By 400 CE, Alexandria was submerged in a sea of political-religious rivalries that drew even the most innocuous seeming of scholars into its ravenous maw. For centuries the intellectual capital of the world, boasting the largest storehouse of scientific and cultural information ever assembled, a succession of feuding prefects and patriarchs, pagans and neo-Platonists, employing mob violence as an all-too-regular form of expression for political grievances, had reduced the gleaming city to a nervous husk of its former glory, and at the twitching center of that husk lay two of the greatest scholars in its long history, a father and a daughter.

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 Patriarchs who did not shudder before the use of violence to neutralize their religious and political opposition. According to Socrates Scholasticus, Theophilus was ruthless in scouring pagan activity from the city, possibly destroying the last volumes from the Great Library in the process, and Cyril employed his predecessor’s Nitrian monks and armed mobs to terrify pagans, Jews and members of rival Christian sects alike when they challenged his authority.

For a person of conscience in that atmosphere, the preservation of the past in the face of an uncertain future was a high calling, and both Theon and Hypatia devoted themselves to preserving the most important mathematical concepts of the past so they might not be lost forever. Theon wrote definitive commentaries on Euclid and Ptolemy, the former of which was our primary source for Euclid’s *Elements *for centuries. It was left to his daughter, then, to continue the tradition and attempt to capture the most recent developments in mathematics.

Most of what she accomplished has been lost to us, swallowed in the twisting vortex of persecutions, censorship, and neglect 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 become famous for cracking was a Diophantine equation, as is Fermat’s 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 *a^*2 + *b^*2 = *c^*2? Is there a way to generally categorise 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 the original authors’ 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 one of the world’s most prominent mathematicians, a woman who could speak of the most modern developments in science and mathematics and their connection with the great Greek philosophical tradition.

Theophilus had had a decent relationship with both Theon and Hypatia. He saw them as harmless neutrals whose Neoplatonism was (in its most abstract incarnation if not in the particular form practiced by Hypatia) 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 is 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 seems to have believed that his arch-rival for pre-eminence in the city, the prefect Orestes, had formed an alliance with Hypatia to put himself in good graces with the city’s remaining but significant pagan population, and that therefore, to enhance his own position and make Orestes more pliant to his future plans, Hypatia had to go. We don’t know if he gave the order to eliminate her, but he stood to benefit from her demise (at least in the short term) and had not shied away from employing violence to solve political problems in the past (much of the tension between Cyril and Orestes lay in each’s willingness to use their authority to foster politically motivated murders and riots), so it is at least likely that he was responsible for stirring up the antipathy to her that resulted in her untimely and gruesome end.

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, if not entirely consistent, sources for her grizzly finale. 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, removing her eyes, and burning the hewn pieces of her body outside the church. They had, in a frenzy of blood, destroyed one of the few fragile connections their city had with its glorious mathematical past, and paved the way for its steady descent into a shadow of its former self.

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, an easily accessible source is Michael A.B. Deakin’s *Hypatia of Alexandria: Mathematician and Martyr *(2007). It contains not only a 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.

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