Hypatia was one of the most eminent mathematicians and astronomers of late antiquity. Scholars traveled from around the classical world to learn mathematics and astronomy at her school.
Her brutal killing at the hands of a frenzied mob of Christian fanatics shocked the Greco-Roman world. Hypatia’s murder was a historical milestone. A thousand years of Mediterranean-centered European classical culture was in crisis – five years earlier Rome had been sacked by the Visigoths. The European Medieval Period, characterized by a thousand years of relatively minimal scientific progress, was beginning.
Beginnings
Hypatia (pronounced hy-Pay-shuh) was born in the second half of the fourth century, most probably between the years 350-370 AD in the Greco-Roman city of Alexandria, Egypt. Like most educated people in the Eastern Mediterranean in late antiquity, Hypatia was a Greek speaker. Her name means ‘supreme.’ We do not know what she looked like.
No details of Hypatia’s mother survive. Hypatia’s father was Theon of Alexandria, an eminent mathematician and astronomer famous for his ‘student edition’ of Euclid’s Elements. Theon’s edition became the go-to version for over a thousand years. Editions based on Theon’s were the only ones known until one predating it was found in the Vatican Library in 1808.
Theon was head of the Mouseion, an academy that taught Neoplatonist philosophy. Hypatia followed in her father’s footsteps, becoming a mathematician, astronomer, and philosopher.
Compared with the stunning progress made by the likes of Euclid and Eratosthenes in Alexandria soon after the city was founded, the output of new ideas from the city’s intellectuals had almost dried up in Hypatia’s era. Nevertheless, Alexandria still held an almost magnetic attraction for scholars. After Athens, it was the Greco-Roman world’s leading center of philosophy.
Lifetimes of Selected Greek Scientists and Philosophers after the Golden Age
Hypatia of Alexandria’s Work
Hypatia was a devotee of Neoplatonism – a mystical philosophy with one overriding theme: that everything in the universe has its origins in ‘the One’ – a transcendent god from which the Cosmic Soul and the Divine Mind come.
A hydrometer floats in a liquid whose density can be read on its scale.
Our best source of information about Hypatia and her achievements is Socrates Scholasticus, a Greek Christian historian who lived in the same era as Hypatia. In his major work The Historia Ecclesiastica, Socrates wrote:
Hypatia – Practical Scientist
Many of Hypatia’s students were Christians who later progressed to senior positions in the church and governments. One of them, Synesius, who became Bishop of Ptolemais, shows us that in addition to mathematics, astronomy, and philosophy, Hypatia probably taught practical sciences. He does this by sending her a letter asking if she can send him a hydrometer.
In another letter, he says that Hypatia taught him how to construct an astrolabe – she learned this skill from her father, who authored On the Small Astrolabe.
An exploded view of a small astrolabe.
An ancient astronomer uses a very simple small astrolabe to measure a star’s angle above the horizon.
In a letter to his friend Herculianus, Synesius recalls that Hypatia is:
“… a person so renowned, her reputation seemed literally incredible. We have seen and heard for ourselves she who honorably presides over the mysteries of philosophy.”
The Astronomy and Mathematics of Hypatia
Hypatia was principally a teacher. The golden days of Eudoxus, Euclid, Aristarchus, Archimedes, Eratosthenes, Appolonius, and Hipparchus were as distant from her in time as Fibonacci and Nicolaus Copernicus are from us.
Hypatia wrote commentaries and reshaped great scientific and mathematical works to make them more understandable for her students. Her contributions to knowledge lay in the improvements she made to the original works.
Revising the Almagest
Hypatia’s work on Book III of Claudius Ptolemy’s great second century astronomical work Almagest still exists. Remarkably, given the number of academic articles written about Hypatia in recent times, this – her only surviving work – is yet to be given a modern translation directly into English. A translation into French was made by Adolphe Rome in 1926.
Book III of the Almagest examines the sun; the length of the year; Hipparchus‘ discovery of the precession of the equinoxes; and an introduction to epicycles.
Epicycles
Ptolemy and then Hypatia tried to build a reliable mathematical model that predicted the movements of planets.
They were hindered by their traditional beliefs that planets must orbit the earth, and the orbits must be circular.
Ptolemy used a series of elaborate ploys to produce a working model that accounted for phenomena such as:
- Retrograde motion: a planet seems to change its direction in the sky.
- Size changes: a planet’s size seems to vary over the course of a period of time.
One of Ptolemy’s ploys was the epicycle, shown as the yellow dashed circle in the diagram.
The epicycle is a small orbit around an imaginary point. This imaginary point travels around the deferent – the large white dashed circle centered on the earth – at a uniform speed.
The epicycle is quite a neat idea. It allows the planet’s distance from Earth to vary and it also produces retrograde motion.
Hypatia developed her own unique calculation methods in Book III, utilizing Babylonian sexagesimal (base 60) numbers and an abacus-like calculator. Like her father, Hypatia used Greek letters for numbers 1-59 and sexagesimals for higher numbers.
Her methods of calculation allowed her to both improve upon and offer criticism of Ptolemy’s original work. The result of this, in addition to her revision of Ptolemy’s text, was her own Astronomical Tables featuring new calculated values for celestial events such as planet conjunctions.
Algebra
The mathematician Diophantus is a mysterious figure about whom little is known. He appears to have flourished in Alexandria about a century before Hypatia, when he authored a series of thirteen books, Arithmetica, describing algebraic equations and their solutions. Diophantus is often described as the father of algebra.
Prior to later Arabic and Byzantine authors, only one mathematician in history, Hypatia’s father Theon, cites Diophantus’ Arithmetica. The Byzantine Encyclopedia Suda compiled in about 1000 AD tells us that Hypatia authored a commentary on Arithmetica.
Only six of Arithmetica’s books survive in the original Greek; four others exist as Arabic translations made in about 860 AD.
The Arabic translations of Books 4, 5, 6, and 7 of Arithmetica contain more commentary on solutions than the Greek versions. These editions may have been copied from Hypatia’s commentary editions of Arithmetica, modified by her to help students at her school.
Conic Sections
In The Historia Ecclesiastica, Socrates Scholasticus says that Hypatia wrote a commentary on Apollonius of Perga’s Conic Sections. This has not survived.
Personal Details and The End
Hypatia never married and had no children.
Although she was a Neoplatonist living in a Christian city, her philosophical teaching did not alienate her many Christian students: if anything it seems to have inspired them to more noble ends.
The Romans, however, were using strong-arm tactics to make Alexandria a Christian city. During Hypatia’s lifetime, all pagan temples were reduced to rubble on the orders of Archbishop Theophilus of Alexandria.
After Theophilus died in 412 AD, his nephew Cyril became archbishop. Cyril was also hostile to Alexandria’s non-Christian communities, such as Hypatia’s Neoplatonists, and began interfering with the city’s secular government. He got into a conflict with the city’s newly appointed Roman governor Orestes, who wanted to keep the Church out of government matters.
Hypatia was seen as an ally of Governer Orestes, and this led to her death. In March 415 AD, a mob of Christian Parabalani attacked her in the street. Among other roles, members of the Parabalani acted as Archbishop Cyril’s bodyguard. Remarkably, it seems the Parabalani took Hypatia into a church in order to hack her to pieces. Fearing that Hypatia’s remains might become a focus for her martyrdom, they took what was left of her body to Cinaron and cremated it.
Other than among Alexandria’s more fanatical Christians, Hypatia’s gruesome slaying was greeted with horror throughout the Roman Empire. Intellectuals were traditionally treated with respect. The Roman emperor Theodosius II sent a team to investigate Hypatia’s murder. The result was that the Parabalani were removed from Cyril’s control and placed under Governor Orestes’s control and their numbers restricted to a maximum of 500.
Hypatia’s Legacy and Soul
Despite Cyril and the Parabalani’s best efforts, Hypatia became a martyr. She was remembered and revered by the Christians of Byzantium, and in more recent times has become a symbol of Enlightenment values.
Hypatia’s role as one of the world’s first female academics, murdered with horrific cruelty, has made her a heroic figure, the subject of highly speculative academic works and novels. The 2009 movie Agora fictionalizes her final years.
As a Neoplatonist, Hypatia believed the ultimate fate of her soul would be a union with the divine.
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Further Reading
Sir Thomas Heath
The Thirteen Books of Euclid’s Elements
Dover Publications, New York, 1956
Morris Kline
Mathematical Thought from Ancient to Modern Times
Oxford University Press, New York, 1972
M.E. Waithe
Ancient Women Philosophers: 600 B.C.-500 A. D.
Springer Science & Business Media, 1987
Alan Cameron, Allan G. Cameron, Jacqueline Long, Charles Anthon Professor Emeritus of Latin Alan Cameron, Lee Sherry
Barbarians and Politics at the Court of Arcadius
University of California Press, 1993
Creative Commons
Exploded view of small astrolabe by Elrond under the Creative Commons Attribution-Share Alike 4.0 International license.