Egypt and a major city of the Eastern Roman Empire. In Alexandria, Hypatia was a prominent thinker who taught subjects including philosophy and astronomy, and in her lifetime was renowned as a great teacher and a wise counselor. Not the only fourth century Alexandrian female mathematician, Hypatia was preceded by Pandrosion. However, Hypatia is the first female mathematician whose life is reasonably well recorded. She wrote a commentary on Diophantus's thirteen-volume Arithmetica, which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's Almagest, based on the title of her father Theon's commentary on Book III of the Almagest.

Hypatia constructed astrolabes and hydrometers, but did not invent either of these, which were both in use long before she was born. She was tolerant toward Christians and taught many Christian students, including Synesius, the future bishop of Ptolemais. Ancient sources record that Hypatia was widely beloved by pagans and Christians alike and that she established great influence with the political elite in Alexandria. Toward the end of her life, Hypatia advised Orestes, the Roman prefect of Alexandria, who was in the midst of a political feud with Cyril, the bishop of Alexandria. Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March 415 AD, she was murdered by a mob of Christians led by a lector named Peter.

Hypatia's murder shocked the empire and transformed her into a "martyr for philosophy", leading future Neoplatonists such as the historian Damascius (c. 458 – c. 538) to become increasingly fervent in their opposition to Christianity. During the Middle Ages, Hypatia was co-opted as a symbol of Christian virtue and scholars believe she was part of the basis for the legend of Saint Catherine of Alexandria. During the Age of Enlightenment, she became a symbol of opposition to Catholicism. In the nineteenth century, European literature, especially Charles Kingsley's 1853 novel Hypatia, romanticized her as "the last of the Hellenes". In the twentieth century, Hypatia became seen as an icon for women's rights and a precursor to the feminist movement. Since the late twentieth century, some portrayals have associated Hypatia's death with the destruction of the Library of Alexandria, despite the historical fact that the library no longer existed during Hypatia's lifetime.

Hypatia was the daughter of the mathematician Theon of Alexandria. 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 Damascius's lost work Life of Isidore, preserved in the entry for Hypatia 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.

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 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." Synesius preserves the legacy of Hypatia's opinions and teachings, such as the pursuit of "the philosophical state of apatheia—complete liberation from emotions and affections".

The Christian historian Socrates of Constantinople, a contemporary of Hypatia, describes her in his Ecclesiastical History: