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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