Hypatia A.D. 370-415
by Professor Edith Prentice Mendez from Sonoma State University
Hypatia of Alexandria (in Egypt) was the leading mathematician and philosopher in the western world at the time she was murdered by a mob in 415 AD. Her position as a woman scholar was unprecedented, although of course Alexandria had seen other powerful women, such as Cleopatra. Many stories have been told about Hypatia, in celebration of her life and in explaining her death. This biography relies on ancient documents to try to trace Hypatia’s life and work.
In Hypatia’s time, Alexandria was the leading center of learning in the Greek tradition. Alexandria had been founded by Alexander the Great, who died in 323 B.C. Alexander had conquered Egypt, and the kings who followed him there established the greatest learning center of ancient times: the Museum and Library of Alexandria. These formed a university or institute for advanced study – “museum” meant dedicated to the muses, the female guiding spirits of arts and sciences.
The first known mathematician at the Museum was Euclid, who lived about 300 B.C. and compiled the “Elements” of geometry and number theory that are still the basis of much of our school geometry today, 2300 years later! Hypatia’s father, Theon, was the last known member of the Museum faculty in the late 4th century AD. We do not know whether Hypatia taught at the Museum or on her own. The collections of the Library had been partially destroyed several times, most recently in 391 AD when the emperor had ordered the adjacent pagan temple destroyed, and the Museum may have been dismantled at that time.
Hypatia lived in a very difficult time of political and religious fighting, and the primary work that remains from her life, and Theon’s, is their editing, commenting on, and preserving mathematics and astronomy books. None of Hypatia’s philosophical teachings seems to have been written down, and she is not credited with any new mathematical developments or proofs. But the preservation of older texts was a vitally important role, and the explanation for students became ever more important as the general level of scholarship declined during the middle ages and teachers were few and far between.
About Hypatia’s education, we know only that she was taught by her father. She may have traveled to Athens to study or stayed in Alexandria all her life. It is almost certain that she never married. We do not know when she was born; estimates range from about 355 to 370 AD. The date of her death, 415 AD is reported by several sources [although not in this form - the AD style of dating was not invented until the 6th century and BC in the 8th! Dates were given in the form of years of the reign of the Roman emperor and the Christian bishop.]
What work did Hypatia do? Texts of that time were written on papyrus scrolls and were very fragile, subject to crumbling and very flammable. Only copies of copies remain today, but without the work of Theon and Hypatia, the works of Ptolemy and Euclid might well have been lost forever, and with them most knowledge of Greek mathematics and astronomy. Most of the surviving editions of Euclid’s “Elements” went through editing by Theon. We do not know of Hypatia’s involvement with these works; perhaps Theon edited Euclid before Hypatia had grown into a scholar in her own right. Theon and Hypatia worked together with the astronomy texts of Ptolemy, writing commentaries for students and developing updated tables of astronomical events. One of Theon’s commentaries is prefaced as “the edition having been prepared by the philosopher, my daughter Hypatia.” Ptolemy, who lived about 150 AD, was the most influential astronomer of ancient times. His geocentric [Earth-centered] theory of the universe was the basis of astronomy in both western and Arabic civilizations until the 16th century and the work of Copernicus and Kepler. Hypatia’s and Theon’s works may well be written notes from lectures to their students. Hypatia had a reputation as an outstanding teacher who drew students to her from all over the region. So preserving some of this teaching through lecture notes is a reasonable extension of her teaching.
Hypatia is also credited with commentaries on the works of two earlier mathematicians, Diophantus and Apollonius. Diophantus lived in Alexandria during the mid-third century AD. His major work was in algebra, and he was one of the first to use symbolism in this algebra. Earlier mathematicians, such as the Babylonians, had written solutions out in words. So, what we would today write as x2 [x-squared] to indicate an unknown quantity times itself, was described by the Babylonians in terms of the specific numbers for a given problem. So they might have said, “multiply 30 by 30.” Diophantus introduced designations such as Y [delta with an index Y] for the general squaring operation. This had the effect of making computations clearer and problems easier to follow. Recently, some chapters of the “Arithmetica” of Diophantus were found in Arabic translation. During the medieval era, Arabic mathematicians were much more advanced than those in Europe, and the newly discovered works were unknown in the European tradition. The Arabic chapters have clearer explanations and are more carefully written than those known only from the Greek tradition. Might they be translations of Hypatia’s editing of Diophantus? This is a reasonable conjecture, but one that cannot be settled without further evidence.
Hypatia was one of several commentators whose work preserved the “Conics” of Apollonius. This work from about 200 BC studied curves such as circles, ellipses, parabolas, and hyperbolas. It was vital to Ptolemy’s development of his astronomy and regained influence in the 17th century when Descartes and Fermat brought geometry and algebra together in analytical geometry. [We call our graph grid the "Cartesian Plane" after Descartes.] Hypatia was not singly responsible for saving the “Conics” for later mathematicians, but she did play a role in that preservation and transmission.
Sadly, the most detailed knowledge that we have of Hypatia is of her death. The Christian Bishop of Alexandria, Cyril, was anxious to assert his leadership over the city. His rival for control was Orestes, the Roman public official and also a Christian. [Egypt had been part of the Roman Empire since Cleopatra's death in 30 BC and Christianity was now the official religion of the empire.] Hypatia had many influential students and friends, including Orestes, and a Christian bishop, but she herself did not become a Christian. Whether Cyril directly ordered Hypatia’s death, or merely encouraged a climate in which she was vulnerable, we do not know. She was caught in battles of religion and politics. A Christian mob dragged her from her chariot and killed her by scraping the flesh from her body with sea shells. A tragic ending for a brilliant and prominent woman mathematician, the earliest for whom we have biographical information.
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