Point of View

The math teachers that I have known over the decades have had varying models for their work. I've self-identified as a storyteller, trying to share interesting things that my listeners may not have heard about.

Not surprisingly I am drawn to mathematical authors who are storytellers, in particular those who have a point of view. People outside the field tend to view mathematics as dry and inhuman, perhaps because of the commercial pressures on introductory textbooks to be as bland as possible. As a teacher I have rarely been enthralled with an introductory textbook while finding some gems among upper-level texts.

My favorite mathematical authors identify an aesthetic about their niches, a way of identifying what is special and beautiful about varying constructs. The trigger for me to write this particular essay is the first sentence of Michael Spivak's A Comprehensive Introduction to Differential Geometry, Volume I, which begins "The nicest example of a metric space is Euclidean n-space ..."

Someone learning the subject does not necessarily have wide experience with metric spaces. They may all seem equally abstract. Spivak is taking the reader by the hand and showing which among the infinite number of examples he happens to think is nicest. That is a generous author, a storyteller.

Others that spring to mind:  Donald Knuth ("I am going to tell you a lie but it is a useful lie . . ."), Paul Halmos, Emil Artin, Paolo Aluffi,  Shahriar Shahriari, the list is long.

One of the hardest things about becoming a mathematician is that the good writing has prerequisites. I try to point my advanced students to the nicest examples of it.