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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Emilie duChatelet 1706-1749

Emilie DuChatelet led a most fascinating life. As a member of the French aristocracy, she had access to all that money and position could buy. She was well educated and closely associated with Voltaire, one of the most prominent thinkers of her day.

DuChatelet was known to both play hard and work hard. Her major work was an important French translation of Newton's Principia.

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Maria Gaetana Agnesi 1718-1799

Born in 18th century Italy, at a time when education for women was virtually nonexistant, this prodigy, encouraged by a mathematician father, became a noted mathematician herself. However, although Maria Gaetana Agnesi lived a long time, only twenty of her eighty odd years were devoted to mathematics. As the eldest of a very large family Agnesi, who never married, spent much of her youth taking care of her many brothers and sisters. Although the historical record is fuzzy about whether or not she became a nun after her father¹s death, Maria Agnesi spent the last forty years of her life living the simple religous life of a nun, in service to the poor and sick.

Agnesi is remembered for her two volume work called Analytical Institutions written when she was about twenty years old. In these volumes Agnesi brought together and clarified, in a single location, the enormously significant field of mathematics that had recently been invented called The Calculus. Her work was termed a triumph of clarity and erudition, demonstrating that women, as well as men, could excel in the world of abstract reasoning.

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Mary Somerville 1780-1872

Mary Somerville was an important popularizer of scientific ideas during her long and productive lifetime. She enjoyed society and worked hard to live a well-rounded life as wife, mother and professional woman.

As a young schoolgirl she was subjected to wearing bizarre types of clothing, considered necessary, at that time, to the development of properly constructed" young women.

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Ada Augusta Lovelace 1815-1852

Many people consider Ada August Lovelace, daughter of the famous English poet George Byron, wife of a member of the British aristocracy, mother, horsewoman and intrepid gambler, to be the inventor of computer programming. After a career as tempestuous as it was brief, Lovelace died tragically young, of uterine cancer.

Throughout much of her life, and with the help of a supportive husband as well as a mother ever eager to lend a controlling hand in managing Ada¹s family responsibilities, Lovelace was able to maintain a complex relationship with Charles Babbage, inventor of the Difference and Analytic Engines. (Babbage¹s inventions are considered to be the precursors to modern calculating machines and computers). Babbage served as one of Lovelace¹s tutors in mathematics and logic when she was in her late teens. Another tutor of the young aristocrat was Augustus DeMorgan, one of the most prominent mathematicians of the time. Later, as a young woman, Ada Lovelace was to become Babbage¹s long time assistant and expositor. When the time came to sign her major work, an elaborate dissertation on the powers and limitations of Babbage¹s invention, Lovelace, as did many women of her time, signed her work with her initials A.A.L. It was to be many years before the identity of A.A.L. became widely known.

To see a reenactment of an interaction between Babbage and Lovelace, go to the 'movies' section of this site. There, videoclips show something of the overwhelming personality of Lovelace, the aristocrat, in the interaction with her mentor and former teacher.

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Sonya Kovalevskaya 1850-1891

Many people consider Ada August Lovelace, daughter of the famous English poet George Byron, wife of a member of the British aristocracy, mother, horsewoman and intrepid gambler, to be the inventor of computer programming. After a career as tempestuous as it was brief, Lovelace died tragically young, of uterine cancer.

Throughout much of her life, and with the help of a supportive husband as well as a mother ever eager to lend a controlling hand in managing Ada¹s family responsibilities, Lovelace was able to maintain a complex relationship with Charles Babbage, inventor of the Difference and Analytic Engines. (Babbage¹s inventions are considered to be the precursors to modern calculating machines and computers). Babbage served as one of Lovelace¹s tutors in mathematics and logic when she was in her late teens. Another tutor of the young aristocrat was Augustus DeMorgan, one of the most prominent mathematicians of the time. Later, as a young woman, Ada Lovelace was to become Babbage¹s long time assistant and expositor. When the time came to sign her major work, an elaborate dissertation on the powers and limitations of Babbage¹s invention, Lovelace, as did many women of her time, signed her work with her initials A.A.L. It was to be many years before the identity of A.A.L. became widely known.

To see a reenactment of an interaction between Babbage and Lovelace, go to the 'movies' section of this site. There, videoclips show something of the overwhelming personality of Lovelace, the aristocrat, in the interaction with her mentor and former teacher.

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Grace Chisholm Young 1868-1944

The young Grace loved to follow her "important" father around, helping him with his carpentry and visiting the British Department of Weights and Measures where he was head.

She was one of the first female undergraduates admitted to Cambridge, although, at that time, women were still not receiving formal degrees.

Grace Young and her husband did much of their mathematical research together ... while Grace took care of him as well as their six children.

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Emmy Noether 1882-1935

In 1933, Emmy Noether was forced out of Nazi Germany. She was fortunate enough to obtain a teaching position at Bryn Mawr College in the United States. Her relationship with her students was particularly warm.

Professor Noether loved to walk. She would often lead her students on Saturday afternoon jaunts. On these trips she would quickly become so absorbed in her mathematics conversations that her students would have to protect her from oncoming traffic.

Upon her death the great to mathematical physicist, Albert Einstein, paid tribute to Emmy Noether in a letter to the New York Times dated May 5, 1935. "In the judgment of the most competent living mathematicians, Fraeulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."

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