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Western Science’s Last Breath Before Dying: Hypatia Of Alexandria (Women in Science 49)

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.

 

 

 

 

 

 

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daledebakcsy

daledebakcsy

5 Comments

  1. October 21, 2015 at 12:56 pm

    daledebakcsy,
    I think I heard about that Agora movie on the life of Hypatia Of Alexandria, but I never got around to watching it.

  2. October 21, 2015 at 7:27 pm

    Really fascinating post, Dale- but so incredibly disturbing.

  3. October 22, 2015 at 6:05 am

    Wow.  There’s so much mangled bad history in this piece it’s hard to know where to begin.

    “a succession of paranoid archbishops employing gangs of religious thugs had leveled the centers of learning and driven out pagan influences”

    This is total garbage.  They had not “leveled” any centres of learning at all and Christians studied alongside pagans because Christianity had long since embraced ancient Greek learning.  Centuries before Hypatia was even born a Christian Alexandrine – Clement of Alexandria – had taught that, just as the Jews had been given a special gift of revelation by God, so had he given the gift of rational analysis to the Greeks.  This is why Hypatia was friends and political allies with the Christian city prefect Orestes and had many Christians amongst her students.

    “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.

    Where are you getting this fantasy from?  None of the sources say any such thing.  Alexandria was a centre of learning with many scholars, not just two.  And these included Jewish, Christian and pagan ones.  This claim is simply nonsense.

    ” Theophilus and Cyril, two archbishops who whole-heartedly believed in the use of violence to wipe out all vestiges of pagan belief and practice.”

     

    Again, this is completely wrong.  Christianity had already began to find ways to synthesise the neo-Platonism of people like Hypatia with their own theology and did so quite happily.  More fantasy.

     

    “Theophilus had destroyed the last remnants of the Great Library in 391”

     

    No, actually, he didn’t.  The Great Library had been destroyed by Aurelian in the previous century.  What Theophilus destroyed was the Temple of Serapis which HAD housed a daughter library but which no longer did so when it was destroyed (after being used as a base by a gang of pagan terrorists).  Writing decades earlier Ammianus referred to the libraries of the Serapeum using the *past tense*.  And none of the five accounts of the destruction of the Temple mentions any library.  This includes the account of the pagan and anti-Christian scholar Eunapius, who would mention the destruction of the library if it had still existed.  This whole idea was invented by Edward Gibbon in 1776 and has been popularised by a garbled and erroneous account by Carl Sagan.  It’s a myth.

    “Cyril employed his predecessor’s armed monks to terrify pagans, Jews, and members of rival Christian sects alike.”

     

    A rather weird and lopsided summary of a series of inter-faith feuds which were started by Jews stoning Christians and included the pagan terrorist gang mentioned above.

    “Theon and Hypatia devoted themselves to preserving the most important mathematics of the past that it might not be lost forever. ”

     

    More fantasy.  This is not found in any of the source material on either of them.  And why would it be “lost forever”?  It was being taught to pagans and Christians in academies and schools all over the Empire and would continued to be so.

     

    “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.”

     

    Total garbage.  Mathematics and astronomy, along with geometry, were both part of the *quadrivium, which with the *trivium* formed the core of the medieval curriculum taught in every cathedral school and, later, university throughout the Middle Ages.  They were central disciplines which, with grammar and rhetoric, were the core of education by the Church.

    ” Cyril …. intimidate(d) the multi-faith-tolerant prefect Orestes into passing exclusively pro-Christian legislation”

     

    More fantasy found nowhere in the sources.  Why are you just making crap up?  Where are you getting this nonsense from?

     

    “Sadly, Hypatia’s death is the best documented part of her life. ”

     

    Sadly, no-one who parrots the myths about her death bother to actually read those accounts and notice that her learning had zero to do with it.  It was a political murder, in revenge for the murder of one of Cyril’s followers in a purely political power struggle for civic dominance between Cyril and Orestes.

     

    “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.”

     

    More total garbage.  Scholarship continued after Hypatia’s political murder because it had zero to do with her scholarship.  Hierocles, Asclepius of Tralles, Olympiodorus the Younger, Ammonius Hermiae and Hermias all continued the tradition of learning in the city in the century that followed.  Hypatia wasn’t even the last female Alexandrine philosopher or even the last pagan female one.  Aedisia taught and studied in the city in the generation that followed her, unmolested by ignorant monks.  Though unlike Hypatia, she stayed out of the city’s dangerous politics.

    The post above is a fairy story – a pseudo historical fable that bears almost no relationship to what actually happened.  Rationalists should educate themselves better and stop repeating irrational myths.

     

     

     

     

     

  4. October 22, 2015 at 7:53 pm

    Generally I don’t engage with commenters who don’t manage a basic level of dignified comportment. This one, however, is a fair representative of the ideas of the Cyril Apologist camp, so I thought he’d be interesting to include. There are, of course, many problems with this analysis. To begin with the bottom-most point:

    – That scientific scholarship continued in Alexandria after Hypatia’s death. This is a relatively standard list of scholars trotted out when people seek to deny that the power struggle between Cyril and Orestes seriously affected the intellectual output of Alexandria. A few minor problems, though – Hierocles studied under Plutarch, and that was in Athens, not Alexandria. He did travel to Alexandria once, and was quickly ejected from the city. Ammonius Hermiae was a philosopher, also trained at Athens, but he did go to Alexandria to teach, until he was persecuted for being a pagan in the late 5th century, at which point he had to convert to Christianity to continue teaching. If one is trying to demonstrate that Alexandria was, after Theophilus and Cyril, an inclusive intellectual community, he’s certainly an odd choice. It’s often pointed out that he wrote about Nicomachus’s Introduction to Arithmetic, which sounds like a mathematical effort on par with Hypatia’s commentaries on Apollonius and Diophantus until you realize that Nicomachus was interested primarily in the neo-Pythagorean mystical qualities of numbers, which is a far cry indeed from Euclid and Apollonius. Olympiodorus the Younger is a bit better choice, were it not for the fact that he didn’t write about science except through the lens of astrology, and nothing at all about mathematics. Taken in total, it’s a curious collection of Aristotelian and Platonic philosophers with varying connections to Alexandria, and who were almost entirely insignificant mathematically. If this is the VERY best list that the Cyril apologists have to offer about the continuation of mathematical scholarship after Hypatia, it is something of a sad affair, and amplifies rather than mitigates the barrenness of post-Hypatian mathematics.

    – What I will give, though, is that there is perhaps greater ambiguity about how many volumes of the original Library were destroyed when Theophilus sent his armed forces to destroy the Temple of Serapis, where they were being housed, than my wording conveys here. Gibbon, as Tim mentions, holds that everything was destroyed. Others say that a significant number of the volumes stored there did not get destroyed and survived into the 7th century, when they were definitively wiped out. The survival of those volumes depends how much you believe a 13th century account of a 7th century event. I obviously am not terribly persuaded by it, but there are people who are.

    – That Hypatia’s death was a political revenge murder, which somehow contradicts the statement “Sadly, Hypatia’s death is the best documented part of her life”…? The connection between the quote and the commentary is tenuous, but let’s leave that be and focus on the comment. We have three fundamental accounts of Hypatia’s death. Socrates Scholasticus says that the Christian community felt Hypatia was in the way of them being able to influence Orestes, and so murdered her in an attempt to cinch their control of the city. Damascius gives a different version, which makes Cyril more directly responsible, and the motivation jealousy. John of Nikiu’s account says that the murder was inspired by a Christian enthusiast named Peter acting on his own to eliminate the pagan “enchantments” of Hypatia. No matter which of those versions you give credence to, or even if you create an amalgam of them, it is clear that there was a culture of religiously justified violence in Alexandria, and that Cyril, if we choose to be absurdly generous about it, did nothing to stop it, and being more realistic given how he treated other opposing religious groups, actively contributed to it.

    – That Alexandria had many scholars, including pagans and Jews. This is true, and that is thanks to Orestes, not Cyril. At the risk of sounding horrendously repetitive, this article is about the mathematical tradition of Alexandria, and as we already saw, that tradition came to a full stop after Theon and Hypatia. It feels like our friend is commenting about the article he wants to argue against, about the continuity of neo-Platonic philosophy, rather than the one that is here, about the Alexandrian mathematical continuum. The curious thing is that, where my article does mention philosophy, it specifically mentions how Theophilus allowed Neo-Platonists to practice because of how their philosophy was increasingly amenable to Christianity, and offered further the example of Augustine as the most famous example of this trend. For Tim to offer, “Christianity was amenable to Greek thought” as a critique after the paragraph that says, “Christianity was amenable to Greek thought” is thus another curious choice. But allowing Neo-Platonic philosophy and allowing paganism are two separate things. Theophilus allowed the former, but came down violently hard upon the latter. To say that paganism was allowed to flourish because Neo-Platonism was taught is thus a bit of bait and switch that is, indeed, a common tactic when trying to excuse the excesses of this era, but isn’t terribly honest.

    Everything else here is more or less a variation on these themes, so we can leave it be for now. Hypatia continues to be controversial, some 1600 years after her murder, as you can see. She brings up a whole culture of religious violence which many would rather forget, and likewise the intellectual sterility left in the wake of such violence. So, there is a lot of verbal re-couching that goes on. Fair treatment of a philosophy is swapped in for oppression of a religious group. Murder becomes justified, as long as it’s in Revenge for something. And the attempt to defend that re-couching can get quite heated, as we see here. People feel very strongly about that defense, to the point of losing their basic notions of civility. This should surprise no one who has been on the Internet, ever. I actually find it kind of great that this woman, so long gone, and so brutally ended, still inspires this amount of excitement.

    Now, I’ll see everybody back here in two weeks for our Big 50th Episode, featuring one of the all-time greats!!

    – Dale

  5. October 26, 2015 at 7:55 pm

    “This one, however, is a fair representative of the ideas of the Cyril Apologist camp”
    The what?  I’m an “apologist” for nothing more than accurate history and, as an atheist, have no interest in being an “apologist” for any bishop.  As a historian, I’m interested in nothing other than unbiased historical analysis – something sorely lacking in the pastiche of misunderstood fact and ideologically driven fantasy in your post above.  Not to mention your errors of fact.  Speaking of which …
    “Hierocles studied under Plutarch, and that was in Athens, not Alexandria. He did travel to Alexandria once, and was quickly ejected from the city.”
    This is just plain wrong.  H.S Schibli’s 2002 study is pretty much the definitive scholarly work on Hierocles and he sets out the fragmentary material we have on his life and analyses it on pages 1-13 of that work.  The evidence is quite clear on the general outline of his life and career – he was born in Alexandria, studied in Athens and then returned to Alexandria and taught there for the rest of his life.  He was never “ejected from the city”.  The city he *was* ejected from was Constantinople – he was publicly flogged there and then exiled for reasons unknown after a short sojourn.  Damascius’ brief account of this episode ends with “he returned to Alexandria and continued to philosophise with his disciples”, making it clear that this was where he had travelled from and therefore where he returned to.  It helps to actually know the material.
    “Ammonius Hermiae was a philosopher, also trained at Athens, but he did go to Alexandria to teach, until he was persecuted for being a pagan in the late 5th century, at which point he had to convert to Christianity to continue teaching”
    More nonsense.  There is no source that says he was “persecuted” and the idea that he converted to Christianity is also without solid foundation.  We have one reference in Damascius that chides him for compromising his philosophy in some way to conform to “the common opinion” but we don’t know what his compromise was nor do we even know if the “common opinion” refers to Christianity (though that is likely). 
    “It’s often pointed out that he wrote about Nicomachus’s Introduction to Arithmetic, which sounds like a mathematical effort on par with Hypatia’s commentaries on Apollonius and Diophantus until you realize that Nicomachus was interested primarily in the neo-Pythagorean mystical qualities of numbers”
    All of these people were.  To try to separate them into “scientists” and “not scientists” is completely anachronistic.  Theon wrote a work on divination and Hypatia’s student Synesius wrote on the Chaldean Oracles.  More relevantly, all of the neo-Platonists I mentioned were well-versed in mathematics, geometry and astronomy.  Ammonius was a renowned astronomer (astronomy being a branch of mathematics in this period) who lectured on Ptolemy and wrote a treatise on the use of the astrolabe.
    “Olympiodorus the Younger is a bit better choice, were it not for the fact that he didn’t write about science except through the lens of astrology, and nothing at all about mathematics”
    Trying to pretend astrology and astronomy were “non-scientific” and “scientific” respectively is another clumsy anachronism.  In this period astrology and astronomy were closely entwined and both were branches of mathematics.  And trying to rule him out on the grounds that he wasn’t a mathematician (in some modern sense of the word) is goalpost shifting anyway.  Your article above creates a fantasy story whereby the wicked old Church is supposedly trying to crush science and pre-Christian philosophy in general (the luridly dramatic stuff about “science’s last breath” etc).  The examples I’ve given show that this is simply not true.  Your article then goes on to make some bizarre and completely unsupported claims about some special Christian hatred for mathematics and astronomy, such as:
    “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”
     This is total nonsense.  As I noted, mathematics, geometry and astronomy were all enshrined in the Seven Liberal Arts that formed the basis of Christian education for centuries.  So there was no special animus against mathematics and astronomy and no attempt to have what we would call “science” draw any “last breath”.  You’re perpetuating a pseudo historical fable that actual historians recognised as nonsense over a century ago.  As Edward Grant notes:
    “With the total triumph of Christianity at the end of the fourth century, the Church might have reacted against pagan learning in general, and Greek philosophy in particular, finding much in the latter that was unacceptable or perhaps even offensive. They might have launched a major effort to suppress pagan learning as a danger to the Church and its doctrines. But they did not.”
    (*The Foundations of Modern Science in the Middle Ages*,1996, p.4)
    They did NOT do the things you claim.  Unless you want to try to tell us that your glib assertions (backed up with no reference to the actual source material) are right and the Distinguished Professor Emeritus in the Department of History and Philosophy of Science at Indiana University, former winner of the Sarton Medal and esteemed world renowned expert in the history of science is wrong.
    “there is perhaps greater ambiguity about how many volumes of the original Library were destroyed when Theophilus sent his armed forces to destroy the Temple of Serapis, where they were being housed, than my wording conveys here.”
    The problem isn’t your “wording”, it’s the fact that your story is contradicted by the evidence.  Again, we have five accounts of the demolition of the Serapeum and NONE of them mention any library being destroyed.  This includes the hostile and overtly anti-Christian account by the philosopher Eunapius.  Then we have the fact that Ammianus’ detailed description of the temple written in the decades before the demolition and most likely based on his own visit there a couple of decades earlier mentions the libraries it had housed *in the past tense*.  Given that all pagan temples were experiencing dwindling funds by the end of the fourth century and that libraries were notoriously expensive to maintain, it makes sense that we get no mention of any library in the demolition accounts because there was none there by that stage.
    “Socrates Scholasticus says that the Christian community felt Hypatia was in the way of them being able to influence Orestes, and so murdered her in an attempt to cinch their control of the city.”
    No, Socrates says that Cyril’s faction, made up of Christians “of a very fiery disposition” felt this way in a dispute with the other Christians who supported Orestes, who Socrates calls “the more sober-minded” Christians.  It was not “the Christian community” against another community, it was two factions, both Christian.
    “Damascius gives a different version, which makes Cyril more directly responsible, and the motivation jealousy.”
    He puts Cyril at the centre of his account and emphasises his jealousy of Hypatia, but his account fits with Socrates – this was a purely political dispute which led to a tit-for-tat killing.
    “John of Nikiu’s account says that the murder was inspired by a Christian enthusiast named Peter acting on his own to eliminate the pagan “enchantments” of Hypatia.”
    Except Nikiu was writing centuries later and used Socrates as his source for this episode.  The “enchantments” stuff is his embroidery on the story and can’t be taken as historical.
    “No matter which of those versions you give credence to, or even if you create an amalgam of them, it is clear that there was a culture of religiously justified violence in Alexandria”
    Religion played zero role in this episode, which was a purely political dispute.  Science and mathematics played zero role as well.  It has no relevance other than as another example of the notoriously violent civic politics Alexandria was renowned for.
    “this article is about the mathematical tradition of Alexandria”
    The article was actually much broader than that.  Not that it matters – the idea that the Church tried to suppress mathematics is as wrong as the idea that it tried to stamp out Greco-Roman learning.  And Hypatia’s death had nothing to do with her learning.
    “The curious thing is that, where my article does mention philosophy, it specifically mentions how Theophilus allowed Neo-Platonists to practice because of how their philosophy was increasingly amenable to Christianity, and offered further the example of Augustine as the most famous example of this trend.”
    That Christianity had long since been open to absorbing all kinds of Greek philosophical ideas, especially neo-Platonism, is quite clear. Your problem is this fantasy that it tried to stamp out mathematics, astronomy and natural philosophy.  You claim this via bold assertions backed up by nothing and then shoehorn in the myth of a library destroyed in the Serapeum and the totally irrelevant story of the political murder of Hypatia.
    Essentially you’ve created a piece of ideologically-driven pseudo historical fantasy fiction out of baseless assumptions about an overt Christian hostility to Greco-Roman learning that didn’t exist and some scraps of actual history that you don’t seem to understand, embroidered with some breathless hyperbole that consists mainly of assertions backed by nothing other than hysteria.  This is classic New Atheist bad history at its most ridiculous

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