by Luke Wolcott
I recently finished teaching a summer program for advanced middle-schoolers; my job was to expose them to math they wouldn’t normally encounter in school. Content-wise, this meant things like group theory, diophantine equations, egyptian fractions, elementary number theory, etc. But I also took this as an opportunity to expose them to a mathematical lifestyle. We explored, we followed our curiosity, we researched.
My students loved to hear about the history behind the math – especially the personal stories. The stories that a community carries are instrumental in defining and transmitting the values and norms of that community. Sure, some of them are apocryphal, some are most certainly false. But I couldn’t resist. I told the legends of Ramanujan, Galois, Cantor, Descartes, Erdos, Noether, etc., enthusiastically blending facts and myths.
While these math legends are entertaining, popular, and often inspiring, they are problematic as a basis for transmitting cultural norms, and as a framework for embedding the math community within society as a whole. Reuben Hersh and Vera John-Steiner, in “Loving and Hating Mathematics,” directly address these issues, and, through a substantial amount of biographical data, fill in the gap between math legend and math reality.
Their book is full of fascinating stories about real mathematicians and the communities they build. Some of the mathematicians are well-known, many of them I’d never heard of. Most stories come from the 20th century – the characters are easier to relate to than, say, Aristotle or Gauss. Often I felt like these were stories about my community, not some ancient or mythologized community.
There is a strong emphasis, throughout the book, on dispelling the popular mistruths about mathematicians. I read about the richly emotional lives of mathematicians, and about the diversity of mathematical friendships and partnerships. There are thorough discussions, beyond simple anecdotes and stories, of gender and age in mathematics. The later part of the book explores conventional and unconventional ways that math can be taught.
My favorite chapter is a discussion of mathematical communities. Bourbaki, the Anonymous Group, Gottingen under Klein and Hilbert, the Courant Institute – my pulse quickens when I read about mathematicians self-organizing around a shared worldview or context. Doing math requires establishing and maintaining somewhat arbitrary conceptual frameworks, and so why not do math by establishing and maintaining somewhat arbitrary cultural frameworks? I think (fondly) of the fierce ethics of MathOverflow posting. If you were to (co-)create a mathematical subculture, what would your manifesto say?