Beyond Euro-American Mathematics

A New York Times op-ed by  earlier this month calls out university philosophy departments for their lack of diversity. “We therefore suggest that any department that regularly offers courses only on Western philosophy should rename itself “Department of European and American Philosophy.”

The Monte Albán observatory in Oaxaca, Mexico. Image: Rob Young, via Wikimedia Commons.

The Monte Albán observatory in Oaxaca, Mexico. Image: Rob Young, via Wikimedia Commons.

Garfield and Van Norden take the position that philosophy deserves to be singled out in a way mathematics and science do not. They write,

Others might argue against renaming on the grounds that it is unfair to single out philosophy: We do not have departments of Euro-American Mathematics or Physics. This is nothing but shabby sophistry. Non-European philosophical traditions offer distinctive solutions to problems discussed within European and American philosophy, raise or frame problems not addressed in the American and European tradition, or emphasize and discuss more deeply philosophical problems that are marginalized in Anglo-European philosophy. There are no comparable differences in how mathematics or physics are practiced in other contemporary cultures.

Putting aside the fact that it is strange to ignore literature, art, history, or religion, departments that are frequently Eurocentric in ways that mathematics and physics are not, it may not be as clear as Garfield and Van Norden think that mathematics departments should not be criticized for being Eurocentric. The apparent universality of mathematics is one of the things that draws people to mathematics, but nothing takes place in a vacuum. Michael Harris, author of the book Mathematics without Apologies and a blog of the same name, writes,

What is or is not ‘comparable’ is in the eyes of the comparer, of course, and it’s no doubt true that cultural differences are no barrier to communication between contemporary mathematical practitioners in Asia and the rest of the world.  Historically, however, mathematics developed around the world in conjunction with a variety of metaphysical traditions, and this has inevitably affected the approaches to foundational matters.

In another post, he suggests that “the most interesting problem currently facing philosophy of mathematics is to clarify how or whether Chinese and European mathematics differ and how or whether these differences reflect differences in the respective metaphysical traditions.”

I taught math history for two semesters, so I’m hardly an expert on how the subject is taught in general, but I did struggle with how Eurocentric my own math history background and the vast majority of math history resources I came across were. Sometimes it seems like the dominant math history narrative is “Greeks (nevermind that many of the ‘Greeks’ were from North Africa and the Middle East, we call them Greeks so you’ll think of them as European) invented mathematics, it died out around 500 CE, and then Italians started doing it again in the 15th century.” If we’re lucky, the narrative might mention Al-Khwarizmi, whose name gave us the word algorithm and whose book Hisab al-jabr w’al-muqabala gave us the world algebra.

Unfortunately, my math history class fell into the Eurocentric model more than I wish it had. I felt I did not have the knowledge base necessary to teach a class specifically on non-European math well, but I did require my students to do projects on mathematics from “non-western” sources. (It’s difficult to figure out the right label here. I wanted my students to research mathematics from someone whose culture is not well represented in math history books. Non-European is not quite right, because many so-called Greeks were from Africa and Asia. Non-western is not quite right because mathematics from the Americas before European conquest very much counts. In the end, I went with “non-western” in scare quotes and a long explanation of what I meant.)

One difficulty we encountered in researching non-western math sources was that my students and I are all products of the same metaphysical tradition, as Harris would call it, in mathematics, and it was difficult for us to understand mathematics from other traditions on their own terms rather than viewing them through our own cultural lens. Another, as I’ll come back to later, was the dearth of documents available for them, especially if they were interested in math from pre-Columbian America, Africa, or Oceania.

Eurocentricism in mathematics is on my mind right now not only because of Garfield’s and Van Norden’s New York Times article and Harris’s response to it but because I’m on vacation in Oaxaca, Mexico, home to several impressive ruins from pre-Hispanic civilizations, including Zapotec and Mixtec. These civilizations are not as well known as the Aztec or Maya, but they, like those more famous Mesoamericans, were accomplished astronomers. (In the ancient world, astronomy and mathematics went hand in hand in a way they don’t today.) On a tour of Monte Albán, the remains of a Zapotec city, we saw buildings oriented exactly to the cardinal directions and an observatory that occasionally aligns with the sun perfectly. (Perhaps we should call it Albánhenge.)

Heartbreakingly, the destruction of indigenous populations and documents from indigenous cultures means we have very few resources for learning about the astronomy and mathematics of ancient Mesoamerican people. I learned this when I saw how limited the choices were for my math history students wanted to find Mesoamerican math sources for their projects, despite the sophisticated astronomical calculations they did. (Go ahead, try to understand the Maya calendar system!)

I would love to share some good online resources on non-Euroamerican mathematics, but sadly, I don’t have many. Offline, The Crest of the Peacock seems to be one of the best books about non-European mathematics out there, and the North American Study Group on Ethnomathematics publishes a Journal of Mathematics and Culture.

Online, the award-winning MacTutor math history archive has some articles about the mathematics traditions of different cultures. (If you’re wondering why they have an article specifically about the mathematics of Scotland, note that the site is hosted by the University of St. Andrews.) The Story of Mathematics, an online math history site, also has some articles about Maya, Chinese, and Indian mathematics. On blogs, the pickings are a bit slim. I do want to toot my own horn a bit and point you to my students’ math history blog, 3010tangents. There, my students wrote about a lot of topics, including the amazing navigation devices of the Marshallese, the number zero in Babylonian, Indian, and Maya mathematics, and The Nine Chapters on the Mathematical Art, a Chinese math text.

Do you have any more suggestions on where to learn about mathematics from cultures who are often left out of the history mathematics? Please share them below.

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5 Responses to Beyond Euro-American Mathematics

  1. Snezana Lawrence says:

    knowledge can only be passed on where there is communication. Ask non-eurocentric non-American scholars and colleagues to suggest their sources perhaps? A translation project?

  2. Peter Rowlett says:

    The Oxford Handbook of the History of Mathematics takes a global approach (but is a book – not exactly what you asked for!):
    https://books.google.co.uk/books/about/The_Oxford_Handbook_of_the_History_of_Ma.html?id=IZN9DwEACAAJ

  3. J Rogel says:

    Mayan and Aztec maths counting systems are base-20. I remember getting a few resources about doing calculation with the Mayan numeric system based on lines, dots and zero (representen by a shell). Will have to dig around and find my notes!
    J

  4. Patrick Fleury says:

    Try “Japanese Temple Geometry” by Fukugawa and Rothman. It is published by Princeton University Press. There is a smaller article called, also, Japanese Temple Geometry by Jill and Claire Vincent of the University of Melbourne. You can find it here:http://files.eric.ed.gov/fulltext/EJ720042.pdf

  5. Niles Johnson says:

    There is some interesting geometry in the Earthworks of native cultures in Ohio (Google for Newark Earthworks). There is definitely something interesting there. For example, they constructed enormous squares and circles with the same area. The Earthworks date from around 2000 years ago. I only found out about them after moving to Ohio, but still haven’t seen a good explanation.

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