Backwards and Forwards: Reflections on Different Approaches to Algebra

Abstract

This chapter is based on my closing remarks at the colloquium that gave rise to this book. But before I get to the main purpose of the chapter, I would like to make a comment triggered by one of the contributions to our closing discussion. Lesley Lee gave a passionate, and very moving, plea that we share the algebra culture more widely. Induction to it, she feels, shouldn’t be restricted to a minority, depriving whole chunks of the general population of the sort of intense pleasure, of fun, of achievement, that all of us were probably fortunate enough to experience.¹ While I empathize very strongly with the general sentiment, I also feel sure that there will always be people who will resist attempts to get them to join the algebra culture. I don’t deplore their resistance; I expect it, even welcome it. There are many other worthy human activities for people to enjoy and profit from. A person can have a very good and useful life without knowing any algebra at ail-any mathematics, even—just as I have managed to get along without any Latin and Greek, and without ever painting in oils, playing football, or learning to meditate.