Regarding Hypatia #2

Sorry, again, for the irrelevance of this post. Same tactics as last time, don’t hit “read more” if Hypatia is of no interest to you. For those interested, this post will be centered on her work as a philosopher and a mathematician.

If you’ve read my previous post (I probably love you but that’s not the point) go ahead and read this one too. For those who don’t know what I’m talking about but are interested in finding out (yay!) go here, read that one first and come back afterwards for part 2.

Whew! I’m nervous about this. Trying to clear the facts in all the available material is like walking through a minefield. I’ve started experiencing a new level of admiration for historian. How do these people cope? When I obsess over a subject and read everything about it (like I do now about Hypatia, big dork that I am) I usually do it for my own benefit and/or entertainment. So being wrong about something is no big deal. Writing about history though makes me feel responsible to you people! I have to have my facts straight. Therefore, I’m nervous. In any case, lets move on.

2) Her work (as we know it so far)

As I’ve already mentioned, Hypatia is known to us as a scholar. A mathematician, an astronomer and a philosopher. Her father, Theon of Alexandria, was a member of the museum of Alexandria and he was also a mathematician and an astronomer. In fact, he is known to us from his commentary (the ancient term for editing as I understand) on the works of Euclid (Euclid’s Elements and Optics) and Ptolemy (he was also somewhat of a poet and more of a pagan than his daughter, he was into all that paganism entailed, hymns and the Orphics etc. Also I need to clarify that it is not proven that Hypatia was a pagan).

We know that Theon had worked together with other scholars, one of whom was his daughter, Hypatia. Of all his students and associates, Hypatia was the one most praised by her father for her work and insight. Other sources from that time support his opinion of her skills by saying that Hypatia even surpassed her own father in both mathematics and astronomy. And here’s the deal, even though all those sources praise her mathematical skills, Hypatia today is mostly recognised as a philosopher. “But um, why, exactly?” one would say (I was more like “why, why why damn it?!”, but thankfully not everyone is crazy. Well, not overly crazy).

This is where things get messy. On the one hand, we know the titles (or at least some of them) of Hypatia’s work by antiquity, medieval and modern historians. Their list goes like this:

►Edited Theon’s commentary on Euclid’s “Elements”
►Wrote commentary on Appolonius’ “Conics”
►A text called “The Astronomical Cannon”. Most likely commentary on one of the works of Ptolemy, either
the “Almagest” or the “Handy Tables”
►Wrote commentary on Diophantus’ “Arithmetica”
►Edited Ptolemy’s “Almagest”
►She was able to construct an Astrolabe. The probable inventor of the Astrolabe is Ptolemy. Whether Ptolemy made one himself is unknown (though it is more than likely that he did). It is likely that Theon actually made one and then it is likely that he taught Hypatia how to make one herself. She in turn, taught her students.
►She invented (I’m really not clear on that, if someone knows please comment) the “Hydroscope” or  “Hydrometer”, depending on what’s the source of the description. Some say it was a device that was used to count the density of liquids or specifically water, either for medical or mystical (?) purposes. I’ve read some strange theories on what that damn instrument actually did, but I’m gonna stick with this theory because it’s the most logical and well-established one. Besides, it’s a theory, so as long as it is neither proven or disproven you can just take it with a grain of salt.

On the other hand, none (if there ever was any) of Hypatia’s original work has been found yet (yes I’m sticking with optimism and add that small yet, go ahead and judge me, I don’t care). Moreover, even from this existing list we are not sure which parts are hers. We don’t know if she wrote commentary on Ptolemy’s “Almagest” or if she edited Theon’s. We don’t know which parts of the commentary on Euclid’s “Elements” are her words, or her father’s but edited by her, or if they’re her father’s alone.

An important part is Diophantus’ work. Diophantus’ major work is the “Arithmetica”, originally comprising thirteen books. Of these, six now survive in Greek and four in Arabic. Here I should note that Diophantus is notorious for his “difficult” ideas as an ancient mathematician. Because of that notoriety, one theory about Hypatia says that our surviving work of Diophantus is through her commentary and that whatever work she did not include into her edition is the work lost to us. If that’s the case, we (as in, the humanity) owe her a great debt. But even if that’s not the case, and the other theory supporting that Diophantus’ work was preserved through the Arabs is the right one, we still might be able to say that we have work truly, actually written by her, no buts or what ifs included. Her commentary on Diophantus’ work may be still here, among us, 1600 years later. But the ugly truth is that still, we can’t know what amount and what exact material is hers and what isn’t. Same goes for the other titles mentioned above.

[ I can’t stop myself from adding this bit of beauty here. Michael Deakin, before writing his book about Hypatia, had published an article for The American Mathematical Monthly, March 1994, Volume 101, Number 3, pp. 234–243. There he spoke of Hypatia’s work as a mathematician, and added this valuable detail concerning Diophantus’ commentary, where even in the worst case scenario where Diophantus’ work was edited before being translated by the Arabs (which would mean that much of the existing commentary was left out) we could still have this: “the most likely of the supposed interpolations to have come from Hypatia’s hand are two “student exercises” at the start of Book II. The first asks for the solution of the pair of simultaneous equations:

where a, b, are known. The next is a minor generalization. It requires the solution of the pair of simultaneous equations:

where a, m and b are known. There is some evidence to link this problem to Hypatia: a nine-word phrase in the original Greek is identical with one from Euclid’s Data, which her father had edited.

Unfortunately I don’t have enough data to clarify how true this detail might be so don’t take it too seriously. Even so, if these two equations are not beautiful to you, then my efforts clearly don’t get this story through and I apologize in advance.

Edit: This information coincides with Wibur Knorr’s assertion that it was Hypatia who simplified Diophantus’ work and that it was her edition the Arabs translated. The only possible objection is that said text is over-simplified, and that doesn’t add up with the description we have of Hypatia as a highly intelligent individual. However, if said simplification had been made for educational purposes, it would all add up. Hypatia would be the commentator, and the text would be trivial work done to help elementary students. Beware, all these are theories, we have no definitive proof.]

It is exactly that uncertainty surrounding her work, that makes modern historians of mathematics not recognise her as a great mathematician (and rightly so I might add, they have no proof, no facts, no nothing). Which leads to her being more known as a philosopher.

The other reason is the extent of Hypatia’s reputation as a philosopher (seriously, some simply said “the Egyptian philosopher” and expected others to understand who they were referring to). Historical sources report her as being a Neoplatonist. We can see that in everything we know about her. In her way of life, her teachings and her position in society. Philosophy was a big part of who she was and what she did.

This last part took me some time to get used to. You see, Neoplatonism was very much like a form of religion. Hypatia following Plato’s teachings taught her students about how they must find the “God-like” part of humanity inside themselves. Her students were taught that by simultaneously training their minds and hearts, by self-improvement, they would rise the “good” inside them towards “The One”, “The Good” described by Plato.

It is no coincidence that her students admired her so. Boy, did they adore her. I mean yeah, I have teachers and professors I admire, I want to believe everyone had at least one beloved teacher in the course of their lives, but no way am I ever gonna admire them the way Hypatia’s students admired her. There’s a reason behind all that exaltation and it’s not just the fact that she was a really great teacher.

Neoplatonists believed that through self-improvement, knowledge, wisdom and a disregard towards material goods and needs they would rise above their mortal existence towards a perfect state of being. Hypatia taught her students the what and the how of reaching that state. She was the guide who could lead them to God (it wasn’t due to chance that many of her students turned to christianity and took positions in the clergy, the similarities between the two beliefs are apparent). And thus, she was so fully worshiped.

Yet again, it’s not only that. Hypatia made her teachings a reality by her way of life, setting standards for herself that were above and beyond of what she expected of her students. She gained such knowledge, sources refer to her as having surpassed all philosophers of her time. She had high morals, lived her whole life in celibacy, led an ascetic way of life (asceticism led to humility and freedom from material needs etc), she was just and highly intellectual and logical and all things nice. Also, all philosophers of Hypatia’s time were treated with a religious reverence. Philosophy was such an elusive concept for the people of that time that they believed only holy people could teach it (that originated in Plato, I think). In Hypatia’s case that religious reverence was amplified and then some, due to her high morals and knowledge. And that is why her reputation had reached such heights.

It was also (in great part) her abilities as a philosopher that gave her such an important position in society. It was her teaching that made all members of higher classes reach for her guidance, it was the character she had created for herself through her teachings that earned the respect of her peers and the acceptance of the Christian community. And it was all those things that gave her influence similar to that of the archbishop.

I’m not even gonna bother with how we don’t have any writings about any of those things first hand. Most are from letters sent from her students (either to her or to each other).

We do have that famous (well, for Hypatia) menstrual cloth story.

There was once a student of hers who fell in love with his teacher. So much so that one day he declared to her his undying devotion (poor chap). Hypatia decided to punish him by showing him one of the clothes she had used during her menstrual cycle, evidence of her female nature. One source adds to that story that Hypatia then encouraged her student to divert his devotion towards music. Some historians accept that addition, some don’t. For my part (and Maria Dzielska’s, I didn’t make this stuff up), if we consider how she was against/disliked all things carnal, it’s not a stretch to believe she would use such a way to point out what she thought as the ugliness and imperfection of human nature (and sexuality) in order to give her student a lesson (no musical encouragement needed for that). Her lesson had to do with how she believed beauty should not be wholly connected with a person or an object. Such beauty (according to Neoplatonism) doesn’t last and therefore is not worthy of one’s time and effort.

I believe this is the end for now. It is safe to say that Hypatia was probably, first and foremost, a philosopher. I found it very interesting to read about how during such a troubled period in history, there was a group of people in Alexandria who managed to make a small model of Plato’s Republic (I should add that it seems there was a sort of hierarchy of students, where a small group had created a circle of belief/trust with their teacher, thought themselves better than the rest and tried even harder to reach that perfect state, though it is doubted that there was any mysticism and ritualistic elements involved) and that was largely due to Hypatia, which in itself is awesome. It is also possible that Hypatia was interested in the cultural background of Greek ideals, not the religious one (and that opinion is supported by the fact that she didn’t involve herself in aiding the pagans when the Serapeum was destroyed, there is no evidence of her taking any part in the whole thing even though she would have been able to use her influence if she had wanted to).

I don’t know if it shows but I was quite out of my depth when it came to the philosophical beliefs of that era (I’m really open to commentary and feedback from people who know better, the point of this whole thing is research and knowledge after all). I had a hard time making sense of how things worked. It was difficult, viewing philosophy as a religious experience and the jump from Camus to Neoplatonism was big. It was fascinating nonetheless and it made the 4th century seem a bit more exotic than it did before I knew any of this (Christ, death, pain, suffering, the end).

I’m so glad the tough part is behind me, I hope I didn’t tire you too much (and that the fact that English is not my native language didn’t add to said tire). Writing about the myths and fantasy-induced martyrdom and sainthood (I’m gonna have so much fun with that one) seems like a field trip now. I can roam free there, no anxiety over being factual. If you’ve read so far, have a great weekend! I hope you’ll come back for the next part 🙂


Maria Dzielska: Hypatia of Alexandria
The Letters of Synesius, Bishop of Ptolemais
Michael Deakin: Hypatia of Alexandria: Mathematician and Martyr
Alan Cameron: Barbarians and Politics at the court of Arcadius

One thought on “Regarding Hypatia #2

  1. Pingback: Regarding Hypatia #3 and #4 | Animestus

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