Teaching What You Really Don’t Know, Part II

This fall I’ll be teaching a new prep: our senior capstone class on the history of math, featuring an intense research project. The course also counts as a Global Perspectives credit for our students, meaning the class should broaden our students horizons beyond a classic western viewpoint.

Which is great. I’m excited for the challenge, and I think it’ll be interesting to explore this material with them and help train them to be more well-rounded. The only problem is…

I don’t know anything about math history.

I know the anecdotes and the just-so stories that get passed down as asides in lectures: Gauss summing  1 to 100, Euler and Hamilton crossing bridges, the cult of Pythagoras’ thoughts on flatulence. But until recently the closest thing I’d ever done to learning real math history was reading The Baroque Cycle. Which doesn’t count.

So now it’s almost August, my summer class is over, and I have a month to learn math history. I’m starting with a book I started awhile ago, Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander. It’s a real gripping read, covering the state of mathematics in the 16th and 17th centuries (so far, I haven’t finished yet) and how the Jesuits’ abhorrence of the concept of the infinitesimal affected first the development of mathematics, and then the development of the Jesuits.

The mathematics in it aren’t completely dumbed down, but are still pretty accessible to a motivated layman, and the author goes through arguments for the utility of the concept of the infinitesimal, as well as the reasons why many thought such a thing is patently absurd. There are also some really relatable stories in the book: colleges throwing shade at their weird mathematics departments, academics struggling to get hired, and people claiming to read the standard treatises of the time, even though it was obvious nobody had the patience to slog through a particular author’s borderline-unreadable text.

I’m selecting some sections for students to read, and one thing I’m having to really pay attention to is the amount of cultural and historical context the author takes for granted. He does lay out a short history of the reformation, and the Jesuits arising in response, but if I pull other sections without that context students might get lost.

Two other books are on the docket once I’ve finished this one. One is Journey Through Genius, by William Dunham. I’ve read bits of this, and one of Dunham’s other books The Mathematical Universe, and I really enjoy his writing. The other is the textbook I’ll use for the course, adopted by the previous instructor, Math Through the Ages by William P. Berlinghoff.  The subtitle is A Gentle History for Teachers and Others, but I’ve been told not to let that fool me into thinking this is kid stuff. I’m sure I’ll let you all know how it goes.

Any other recommendations for math history? Books? Podcasts? Documentaries? Especially ones with a non-Western focus? Lay ’em on me, because I’ve got a whole semester to fill.

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12 Responses to Teaching What You Really Don’t Know, Part II

  1. Avatar David Chamberlain says:

    My ‘Port of First Call’ is “A History of Mathematics” by Boyer and Merzbach. 9780471543978.
    632 pages of text followed by 32 pages of References organised by chapter and 11 pages of General Bibliography. Merzbach did a fantastic job of editing the original and making it readable to a general audience. I have tried, and failed miserably, to get through Boyer’s “The History of Calculus and its Conceptual Development’, but his writing style I can only think must have been ‘old-fashioned’ when originally written.
    The book covers the period from pre-history until about 1950, with a third of the book dealing with up to around 1000 AD and very little post 1900.
    For me, one beauty of the book is that one can, quite literally, open the book at any page and read as if nothing prior to that page mattered.
    It has one weakness (again a personal thing) in that there is a very strict definition of mathematics and therefore contains nothing on the development of statistics.

  2. Avatar David Chamberlain says:

    Re. my earlier post. I forgot to add that, apart from a couple of chapters, this is very much a western world view. China gets one chapter, India another, but one could be forgiven for thinking that only Europe and, to a lesser extent, North America contributed much. That there is relatively little about the US is, I think, entirely due to the time period for the work.

  3. Avatar Mark Hartman says:

    Where do you teach? I’d love to take the course!

  4. Avatar Ana Rita Pires says:

    I recently asked a former colleague for advice about history of math books (for a friend who is teaching it next semester).
    The former colleague had taught history of math out of “Mathematics and its history” by John Stillwell. He said it was very good for the professor, but that the exercises are not very good for the student. But he would use it again if teaching advanced students.
    He added that the book by Victor Katz looks more accessible and might be better for less sophisticated students.
    He also mentioned a Springer book on the history of calculus by CH Edwards that he liked but thought it might be too specialized.
    Hope this helps a bit!

    • Avatar smalec says:

      I’ll have to track these down. Thanks!

    • Avatar Russ Woodroofe says:

      I also taught out of Stillwell. I liked it, and I don’t think the students hated it. It probably helps if you’re teaching seniors who already know some stuff. The exercises are more math-based than history-based, and some of them presume some maturity. I mixed some essay and short-answer type questions in with some math-based questions, and met students in a group once/week to provide some homework guidance.

  5. Avatar Judith Khan says:

    Great Moments in Mathematics before 1650 by Howard Eves published by MAA Duolciani Mathematical expositions No 5 ISBN-0-88385-300-0

    Great Moments in Mathematics after 1650 by Howard Eves published by MAA
    Duolciani Mathematical expositions No 7 ISBN-0-88385-310-8

    Episodes from the early history of mathematics by Asger Aaboe
    published by Random House for SMSG
    library of congress catalogue # = 63-21916

  6. Avatar Ricardo Sanchez says:

    Amir Alexander books are a good source, since your course is for a broad audience .
    He has another about Fermat’s Last Theorem. “Men of Mathematics” by Bell (it in ludes women), “History of Mathematics” by Edwards and “Maria Kovaleshkaya” by editor MIR. There are also beautiful talks at the JMM San Diego 2018, about the history of Mathematics between England and USA.

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