Reading is a vice for me—I can lose hours, nights of sleep, whole weekends in novels. Often I read non-fiction to keep from getting so sucked in, and mostly that means general audience (GA) math. Everyone who has read many GA math books would probably agree that some are not good. It can be hard to strike a balance between including enough math to say something substantial and being willing to lie or speak generally enough for the book to be understandable. I think it may be really hard to do this perfectly for a truly general audience, which is the dark secret of some of these books—they are very difficult or impossible for non-mathematicians to understand, though they try very hard to be perfectly accessible and take great pains to explain concepts in non-frightening terms. However, if you are not used to reading math this can still be very dense, and who but a mathematician would care much about these topics anyway? So these books are often not good for a general audience, but perfect for someone with a PhD in a different area of math. No complaints here, as that audience is me. Presumably many writers, and certainly their publishers, want to reach more people; for example, at least undergraduate math majors. Good GA math books are actually perfect for undergraduate math majors, and I often find myself loaning out my books to students. Most are not returned.
I read two GA math-related books this fall that in fact reached much farther than the math world: Hidden Figures, by Margot Lee Shetterly and Birth of a Theorem, by Cedric Villani. These books both escape the GA trap in different ways. Hidden Figures is the true story of black women mathematicians working for NASA beginning during World War II (in case you’ve been under a rock and haven’t heard about the movie that is coming out soon). This carefully-researched book introduced me to a part of mathematical history that I had no idea existed. Many of the “West Computers,” as they were called, had originally pursued mathematics for joy, as they did not need to learn much higher mathematics to teach in high school, essentially the only mathematical path available to black women at the time. I loved reading about the pride that these women took in their work when a path was finally opened to them at NASA. I also had no idea of the major role that they played in many of NASA’s achievements, and the difficulties they faced down in the process.
How does Hidden Figures avoid the GA problem? By including very little math. Several physics/aeronautics ideas are generally explained, but it doesn’t contain a single equation. That makes Hidden Figures a truly general audience book, with additional interest for mathematicians. Which is great. I didn’t learn any math here, but I learned a lot that is relevant to my life as a mathematician, and really my life as an American, or a human in this time. Math is essential to this story, if only as the medium for these women’s undeniable awesomeness. Because they were doing math, there was some limited sense in which their correctness and in the end their contributions could not be denied. The answers were right, and the rockets flew. The importance of their contributions, however, is still being fully understood, and this book plays a big part in that.
Birth of a Theorem is in some ways a total contrast. It is the story of Villani and his collaborator Clement Mouhot’s proof of a fantastic result in mathematical Physics, after which Villani won the Fields medal in 2010, told through Villiani’s journal entries, emails, some mathematical and historical interludes, and many pages of just plain really hard mathematics. Villiani talks about his work with passion and self-awareness. He is not at all condescending in describing what he does—he explains things in a way, but also doesn’t expect to teach the reader everything. In fact, I didn’t understand much of the math from Birth of a Theorem. If you already knew a lot about this area, perhaps you would. But even as he uses all kinds of mathematical terms without definition, they take on the character of foreign language passages in a novel—you really don’t have to understand to get the feeling of it. He describes the many horrifying setbacks and surges of joy that come with trying to prove something hard. He describes his favorite music and his favorite theorems with some of the same devotion. It seems to me that Villani is totally obsessed with math, in the same way artists can be totally obsessed with art. It’s basically about creativity at a really high level, in the form of mathematics.
I loved reading these books in sequence because it juxtaposed incredibly different paths in mathematics: Villani, already a world-famous mathematician before winning the Fields medal, now a figure in French popular culture and writer of a book with blurbs by Patti Smith and Nassim Nicholas Taleb. The West Computers, just now being discussed at all, 70 years after they started at NASA.
To bring it back to undergraduates, I think these books could start a really good student discussion on what it means for mathematics to be important, and how we value people’s contributions to math. There are also great GA books out that do teach a lot of math along with the stories; for example, Journey through Genius by William Dunham, and The Code Book, by Simon Singh. So many big ideas in (and whole areas of) math just don’t fit into most undergraduate programs. Books like Hidden Figures and Birth of a Theorem don’t really teach much math, but do teach a lot about math culture, which is also very difficult to bring into undergraduate math classes but could give our majors a much greater sense of being part of a community. This leads to one of my current dream courses to teach: Math Book Club. This is not my idea; I heard about it from Dr. Amy Ksir, who teaches a wonderful Math Book Club class at the US Naval Academy. I sat in on her class and was really impressed. At the end of the semester, students write up book reviews and submit them for potential publication. After talking to Amy, I started to think about my own version, which I want to develop as a course sometime in the next few years. In my dreams, Math Book Club would help students expand and fill in their pictures of the general mathematical world, as well as have these discussions about what math means.
What would you read in your Math Book Club? How do you share the broader world of math with your students? Please let me know in the comments!