Hypatia: Great Mathematician or Geometry Teacher?

Image of HypatiaHypatia, 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.

Hypatia from the "The School of Athens" by Raphael

Hypatia from the “The School of Athens” by Raphael

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

Hartmann astrolabe

Hartmann astrolabe from Yale University

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.






Hypatia: Her Life and Times

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Hypatia: Hher Life and Times coverLike 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!

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