Thinkers and teachers

Hypatia

About 355 to 415

Who was Hypatia, and what is truly known of them?

What is known

Mathematician and Platonist philosopher of Alexandria, daughter of the mathematician Theon, whose commentary on Ptolemy she helped to revise. A Byzantine lexicon says she wrote on Diophantus, on the Conics of Apollonius and on astronomical tables; none of it survives for certain under her name. She taught in public, to pagans and Christians alike, and letters to her survive from her pupil Synesius, later a bishop, who asks her for an instrument to weigh liquids. In March 415, during a feud between the governor Orestes, who took her advice, and the bishop Cyril, a Christian crowd led by a church reader named Peter pulled her from her carriage, killed her in a church and burned her body. The fullest account is by a Christian of the time, Socrates of Constantinople, who condemns the murder.

The teaching

Taught from what her pupil Synesius, Socrates of Constantinople and Damascius record, with the books she taught.

Philosophy in the open

Hypatia taught the Platonism of Plotinus, and taught it in the open. Wearing the philosopher's plain cloak, she went about the city and explained Plato, Aristotle or any other philosopher to whoever wished to hear. Synesius calls her the one who rightly leads the rites of philosophy, using the language of the mysteries for a teaching given to all who came. For her, as for the school she followed, philosophy was a way of life as much as a study: the soul was to be turned from the body and its passions towards the beauty and the One above them.

Beauty and the body

Damascius tells how one of her students fell in love with her. She turned him from it with a sign of the body's uncleanness, telling him that this was what he loved, and that it was nothing beautiful; others said she cured him with music. Either way the lesson is Plato's: a love that stops at a body has taken an image for beauty itself, and the teacher's work is to turn the lover upward.

The heavens as a ladder

In her school mathematics was the ladder of philosophy. Synesius, sending a friend an instrument he had made with what she taught him, a flat map of the heavens on which the stars could be set to rise and set, writes that astronomy is a noble science in itself and also a step towards the holy science beyond it, for the heavens are the nearest image of what lies above them. To learn the shape of the sky and the laws of number was to train the mind to think what the senses cannot see.

Number

She wrote on the Arithmetic of Diophantus, a book of problems in numbers, and taught its method. An unknown number is named once, with its square and its cube, and the conditions of a problem are written as two equal sums; what is subtracted on one side is added to both, and like is taken from like, until a single kind is left equal to a number and the unknown is found. The answers sought are numbers that can be written as fractions, and a problem may have many: to divide a given square into two squares, sixteen becomes two hundred and fifty-six twenty-fifths and one hundred and forty-four twenty-fifths.

The cone and its sections

She wrote too on the Conics of Apollonius, which teaches that three curves are cut from one cone. A plane that slants through the cone and meets every line on its side gives the ellipse, of which the circle is the special case; a plane parallel to a line on the side gives the parabola; a plane that cuts both halves of the double cone gives the hyperbola, in two branches. Apollonius named them from the old method of applying areas: in the parabola the square on a line exactly equals a given figure, in the ellipse it falls short and in the hyperbola it exceeds, which is what the three Greek names mean.

The heavens in tables

She wrote on the astronomical tables by which the places of the sun, moon and planets are reckoned for any hour. The part of her father's commentary on Ptolemy that bears her name treats the sun: how the year is measured from the solstices and equinoxes, why the sun seems to move faster in one part of its circle than in another, and how a circle set a little off the earth's centre explains it. To read such tables is to see the heavens as a work of reason, regular enough to be reckoned years ahead.

The instrument for water

Synesius asks her in a letter to have made for him an instrument he describes: a tube the size of a flute, marked along its length with a line of notches and closed at one end by a weighted cone, so that it stands upright in water. Set in a liquid, it sinks to a depth that the notches measure, and so shows the weight of the liquid. It is the instrument now called a hydrometer, and the letter shows a teacher to whom geometry and the heavens went together with things made by hand and put to use.

Orders and memberships

None. She taught the Platonism of Plotinus as a public teacher, and nothing shows that she practised theurgy or any rite.

The legend

That Cyril ordered her death: no writer of the time says so, though a pagan a century later blames his envy. That she was young when she died; she was probably near sixty. That she invented the astrolabe, which is older than she was. That the library of Alexandria burned with her; it was long gone. A bishop of the seventh century called her a witch and praised her killers.

What was forged, or is false

A letter under her name to Cyril, in Latin, pleading for Nestorius. It speaks of events that came at least sixteen years after her death.

Their works

Revision of Theon’s Commentary on PtolemyTreatise, late 4th century
Her father Theon headed the third book of his commentary on Ptolemy’s Almagest as an edition revised by the philosopher, his daughter Hypatia. It is the one place where her hand can be said to survive, in a work on the movements of the heavens used by astronomers for centuries.
How much of the surviving text is her work and how much her father’s cannot be told apart.
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Commentary on DiophantusTreatise, late 4th century
The Suda, a Byzantine lexicon, lists a commentary by her on the Arithmetica of Diophantus, a book of problems in numbers. Some scholars think that the parts of the Arithmetica that survive, in Greek and Arabic, carry her explanations within them.
No copy under her name survives, and whether any of the extant text is hers is disputed.
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Commentary on the Conics of ApolloniusTreatise, late 4th century
The same lexicon lists a commentary by her on the Conics of Apollonius, the ancient study of the curves made by cutting a cone. It shows the range of her teaching, from number to geometry to the heavens.
It is lost and known only from that one notice.
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Letters of SynesiusLetters, about 395 to 413
Seven letters from her pupil Synesius of Cyrene, later bishop of Ptolemais, address her as mother, sister, teacher and benefactor. He asks her for an instrument to weigh liquids, sends her his books for judgement, and writes to her in grief near his death. They are the nearest view of her as a teacher.
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Ecclesiastical History of SocratesAccount, about 440
The church history of Socrates of Constantinople, written within a generation of her death, which praises her learning and modesty, tells of her public teaching, and describes her murder by a Christian crowd in 415. He condemns the killing as wholly foreign to the spirit of Christianity. It is the fullest account of her death.
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Life of IsidoreAccount, early 6th century
A history of the last Platonist philosophers by Damascius, head of the school at Athens, which praises her as a teacher and blames her death on the envy of the bishop Cyril. It is the pagan side of her story, written a century after her death, and survives only in fragments.
It survives in fragments, and its charge against Cyril is not borne out by any writer of her time.
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How the house tells a life

This life is told from the record, with what is documented, what is legend and what was forged kept apart. A membership in an order is stated only where documents show it. A person’s chart explains none of their deeds.

The arts it feeds

Sacred geometry

Lives near it in time