A fanatical Christian mob attacked and killed the first known woman mathematician, head of the Neoplatonist school of philosophy at the Alexandrian museum.

Ancient Greek philosophy moved toward a greater emphasis on science and mathematics after the death of Alexander the Great in 323 b.c.e. His empire was divided among his generals, and Ptolemy Soter established a dynasty of Greek-speaking kings in Egypt with his capital at the still unfinished city of Alexandria, where the western branch of the Nile River empties into the Mediterranean Sea. He also founded the Museum of Alexandria, which was similar to a modern research university and lasted for seven hundred years. Scholars from all around the Greek-speaking world were invited to join the museum on the condition that they would deposit their scrolls and manuscripts in its library, which at its highest point included some 600,000 volumes. Among its greatest mathematicians and scientists were Euclid, Aristarchus of Samus, Apollonius of Perga, Diophantus, Hipparchus, and the astronomer Ptolemy. Hypatia
Theon
Synesius of Cyrene
Cyril of Alexandria, Saint

Hypatia was one of the last significant mathematicians associated with the Alexandrian museum and the earliest known woman mathematician and astronomer. By her time, Alexandria was the third largest city in the Roman Empire, having been conquered by Julius Caesar some four centuries earlier. The museum had diminished in importance, many of its books having been burned by Roman soldiers, and there were separate schools for Jews, pagans, and Christians. Although Hypatia’s original writings have not survived, she is known from letters that she received from her student Synesius of Cyrene and from references in the Historia ekklesiastike (fifth century c.e.; Ecclesiastical History, 1844) of Socrates Scholasticus. She was born about 370 c.e., but estimates range from as early as 355, based on the fact that Synesius studied under her, to 390 to 395, when she was an established scholar.

Hypatia’s father, Theon of Alexandria, was a member of the museum and a prominent teacher of mathematics and astronomy. His writings describe a solar and a lunar eclipse he predicted at Alexandria in 364 c.e. He is best known for his student commentaries on Euclid’s works on geometry and optics and on Ptolemy’s works on astronomy, but he also wrote poetry and interpretations of omens. Theon raised Hypatia to be strong in both mind and body. He taught her mathematics and astronomy as well as the arts, literature, speech, philosophy, and such disciplines as swimming, horseback riding, and mountain climbing. She eventually surpassed her father’s mathematical skills.

Although Hypatia was considered to be both bright and beautiful, she was also known for prudence and self-control and avoided the marital expectations of her time in favor of scholarship. She was soon recognized as a gifted scholar, and by 390 c.e., she was well established as a teacher. By 400, she became the salaried head of the Neoplatonist school, where the emphasis on Platonic philosophical ideas supported her interest and gifts in mathematics. She is thought to have assisted her father in writing an expanded version of Euclid’s Stoicheia (compiled c. 300 b.c.e.; Elements, 1570), which was the only known Greek text of this important synthesis of Greek geometry until the discovery of an earlier one in the Vatican in the late nineteenth century. She also assisted him in his commentary on Ptolemy’s influential astronomical treatise, Mathēmatikē syntaxis (c. 150 c.e.; Almagest, 1948).

Hypatia’s students were aristocratic young men from Egypt, Cyrene (Libya), Syria, and as far away as Constantinople (now Istanbul, Turkey). Although she was pagan, her students were both pagans and Christians, and many of them became important civil and ecclesiastical leaders. Some continued to look to her for guidance for many years after studying with her. A long correspondence with Synesius of Cyrene lasted even beyond his consecration in 410 as bishop of Ptolemais by Theophilus, the patriarch of Alexandria. His letters show that she had extensive knowledge of Greek philosophy and literature as well as mathematics and science. He often asked for her advice on his own writings and even sought her politica influence on occasion. The Byzantine church historian Socrates Scholasticus wrote that her knowledge exceeded all other contemporary philosophers, and there is general agreement that she surpassed her father in mathematics and astronomy.

In addition to collaborations with her father Theon, Hypatia is known to have written several works on mathematics and astronomy that have not survived. Her most important work was in the new field of algebra, expanding and commenting on the third century work of Diophantus of Alexandria on indeterminate equations (with multiple solutions) and on quadratic equations. She also wrote a treatise on planetary motion entitled Astronomical Canon and Treatise on the Conics of Apollonius, which developed Apollonius’s third century geometry of the curves formed by the intersections of a plane with a cone. Her interest in scientific instruments is clear from some of Synesius’s letters. In one, he inquires about the construction of a hydroscope for measuring the density of liquids. In another, he asks about the construction of an astrolabe for measuring the positions of stars and planets. She is also credited with an apparatus for distilling sea water.

By the time of Hypatia, Christianity had become the official religion of the Roman Empire. As Christianity became established in Alexandria at the end of the fourth century c.e., rioting often erupted between those of opposing religions. In the year 412, Cyril (later Saint Cyril) became patriarch of Alexandria and began a campaign opposing schismatic Christian groups and driving many Jews from the city. This led to hostility between Cyril and Orestes, the Roman prefect of Egypt and a good friend of Hypatia. Five hundred monks from the Nitrian desert assembled to defend Cyril of Alexandria, and one of them threw a stone that wounded Orestes. The monk was arrested and tortured and then died, but Cyril hailed him as a martyr.

Because of her friendship with Orestes, Hypatia came to be viewed by some Christians as not only a pagan philosopher but also as an obstacle to friendship between the patriarch and the prefect. During Lent in March of 415 c.e., a fanatical mob of antipagan Christians led by a church reader named Peter dragged Hypatia from her chariot into the Caesarium, then serving as a church. There, according to Socrates Scholasticus, they stripped her and scraped her skin with sharp shells until she died. They then dismembered her body and burned it to ashes at a place called Cinaron. Many of her students then left to study in Athens, which gained a reputation in mathematics by 420. The Alexandrian Neoplatonic school continued until the Arab invasion of 642, when the remaining books in the library were used to fuel the city’s baths for six months; probably among them were the works of Hypatia.

Hypatia was the only female scientist of the ancient world whose life is well documented, and perhaps the most famous of all women scientists until Marie Curie. As one of the last pagan scientists in the Western world, her death also came in the last years of the Roman Empire. Her life and death mark the beginning of the end of ancient Greek science and more particularly the end of the Alexandrian tradition that had flourished in its museum and libraries for some seven hundred years. Because of her qualities of beauty and intellect, she has been romanticized in historical and fictional accounts.

Hypatia’s early work with her father Theon in correcting and commenting on Ptolemy’s Almagest helped to preserve it as the standard reference on astronomy for a thousand years. Their version of Euclid’s Elements became the basis for all later editions of Euclid. Even though Hypatia’s own works did not survive, they have still had an important influence. Her careful commentary on the algebraic work of Diophantus most likely led to the survival of most of his original thirteen books of the Arithmetica (c. 250 c.e.; “Arithmetica” in Diophantus of Alexandria: A Study in the History of Greek Algebra, 1885). Six of the surviving works are in Greek and four are translations in Arabic, all of which contain notes and interpolations that probably come from Hypatia’s commentary.

• Alic, Margaret. Hypatia’s Heritage. Boston: Beacon Press, 1986. Includes a chapter on Alexandrian science highlighting the life and work of Hypatia.
• Duckett, Eleanor Shipley. Medieval Portraits from East and West. Ann Arbor: The University of Michigan Press, 1972. A chapter on Synesius of Cyrene and Hypatia contains several excerpts from the letters of Synesius to Hypatia.
• Dzielska, Maria. Hypatia of Alexandria. Translated by F. Lyra. Cambridge, Mass.: Harvard University Press, 1995. The most complete and authoritative biography of Hypatia.
• Osen, Lynn M. Women in Mathematics. Cambridge, Mass.: The MIT Press, 1974. A chapter on Hypatia emphasizes her mathematical work.
• Porter, Neil A. Physicists in Conflict. Philadelphia: Institute of Physics Publishing, 1998. A chapter on medieval conflicts has a short section on Hypatia’s conflict with Saint Cyril.

Euclid; Hypatia; Ptolemy (astronomer). Hypatia