By 400 CE, Alexandria was a nervous husk dancing the edge of zealous self-annihilation. For centuries the intellectual capital of the world, boasting the largest storehouse of scientific and cultural information ever assembled, a succession of paranoid archbishops employing gangs of religious thugs had leveled the centers of learning and driven out pagan influences until all that remained of the city’s glorious tradition were two people, a mathematician and his daughter, doing what they could to preserve what had not yet burned from the increasingly irrational and violent mob behavior of their Christian overlords.
The father’s name was Theon, and the daughter was Hypatia (c.370-415). They were the inheritors of one of the most robust mathematical traditions in the history of the world, the terminus for a line stretching back seven centuries through Ptolemy, Diophantus, Apollonius, and Euclid. Had they lived in better times, they might have been the originators of startling new mathematical theories. But they didn’t. They lived under the rule of Theophilus and Cyril, two archbishops who whole-heartedly believed in the use of violence to wipe out all vestiges of pagan belief and practice. Theophilus had destroyed the last remnants of the Great Library in 391, and Cyril employed his predecessor’s armed monks to terrify pagans, Jews, and members of rival Christian sects alike.
In that atmosphere, there was no question for a person of conscience of luxuriously formulating new mathematics. Instead, both Theon and Hypatia devoted themselves to preserving the most important mathematics of the past that it might not be lost forever. Theon wrote definitive commentaries on Euclid and Ptolemy, the former of which was our only source for Euclid’s Elements until the 19th Century. It was left to his daughter, then, to continue the tradition and attempt to capture the most recent developments in mathematics before Cyril could finish what he had begun.
Most of what she accomplished has been lost to us, swallowed in the twisting vortex of sanctioned ignorance that followed her violent death, but we at least know what she wrote about, and that was the conic theories of Apollonius and the algebraic theories of Diophantus. Conics include hyperbolas, parabolas, and ellipses, and model everything from the path of an object in projectile motion to the orbits of planets and comets to the stored energy in a compressed spring. They had been investigated prior to Apollonius, but his expanded treatment of them, and in particular the addition of quasi-Cartesian reference frame elements, was the definitive statement of antiquity’s geometric genius.
Diophantus, meanwhile, investigated methods for finding particular and general solutions to algebraic equations. The problem that Julia Robinson became famous for cracking was a Diophantine equation, as is Fermat’s famous Last Theorem. Diophantus was interested in equations of several variables for which only rational answers were allowed (though today Diophantine analysis only allows integer solutions). What possible rational values of a, b, and c are there such that a2 + b2 = c2? Is there a way to generally categorize all possible triplets of answers? This thinking, had it been followed through, would have allowed European number and algebraic theory to grow and flourish as its geometric thought had. As it was, that mathematical rebirth would have to wait a millennium, when Arabic algebraic techniques reinvigorated Western thought.
These then, and perhaps much more, were the subjects Hypatia wrote about. According to the few scant remnants we have and second-hand accounts of her work, she made no original contributions to these fields, but contented herself with producing clear editions which included worked out examples that clarified their points and checked their results for a more general readership.
For Hypatia was, above all things, a teacher. Followers thronged to her dwelling to hear her talk about mathematics, astronomy, and Neoplatonic philosophy. After the death of her father, she was the world’s most prominent mathematician, a woman who could speak of the most modern developments in science and mathematics and their connection with the great Greek philosophical tradition. She didn’t originate anything, but nobody else at the time did either. Research mathematics was dead in Europe, and would remain so for a thousand years to come.
Why was that? How could an entire, robust tradition of intellectual endeavor, spanning seven centuries of continual progress, simply end? Persecution certainly played its role. Mathematics and astronomy were associated with astrology in the Christian theology of the time. To be interested in the relations of numbers and the movements of the stars was to be, according to the conspiratorial mindset of the early Church, engaged in ungodly divination which sought to thwart God’s majestic plan. And that could not stand.
Theophilus had had a decent relationship with Theon and Hypatia. He saw them as harmless neutrals whose Neoplatonism was, in its most abstract incarnation, highly compatible with emerging Christian philosophy (Augustine of Hippo, Hypatia’s contemporary, would in fact earn himself a Sainthood for his cunning if curious amalgam of Neoplatonism and Christianity). That’s not to say Theophilus was a nice guy. His use of violence to destroy pagans he didn’t find useful was brutal and complete. But he was at least willing to let Theon and Hypatia be.
Not so his successor, Cyril. Cyril was a violent anti-Semite and anti-pagan willing to give Alexandria over to religious mob rule if it meant the eradication of his perceived enemies. He employed Theophilus’s armed monks to terrify Novatian Christians into leaving, to threaten the Jewish population, and to intimidate the multi-faith-tolerant prefect Orestes into passing exclusively pro-Christian legislation. We do not know if he gave the order to eliminate Hypatia, but he created an atmosphere of religiously sanctioned holy violence that inevitably redounded to her death.
Sadly, Hypatia’s death is the best documented part of her life. While we have to sift through scraps and stylistic theories to attempt to reproduce her living work, we have multiple sources for her grizzly end. She was stopped by a Christian mob while riding through the streets in her carriage. They seized her, dragged her inside a nearby church, and beat her to death with roofing tiles before ripping her body apart, limb from limb, and burning the pieces outside the Church. They had, in a frenzy of blood, destroyed the last fragile connection their city had with its glorious past, and paved the way for its steady descent into self-contented irrelevance.
Cyril was declared a saint in 1883 for his contributions to Christianity.
FURTHER READING: There is a good deal written about Hypatia, which is somewhat surprising given the absolute dearth of information we have about her. Most of it, however, is fiction, and most of the non-fiction is not in English. For the English speaker, your best bet is Michael A.B. Deakin’s Hypatia of Alexandria: Mathematician and Martyr (2007). It contains not only a well-researched biography, but appendices about the mathematics Hypatia is thought to have studied and complete translations of all the original source material we have pertaining to her life and work. Or, if you don’t like reading, you can always check out the film Agora (2009), a dramatization of Hypatia’s life that pulls no punches when it comes to Cyril’s resplendent horridness.