You’ve always wanted to learn the truth about the interaction between numbers and names, haven’t you? James Propp will be your teacher. In this month’s Mathematical Enrichments, he makes this observation:

 Poincaré once wrote “Mathematics is the art of giving the same name to different things,” and he wasn’t wrong, exactly.

There is no geometry in Propp’s essay, so you might want to characterize it as “pointless”—but you would be wrong. The essay touches on many other branches of mathematics, and is so clear and well-written that I would happily assign it to my Honors Precalculus class if I were still teaching such a class. Being mathematics rather than fiction, you can’t read it quickly; if I really were to assign it, we would take several days to discuss it. But that investment in time would pay off handsomely. Do read it. Slowly. You’ll learn a lot and will enjoy it to boot.

Categories: Math, Teaching & Learning