## Hypatia: Great Mathematician or Geometry Teacher?

Hypatia, the Lady Philosopher of Alexandria, is best known for her gruesome murder at the hands of a mob in AD 415. Her martyrdom takes pride of place in the historical narrative of many groups including mathematicians and scientists. I’ve written extensively about my search for the “real” Hypatia and the politics surrounding her death. I’m still fascinated and set up a Google Alert on her name, so I can participate in online discussions. Mostly I get hits on her namesake philosophy magazine (they’re looking for a new editor), the digital archival materials software (recently released version 0.8.0) and the woman who blogs about her cat (Hypatia doesn’t like the new kittens.) About once or twice a month there will be a post from a student at some public Q&A site, “So I’m doing a paper on Hypatia. I heard she invented the hydroscope and helped her dad with his math book. What else did she do?”

I realized many people (not just students) are puzzled over Hypatia’s contributions to math and science. There’s a lot of magical thinking about her life and work. The movie *Agora* used a mythical search for heliocentrism (the sun as the center of the solar system vs. the Ptolemaic earth-centered view, held by most people at the time) as a metaphor for Hypatia’s scientific thinking. So what did she do? Did she discover any important scientific or mathematical principles? Was she merely a glorified teacher who would be lost to history except for her extraordinarily brutal death? Here’s my best take on Hypatia’s contributions…and students remember this is copyrighted material; no cutting and pasting for your papers, but feel free to check out the reference at the end, quote and attribute!

## A Little History

To understand Hypatia’s contributions we have to understand her times and what knowledge came before her, as well as the sources of our current knowledge on her work. The early fifth century was a time of major political and religious upheaval. Barbarians threatened the Roman Empire and sacked Rome itself in 410 sending shock waves around the Mediterranean. The institution that was to become the Catholic Church emerged from three centuries of external persecution and internal conflict to flex its political muscles, both locally and in Imperial politics. The vast majority of people were poor and uneducated. Literature, rhetoric and history were more likely to appeal to the educated elites. Philosophy teachers, including Hypatia, taught “higher” mathematics and logic as a means of disciplining the mind and making one more open to the religious aspect of ancient philosophy, but only a special few were deemed worthy of such instruction.

In antiquity, there were four branches of mathematics: arithmetic, geometry, astronomy and music. The first two were “pure” the second two “applied.” Hypatia, according to Hesychius, worked in the first three. She studied and taught both arithmetic and geometry for philosophic discipline, not for practical applications. Astronomy was practical and used extensively to predict eclipses, construct calendars and aid navigation. Many “magicians” studied astronomy to conduct astrology, which was rampant at the time, even though banned by the Church. One of the (highly unlikely) charges against Hypatia by the Church was that she engaged in astrology.

We know Hypatia’s father Theon edited and commented on the “definitive texts” in math and astronomy, making them useful for students (some of them not so bright!) There is evidence that Hypatia contributed to his later editions. The *Suda Lexicon* also says she wrote three books, “a Commentary on Diophantus, [one on] the astronomical *Canon*, and a Commentary on Apollonius’s *Conics*.” Some modern scholars also suggest she wrote or edited a number of other mathematical texts that survive. Let’s take a look at what we know and what we don’t.

In the late fourth/early third century BC, Euclid compiled his *Elements* a text on geometry which included a system of rigorous mathematical proofs that remains the basis of mathematics today. His work was expanded by Apollonius (262 – 190 BC) who more fully developed three-dimensional geometry in “conics” and Diophantus (200 – 284 AD) who founded the branch of mathematics known today as number theory. In astronomy, Ptolemy‘s (90 – 168 AD) *Almagest* laid out the basis for an earth-centered solar system that held sway until Copernicus (1473 – 1543 AD) proved sun-centered heliocentricsm centuries later. These four men comprised most of the modern thinking on arithmetic, algebra, geometry and astronomy at the time.

## Helping Daddy with his Math

Theon used the *Almagest* to teach astronomy because it didn’t require any earlier knowledge of the subject other than familiarity with Euclid’s geometry. Ptolemy taught the needed math in the text. Theon wrote a note in a surviving commentary on Book III of the *Almagest* indicating “my philosopher-daughter Hypatia” contributed to this later edition. Most historians consider the proof of her contribution a technical enhancement where Books III and IV use a new and more efficient way of doing long division. The other books in the *Almagest* use an older method. [As a side note, Hypatia didn’t have the Arabic numerals we use—including the zero. She did all her calculations using Greek letters. Try doing long division with that!]

It’s believed that Hypatia did write the books mentioned in the *Suda* and possibly some other books that are lost. All those dealt with more complicated or “higher” math which would have been of interest to (and therefore saved by) only a few people. Identifying her specific contributions in the surviving texts is problematic. Some scholars believe she prepared the “commentaries” to teach the advanced conics of Apollonius and higher math of Diophantus that survive from antiquity; but that is conjectural. Her name isn’t on any of the surviving documents. There is a lot of scholarly research devoted to analyzing who added what in the various editions of the ancient texts and to what purpose. The upshot is that very little of Hypatia’s writing has come down to us, and most of that, not in its original form.

After all the academic wrangling, no one suggests that Hypatia contributed any *new* mathematical thinking (other than the more efficient long division.) All evidence shows her teaching what was already known (including the most advanced work) in an accessible way.

## Geek Girl

But what about her scientific contributions: heliocentrism, the astrolabe and the hydroscope? Although the movie *Agora* proposed that Hypatia could have discovered heliocentrism based on her study of conics and astronomical observations; that is highly unlikely. I discuss the possibilities in depth here. Although it makes for a wonderful dramatic arc, there just isn’t any evidence for it. As for the astrolabe, it is a navigational instrument that was probably known in Ptolemy’s time and Theon wrote about it. So Hypatia certainly built them and instructed others in how to do it, but didn’t invent it. The same can be said for the hydroscope that her former student Synesius asked her to build and send to him. It’s generally thought this is a hydrometer (or possibly a urinometer), to measure the density of liquids, which is based on Archimedes‘ principles. The principles seem well known to both teacher and student, with no evidence that she invented this device.

So to answer the question implied by my title: does Hypatia’s lack of original contributions in math and science make her “merely” a teacher, undeserving of any praise or remembrance beyond her shocking murder?

## Hypatia’s Legacy

Hypatia and her father Theon were probably the foremost mathematicians in the Roman Empire, and most likely the world, during their lifetimes; but that doesn’t mean they were great mathematicians in the same way as Euclid and Diophantus. They are best understood in the context of the times. The famous Alexandria Museum was dying; the Great Library dispersed and diminished. Only a tiny elite studied the great mathematicians and conserved their work in a time of rampant anti-intellectualism. Faith and astrology were more important to everyday people than math and astronomy; and much more accessible.

Hypatia studied and understood higher mathematics. She devoted herself, as a teacher, to preserve the knowledge of the past through a turbulent time. She was much more than a “mere” geometry teacher. She and her father passed that knowledge of higher mathematics on through their students and their writing. It is through *their* texts and commentaries that the work of Euclid, Ptolemy, Diophantus and other important thinkers came down to us. Without their writing and teaching, higher mathematics might have faded away and needed to be rediscovered later, delaying any number of scientific discoveries. **So Hypatia’s career is not the spectacular stuff of modern myth-makers, but given her times, her sex, and her opportunities; it’s a crucial and important legacy.**

### Thank you, Hypatia!

**Note**: *I relied heavily on the work of Professor Michael A. B. Deakin in his *Hypatia of Alexandria: Mathematician and Martyr* (Prometheus Books, 2007) for the “what we know” part of this essay. He goes into much more detail as to the exact nature of Hypatia’s contributions, the scholarship around analysis of her contributions; and has an extensive bibliography of research articles. I reviewed his book here and highly recommend it.*

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**Hypatia: Her Life and Times**

**Print book and eBook now available in all digital formats.**

Like most bloggers, I obsess over my “views” and track which articles are most popular. Hands down, anything about Hypatia draws the most readers and generates the most discussion. As a favor to my readers and Hypatia fans, I put all the material in one place. This article and many others from this blog and guest posts on other sites are now collected in eBook and print versions (buy direct or order from any online or private bookstore). If you feel you can’t afford the $2.99 for the eBook, contact me through this website and I’ll send you a free PDF copy. Check it out and let me know what you think!

Excellent summary. It’s important to note how crucial those long links in science as they sometimes scan centuries, and, at times, political and social upheaval. Thanks for the post – though I’m not doing a paper. 🙂

Wonderful post, Faith! Well said.

Thanks tmso and Lavender! Obviously, both science and history are passions of mine. It’s fun to be able to combine them.

There is another book worth mentioning; Hypatia of Alexandria by Maria Dzielska (Harvard University Press 1996)

Thanks Witold! I loved Dzielska’s book and reviewed it elsewhere on my site. She did a great job of reviewing the literary myths about Hypatia and covering her philosophy. However, she didn’t cover the math and science. I highly recommend that people read both Dzielska and Deakin for a more complete picture.

Thanks for the fascinating post, Faith. I always look forward to your news and you haven’t disappointed. I have to admit that while ‘Agora’ was a feast for the eyes it did lack a deal of credibility. Sad to think that we might be heading for a period of anti intellectualism in our time as well.

The parallels

arestriking. I shudder every time I hear political and religious leaders disparaging established science such as evolution or climate change as “only a theory” without understanding the scientific process. Equally disturbing are the attacks on “the elites” who are specialists in their fields, as if being knowledgeable about something is a badge of shame. My solace is that I believe we’re well past the tipping point in dispersing general science and that basic knowledge won’t be lost, except in a species extinction event.Excellent article. Although a former math and science teacher, I admit that my interest in Hypatia was sparked mostly by the religious conflict of the day. So thank you for the science and math information.

I am sorry to say I disagree with you. There is evidence that Hypatia worked out the formula for calculating the volume of a cone. She was the last librarian of the great library in Alexandria. The concept of “last” has some significance. It is no coincidence that approximately 40,000 volumes were lost to posterity in close proximity to her murder. There are several theories concerning the demise of the library but none as compelling as that it was burned by Christians during her stewardship, thereby offering a very credible explanation of why she was the last librarian. Then too, you’ve got to deal with the motive for her very gruesome murder. She didn’t get flayed because she was just some run of the mill librarian or teacher. Bishop John of Nikiu thought enough of her as an adversary to the church that she made it into his Chronicles with him gloating away at the methods used to dispatch her. Women don’t get into history for their mediocrity and so I fear you have missed a lot of forest for a very few trees.

Barry S. Willdorf

Thanks for your comments, Barry. I do get your point about her gruesome murder and how important she was in history. I concentrated on those few trees because I’ve covered a lot of the forest in other posts (see my Agora series, book reviews of Hypatia biographies, guest blogs, and my essay on Hypatia’s life.) I’m fascinated by Hypatia, her life and accomplishments. She was a remarkable woman, particularly in this time of great instability and given the obstacle of her sex. Given that I covered those points earlier, this post is dedicated strictly to her math and science accomplishments

becausethey are so often unknown and/or misunderstood. As to your comments regarding the evidence for Hypatia working out the formula for calculating the volume of a cone, I’d be happy to revisit the issue and add a note to my post, if you tell me your sources. Math isn’t my specialty and I relied heavily onHypatia of Alexandria: Mathematician and Martyrby Michael A. B. Deakin, Proffessor of Mathematics at Monash University for the “what we know” part of this post. I don’t recall he included that bit. I may be wrong and missed it in the details. I’m happy to stand corrected with reputable sources.However, I will take issue with your characterizing Hypatia as “the last librarian” of the “Great Library.” From what I’ve read (please see my post on “Burning Books: What Really Happened to the Great Library” and the references at the end) the “Great Library” had declined significantly by Hypatia’s time and the publicly-funded post of “librarian” (more accurately the head of the Museum of which the Library was a part) probably did not exist. Her father Theon, is sometimes associated with the Museum. It is generally acknowledged that Hypatia held a Philosophy teaching chair in Neoplatonism and gave public lectures and private instruction to a small elite group of students. Whether that post was publicly funded or not, is still debated. Also the “40,000 volumes” lost sounds as if it comes from Livy in describing the fires set by Caesar in Alexandria in 48 B.C., “that by chance, at the time of the fire some 40,000 book scrolls of excellent quality were burned in a harbor warehouse.” That’s the only specific number I’ve ever run across referencing any loss at the library (and those volumes were likely trade goods, since they weren’t actually in the Museum/Library, but in harbor warehouse.) Again, happy to stand corrected if you site me your sources. I’m all for getting the truth out…to the extent we know it. Unfortunately, the sources are sparse on Hypatia.

Thanks, Faith. That was interesting, and it gave me food for thought.

Writing my own novel on Hypatia, Deakin and I were penpals. But as he said to me: “The only true source material for Hypatia amounts to 16 pages.” So…to find Hypatia I looked at what she looked at: the philosophers she admired most, the alchemists, and the mathematicians. And then I looked at the Alexandria of her day, at the state of the Roman Empire,and most especially, at the developing Christian church. And then I created the Hypatia that could have, would have, been in a world like hers.

who is the inventor of geometry ?

No one person is known as the “inventor” of geometry, but Euclid is frequently called the “Father of geometry.” According to Wikipedia: “He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His

Elementsis one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.[1][2][3] In theElements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor….Although many of the results inElementsoriginated with earlier mathematicians, one of Euclid’s accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later. There is no mention of Euclid in the earliest remaining copies of theElements, and most of the copies say they are “from the edition of Theon” or the “lectures of Theon”, while the text considered to be primary, held by the Vatican, mentions no author. The only reference that historians rely on of Euclid having written theElementswas from Proclus, who briefly in hisCommentary on the Elementsascribes Euclid as its author.”Hi Faith,

I’m very glad you left a comment on my movie blog the other day. Watching Agora made me extremely curious and I would love to know more about Hypatia. Thanks for the book suggestions. What fascinates me a lot about her, is how dedicated she seemed to her work, the celibacy. The gruesome murder is shocking but it’s unfair that it overshadows her work.

I will come back and read your blog more carefully. Should you wonder, I have logged in with my second blog, my book blog.

Thanks again and good luck with the novel. It’s not finished yet?

I might be a potential future reviewer (if you like).

Hi Caroline! Thanks for commenting. Hypatia is a fascinating woman and unusual for her times. I agree that it’s a shame her brutal murder seems to overshadow her actual accomplishments. She was a gifted mathematician, teacher and respected civic leader. She led an exemplary life based on the philosophy she loved and taught. Only a handful of women in ancient times could be considered in the same light and few combined all those characteristics. On the other hand, there is a great deal of myth-making around her. I personally feel her actual accomplishments are sufficiently great without attributing to her unfounded “discoveries” such as heliocentricism. But I don’t blame people for their hero-worship. She’s definitely one of mine. I wrote my novel because I wanted to tell her story. The book (

Selene of Alexandria) is completed and available in print and ebook form. I’ll be in touch about a possible review.Thanks again for posting!

From my reading I understand that geometry was considered to be an a subject for advanced study in mathematics and, as such, it was considered as essential for training the mind in the logical mode of thinking which was a prerequisite for the study of philosophy. This being so, how could anyone become a philosopher without first becoming a mathematician? Had the quality of teaching in philosophy declined in the years separating Hypatia and Damasius? As far as I can make out his comment about Hypatia being a mere geometer would be like someone referring to “a mere nuclear physicist” today.

As a mathematician I feel humbled and privileged to live in a time where one can learn about the struggles of the ancients from the safety of my bedroom. To be persecuted for practicing our art is truly a tragedy. Thank you for your blog and thank you hypatia and all the others lost to time for your sacrifice.

this really help me know more about hypatia. I admire her more than before now. thanks faith! Thanks Hypatia!

hypatia is the first feminist in the history