SOURCE: "Hypatia 370-415" in Women in Mathematics, The MIT Press, 1974, pp. 21-32.

[In the following excerpt, Osen presents an overview of Hypatia's life, emphasizing her skill in mathematics.]

During the pre-Christian era, the philosophical schools of Plato and Pythagoras served to create a favorable social climate in which at least some women could pursue an academic career. Because the emphasis on and love of mathematics was so strong in these schools, this tradition persisted long after the Christian era began.

Athenaeus, a Greek writer (ca. A.D. 200), in his Deipnosophistoe, mentions a number of women who were superior mathematicians, but precise knowledge of their work in this field is lacking. It is probable that there were many women who were well educated in the general science of numbers at this time, judging from the pervasive interest in the subject and the rigor with which women sought an education.

A few Greek women enjoyed comparative freedom in these pursuits, although the class of women known as hetaerae attracted the most public notice. These slave women were usually paramours of the ruling class, although some were freed women or women of free birth; many of them, particularly those from Ionia and Aetolia, strongly impressed themselves on the Greek conscience with their intelligence, wit, and culture. They had keen intellects, and their work in abstract studies made some of them apt students and competent teachers. No doubt the legacy left by these women over the ensuing centuries contributed also to an auspicious social climate within which the formidable genius of Hypatia could flourish in the later part of the fourth century A.D.

Hypatia was the first woman in mathematics of whom we have considerable knowledge, but the story of her life that has come down to us is not a particularly happy one. Despite the good fortune of her legendary talents, her beauty, her long life of hard work, and her celebrated accomplishments in mathematics and astronomy, the story of her eventual martyrdom excites almost the same sympathies as a classic Greek tragedy. Although nearly a thousand years separated her from the time of Aspasia, in many ways Hypatia was also a true daughter of Greece.

Hypatia was born around A.D. 370, and her father, Theon, was a distinguished professor of mathematics at the University of Alexandria. He later became the director of the University, and Hypatia's early life was spent in close contact there with the institute called the Museum.

We know little about Hypatia's mother, but the family situation must have been a fortunate one, for Theon was determined to produce a perfect human being. As Elbert Hubbard (1908, p. 83) remarked, "… whether his charts, theorems and formulas made up a complete law of eugenics, or whether it was dumb luck, this we know: he nearly succeeded."

From her earliest years Hypatia was immersed in an atmosphere of learning, questioning, and exploration. Alexandria was the greatest seat of learning in the world, a cosmopolitan center where scholars from all the civilized countries gathered to exchange ideas. As Theon's daughter, Hypatia was a part of this stimulating and challenging environment. In addition, she received a very thorough formal training in arts, literature, science, and philosophy.

Theon was his daughter's tutor, teacher, and playmate; his own strong love of the beauty and logic of mathematics was contagious. We know that he was influential in this part of Hypatia's intellectual development, which was eventually to eclipse his own.

At the time, mathematics was used mainly for calculating such obscure problems as the locus of a given soul born under a certain planet. It was thought that mathematical calculations could determine precisely where such a soul would be on a future date. Astronomy and astrology were considered one science, and mathematics was a bond between this science and religion.

These disciplines were a part of Hypatia's early training, and, in addition, Theon introduced her to all the systems of religion known to that part of the civilized world. He had a rare talent as a teacher, and he was determined to transmit to Hypatia not only the accumulated fund of knowledge but the discrimination needed to assimilate and build upon this fund. Toward this end, he was particularly concerned that she be discriminate about religion and that no rigid belief take possession of her life to the exclusion of new truths. "All formal dogmatic religions are fallacious and must never be accepted by self-respecting persons as final," he told her. "Reserve your right to think, for even to think wrongly is better than not to think at all" (Hubbard 1908, p. 82).

Theon also established a regimen of physical training to ensure that Hypatia's healthy body would match her formidable, swift, well-trained mind. He devised a series of gentle calisthenics that she practiced regularly; she was taught to row, swim, ride horseback, and climb mountains, and a part of each day was set aside for such exercise.

To the Romans the art of the rhetor, or orator, was one of the most consequential of the social graces; the ability to impress others by one's personal presence was indeed a most extraordinary gift. As part of the preparation for becoming the "perfect human being" that Theon had determined she should be, Hypatia was given formal training in speech, and there were lessons in rhetoric, the power of words, the power of hypnotic suggestion, the proper use of her voice, and the gentle tones considered pleasing. Theon structured her life minutely and precisely, leaving little to chance or circumstance, but he was not content to produce such a powerful personality without giving her an understanding of her responsibility to others. He cautioned her about the vulnerability of the permeable, impressionable mind of the young, and he warned her against using the cosmetic effect of rhetoric and pretense to influence or manipulate others. His training urged her toward becoming a sensitive, gifted, and eloquent teacher, and these qualities are reflected in her writing:

Fables should be taught as fables, myths as myths, and miracles as poetic fancies. To teach superstitions as truths is a most terrible thing. The child mind accepts and believes them, and only through great pain and perhaps tragedy can he be in after years relieved of them. In fact men will fight for a superstition quite as quickly as for a living truth—often more so, since a superstition is so intangible you cannot get at it to refute it, but truth is a point of view, and so is changeable (Hubbard 1908, p. 84).

As a further part of her education, Hypatia traveled abroad and was treated as royalty wherever she went. Some accounts say that Hypatia's travels extended over a period of 10 years; others say she spent only a year or so in travel. It is probable that her trips extended over a long period of time and were not continuous, but it is known that for a while she was a student in Athens at the school conducted by Plutarch the Younger and his daughter Asclepigenia. It was here that her fame as a mathematician became established, and upon her return to Alexandria, the magistrates invited her to teach mathematics and philosophy at the university. She accepted this invitation and spent the last part of her life teaching out of the chair where Ammonius, Hierocles, and other celebrated scholars had taught.

She was a popular teacher; Socrates, the historian, wrote that her home, as well as her lecture room, was frequented by the most unrelenting scholars of the day and was, along with the library and the museum, one of the most compelling intellectual centers in that city of great learning. She was considered an oracle, and enthusiastic young students from Europe, Asia, and Africa came to hear her lecture on the Arithmetica of Diophantus, the techniques Diophantus had developed, his solutions of indeterminate problems of various types, and the symbolism he had devised. Her lectures sparkled with her own mathematical ingenuity, for she loved mathematics for its own sake, for the pure and exquisite delight it yielded her inquisitive mind.

Hypatia was the author of several treatises on mathematics. Suidas, the late-tenth-century lexicographer of Greek writings, lists several titles attributed to her, but unfortunately these have not come down to us intact. Most were destroyed along with the Ptolemaic libraries in Alexandria or when the temple of Serapis was sacked by a mob, and only fragments of her work remain. A portion of her original treatise On the Astronomical Canon of Diophantus was found during the fifteenth century in the Vatican library; it was most likely taken there after Constantinople had fallen to the Turks.

Diophantine algebra dealt with first-degree and quadratic equations; the commentaries by Hypatia include some alternative solutions and a number of new problems that she originated. Some scholars consider these to have been in Diophantus' original text, but Heath (1964, p. 14) attributes them to Hypatia.

In addition to this work, she also wrote On the Conics of Apollonius, popularizing his text. It is interesting to note that, with the close of the Greek period, interest in conic sections waned, and after Hypatia, these curves were largely neglected by mathematicians until the first half of the seventeenth century.

Hypatia also wrote commentaries on the Almagest, the astronomical canon of Ptolemy's that contained his numerous observations of the stars. In addition, she coauthored (with her father) at least one treatise on Euclid. Most of these works were prepared as textbooks for her students. As was the case with her commentaries on Conics, no further progress was made in mathematical science as taught by Hypatia until the work of Descartes, Newton, and Leibniz many centuries later.

Among Hypatia's most distinguished pupils was the eminent philosopher Synesius of Cyrene, who was later to become the wealthy and influential Bishop of Ptolemais. His letters asking for scientific advice have furnished us with one of the richest sources of information concerning Hypatia and her works, and they indicate how keenly he valued his intellectual association with her (see, for example, Hale 1860, p. 111).

References are found in Synesius' letters crediting Hypatia with the invention of an astrolabe and a planesphere, both devices designed for studying astronomy. His letters also credit her with the invention of an apparatus for distilling water, one for measuring the level of water, and a third for determining the specific gravity of liquids. This latter device was called an aerometer or hydroscope.

Hypatia's contemporaries wrote almost lyrically about her great genius. Socrates, Nicephorus, and Philostorgius, all ecclesiastical historians of a persuasion different from that of Hypatia, nevertheless were generous in their praise of her characteristics and learning. Her popularity was wide and genuine, and it is said that she had several offers of marriage from princes and philosophers, but to these proposals she answered that she was "wedded to the truth." This pretty speech was no doubt more an evasion than a verity; it is more likely that she simply never met a suitor whose mind and philosophy matched her own. Although she never married, she did have love affairs, and various imaginary romances have been credited to her.¹

Her renown as a philosopher was as great as her fame as a mathematician, and legend has it that letters addressed to "The Muse" or "The Philosopher" were delivered to her without question. She belonged to a school of Greek thought that was called neo-Platonic: the scientific rationalism of this school ran counter to the doctrinaire beliefs of the dominant Christian religion, seriously threatening the Christian leaders. These pietists considered Hypatia's philosophy heretical, and when Cyril became patriarch of Alexandria in A.D. 412, he began a systematic program of oppression against such heretics. Because of her beliefs and her friendship with Orestes, the prefect of Egypt, whose influence represented the only countervailing force against Cyril, Hypatia was caught as a pawn in the political reprisals between the two factions.

Cyril was an effective inquisitor. He began by inflaming the passions of the populace, setting mobs on his detractors, leveling the synagogues, and almost completely usurping the state and authority of a civil magistrate. The turbulent mood of his own faithful and the political events that followed his actions convinced him in A.D. 415 that his own interests would be best served by the sacrifice of a virgin. At his direction, a mob of religious fanatics set upon Hypatia, dragging her from her chariot while she was on her way to classes at the university, pulling out all of her hair, and subsequently torturing her to death. Edward Gibbon wrote (1960, p. 601)

In the bloom of beauty, and in the maturity of wisdom, the modest maid had refused her lovers and instructed her disciples; the persons most illustrious for their rank or merit were impatient to visit the female philosopher; and Cyril beheld with a jealous eye the gorgeous train of horses and slaves who crowded the door of her academy. A rumour was spread among the Christians that the daughter of Theon was the only obstacle to the reconciliation of the prefect and the archbishop; and that obstacle was speedily removed. On a fatal day, in the holy season of Lent, Hypatia was torn from her chariot, stripped naked, dragged to the church, and inhumanly butchered by the hands of Peter the reader and a troop of savage and merciless fanatics; her flesh was scraped from her bones with sharp oyster-shells, and her quivering limbs were delivered to the flames. The just progress of inquiry and punishment was stopped by seasonable gifts; but the murder of Hypatia has imprinted an indelible stain on the character and religion of Cyril of Alexandria.

Orestes felt a responsibility for Hypatia's cruel death and did what he could to bring the culprits to justice. He reported her death to Rome and asked for an investigation. Then fearing for his own life, he quit the city. The investigation was repeatedly postponed for "lack of witnesses," and finally it was given out by the Bishop that Hypatia was in Athens and there had been no tragedy. Orestes' successor was forced to cooperate with the Bishop, and as one historian phrased it, "Dogmatism as a police system was supreme" (Hubbard 1908, p. 102).

Hypatia's place in history seems relatively secure. Indeed, very often she is the only woman mentioned in mathematical histories. Her life and times have been romanticized by Charles Kingsley in his book Hypatia: or New Foes in Old Faces (1853), but his novel almost totally ignores Hypatia's significant work in mathematics. Neither is it to be recommended as a reliably authentic source of information, either about Hypatia or life in Alexandria during the fifth century A.D. …

Notes

¹ Although Suidas (ca. tenth century) implies that Hypatia was married to Isidorus of Gaza, the Neoplatonist, most historians discount this as fiction rather than fact. The romantic aspect of her life has inspired a great deal of speculation; see J. Toland, Hypatia, or the History of a Most Beautiful, Most Vertuous, Most Learned … Lady (London, 1720).

References

… Gibbon, Edward, 1960. The Decline and Fall of the Roman Empire. (An abridgement by D. M. Low). New York: Harcourt, Brace, and World.…

Hale, Sarah Josepha, 1860. Women's Record: or Sketches of All Distinguished Women from the Creation to A. D. 1854. New York: Harper & Brothers Publishers.

Heath, Thomas L., 1964. Diophantus of Alexandria: A Study in the History of Greek Algebra. New York: Dover Publications.…

Hubbard, Elbert, 1908. Little Journeys to the Homes of Great Teachers. Vol. 23. New York: The Roycrofters.

Kingsley, Charles, 1853. Hypatia or New Foes with Old Faces. Chicago: W. B. Conkley Company.