Hypatia

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Hypatia of Alexandria (born c.350–370, died 415) was a Greek mathematician, astronomer, and Neoplatonist philosopher, the most prominent thinker in the city in her generation and the head of its leading Platonist school. She is the earliest woman in the history of mathematics about whom anything substantial is known, and her death — torn apart by a Christian crowd in the streets of Alexandria — has made her a symbol attached to causes she never held. The record that survives is small and uneven: a handful of letters, a one-sentence attribution in a mathematical preface, a paragraph in a church history, a late and hostile chronicle. Out of these fragments the figure has been rebuilt many times, and the rebuildings have rarely agreed.

The work

What can be established about her work is firm but spare. She was the daughter of the mathematician Theon, the last figure firmly attached to the scholarly life of the Alexandrian Museum, and she succeeded to and surpassed his teaching. The single contemporaneous notice of her mathematical activity is a line in the heading to Theon’s own commentary on the third book of Ptolemy’s Almagest, where he records that the edition was prepared by the philosopher his daughter Hypatia — father and daughter editing together the canonical handbook of ancient astronomy, the work that fixed the geocentric heavens for a thousand years. The later sources, chiefly the Byzantine lexicon known as the Suda, credit her with a commentary on the Arithmetica of Diophantus — the thirteen-book treatise that is the high-water mark of Greek algebra, parts of which may survive folded into the transmitted text — with a commentary on the Conics of Apollonius of Perga, the geometry of the section curves that would not be surpassed until the seventeenth century, and with an astronomical canon. None of her own writing survives intact under her name. Her labor was the labor of the late-antique commentator: not the discovery of new theorems but the preservation, clarification, and teaching of a difficult inheritance, the editing that keeps a text alive long enough to be copied again. It is easy to undervalue that work from a distance, but it is the reason any Diophantus or Ptolemy reached the Middle Ages at all. The fourth-century mathematician inherited a corpus already centuries old and partly corrupt; the commentator collated manuscripts, smoothed proofs, supplied worked examples and intermediate steps the originals had compressed, and produced a teaching edition through which the next generation could actually learn. Where the surviving Diophantine text shows signs of such expansion — added auxiliary problems, clarified procedures — some scholars have wondered whether the additions are Hypatia’s, which would make her, in those passages, the most concrete trace of a woman’s hand in the history of ancient mathematics. The argument cannot be closed, but it marks the kind of contribution the period rewarded: the Arithmetica she handled is the most original surviving work of Greek algebra, a treatise on indeterminate equations so far ahead of its setting that it had no real successor in antiquity, and to edit it competently was itself a feat of comprehension.

That the work was practical as well as textual is the testimony of her pupil Synesius of Cyrene. His letters mention instruments associated with her circle — an astrolabe for measuring the positions of the stars, and a hydroscope, a graduated float for gauging the density of liquids — described as the kind of thing learned from her or made under her guidance. The picture that emerges is of a school where mathematics was not an ornament but the discipline through which the mind was trained to ascend: geometry and astronomy first, then philosophy. Around a decade after her death the young Proclus would follow that same Alexandrian sequence before going on to Athens, and it is from his curriculum that the shape of hers is partly reconstructed.

The teaching

She taught philosophy publicly, lecturing on Plato and Aristotle to a circle of students drawn from across the eastern empire — pagans and Christians together, men who went on to provincial governorships, bishoprics, and the imperial bureaucracy, and who kept up an admiring correspondence with her for the rest of their lives. Even her age is a matter of inference: the sources fix neither her birth nor her exact years, and estimates run across two decades. Maria Dzielska’s reconstruction places her birth around 355 and makes her a woman of about sixty at her death, already a senior figure when Synesius sat in her lecture room in the 390s; older scholarship, working from a supposed age of forty-five, set her birth nearer 370. The difference is not idle: on the earlier dating she was the established matriarch of Alexandrian philosophy for a full generation before she was killed, a fixture of the city’s public life rather than a young teacher overtaken by events.

The fullest near-contemporary witness is the set of letters from Synesius, a Libyan aristocrat who studied with her in the 390s, became a Christian and eventually bishop of Ptolemais, and yet went on addressing her as his teacher and the mother of his intellectual life. These letters are the only first-hand voice that reaches her, and the loyalty in them survives the convert’s change of allegiance: a Christian bishop writing to a pagan philosopher as the one who taught him how to think. That a woman lectured in the open, walked through the city in the philosopher’s worn cloak, and spoke to magistrates without deference struck the ancient sources less as scandal than as the natural authority of the trained mind — a measure of how completely paideia, the long Greek education in letters and number, could override the ordinary expectations of sex.

The setting amplified the position. Alexandria was the oldest and most contentious intellectual capital of the eastern Mediterranean, the city of the Museum and the Library, of the Septuagint and the Hermetica, where Greek philosophy, Egyptian temple-learning, the Jewish scriptural exegesis of Philo, and an increasingly powerful Christianity all pressed against one another. A philosopher who held the leading chair there was not a private sage but a civic figure, consulted by the prefect, courted by ambitious families, visible in the public business of a city that rioted easily. Hypatia’s standing came from her command of the Platonic and Aristotelian curriculum and from the moral authority the office carried; it also placed her, without her seeking it, near the fault line along which the city was about to tear.

Her Platonism

Her Neoplatonism placed her in the line descending from Plotinus, the third-century founder of the school, in whose system all things proceed by emanation from a single transcendent source — the One, beyond being and beyond name — through Nous, the divine Intellect, and the world-Soul, and in whom the philosopher’s whole task is the ascent of the soul back toward its origin. For Plotinus that return was the work of thought and purification: the mind that lifts itself above the realm of sense becomes, in the words of the Enneads, aware of beauty in the conduct of life, in actions, in character, and in the pursuits of the intellect. Hypatia’s Platonism appears to have kept that austere, contemplative, mathematical cast.

By her time, though, the school had largely fused philosophy with religious practice. The dominant new current was the theurgy of Iamblichus — the doctrine that the soul, having fully descended into matter, cannot climb back by thought alone but must be raised by sacred rites the gods themselves established, drawing on the Chaldean Oracles and a cosmos woven with answering tokens. Whether Hypatia embraced that theurgic-ritual side, or held to a sparer Plotinian intellectualism in which number and dialectic do all the lifting, is genuinely unsettled and cannot be decided from the surviving evidence. The reading favored by Edward Watts makes her a deliberately old-fashioned Plotinian, teaching a mathematics-first Platonism well suited to a religiously mixed Alexandrian audience precisely because it asked for no pagan ritual; other scholars, reading the same Synesian material, allow that theurgic and devotional elements may have had their place in a fuller curriculum. The gap in the evidence is genuine, and the two portraits — the cool geometer of the One, and the priestess of a sacramental cosmos — both have to be drawn from the same few letters.

The killing

The circumstances of her death are better attested than her thought. In 415 Alexandria was riven by a power struggle between the Roman prefect Orestes, the emperor’s civil governor of Egypt, and Cyril, the patriarch of the city — a contest over jurisdiction, over the management of the Jewish community and the monks, and over who in practice ruled Alexandria. The patriarchate of this period commanded a formidable street presence — among other forces a corps called the parabalani, nominally a guild of stretcher-bearers and attendants to the sick, in practice available as a body of enforcers — and the prefect’s civil authority had worn thin against it. Orestes himself had been stoned in the street by monks not long before; one of them was tortured to death for it and afterward honored by Cyril’s party as a martyr, a sign of how far past compromise the quarrel had gone. Hypatia, a respected pagan and a friend of Orestes whose counsel he was thought to value, became the object of a rumor that she was the obstacle preventing a reconciliation between the two men — a charge that turned a philosopher’s friendship with the governor into a political offense. During Lent, in March, a crowd led by a church lector named Peter seized her in the street, dragged her into a church called the Caesareum, stripped her, killed her with broken tiles, tore her body apart, and burned the remains at a place called Cinaron.

The account is that of Socrates Scholasticus, a Christian church historian writing in Constantinople within a generation of the event. He opens by describing Hypatia as a woman who had so far surpassed the philosophers of her own time, who had succeeded to the school of Plato and Plotinus and drawn students from a distance, and who through the self-possession of a cultivated mind appeared without embarrassment before the magistrates. He sets down the killing as an atrocity, and records that it brought no small reproach upon Cyril and upon the whole church of Alexandria — adding that nothing could be further from the spirit of Christianity than massacres and fights of that kind. He does not assign Cyril the order, and the question of the patriarch’s direct responsibility is one the ancient record leaves exactly where Socrates left it: as opprobrium, not as proven command. Two centuries later the Coptic bishop John of Nikiû would retell the episode from the opposite side, recasting Hypatia as a sorceress who had beguiled the prefect with her arts and her death as the city’s deliverance — a measure of how quickly the same killing could be made to mean its own opposite.

Afterlives

Later ages remade her many times over. John Toland, in the anticlerical Tetradymus of 1720, made her death an indictment of priestcraft and a proof that women could be men’s intellectual equals; Voltaire had her murdered for teaching Homer and Plato; Edward Gibbon gave the scene the polished venom that fixed the image of the philosopher torn apart by fanatics; Charles Kingsley’s 1853 novel turned her into a tragic heroine of a decaying world; the twentieth century took her up as a martyr to reason, a feminist emblem, and a closing figure for classical antiquity, the popular version often folding her death together with the destruction of the Library — two endings the actual chronology keeps decades apart. The reading of “martyr to reason against fanaticism” is a projection of later quarrels onto a woman who left no creed of that kind; so too, on the other flank, is the witch of John of Nikiû.

Sources and study

The two contemporary witnesses are slender and indispensable: the letters of Synesius of Cyrene, the only first-person testimony, and the death-notice of Socrates Scholasticus, Ecclesiastical History VII.15, written within living memory of the event. To these the Suda (tenth century) adds a longer but compromised entry drawn largely from the lost Life of Isidore of the Neoplatonist Damascius, which confuses chronology and appends an admiring portrait of unclear reliability. Her philosophical milieu can be read directly in the hosted Enneads of Plotinus in Stephen MacKenna’s translation and in the Dialogues of Plato, the two authors her school took as its scripture. Modern scholarship has worked hard to separate the woman from the legend: Maria Dzielska’s Hypatia of Alexandria (Harvard, 1995) dismantled the Romantic martyrology and argued for a later birth and a sexagenarian death, and Edward Watts’s Hypatia: The Life and Legend of an Ancient Philosopher (Oxford, 2017) reconstructed her as a working Plotinian teacher embedded in civic Alexandria rather than an emblem of a dying paganism. Each reading of Hypatia says as much about its own moment as about the woman, of whom the ancient record preserves a teacher of mathematics and Plato, and the manner of her killing.

→ In the library: Plotinus — The Enneads (MacKenna) · The Dialogues of Plato (Jowett)

→ Related: Neoplatonism · The One · Nous · Emanation · Platonism · Plato · Aristotle · Alexandria · Ptolemy · Cyrene · Soul · Theurgy · Iamblichus · Proclus · Classical Antiquity