On Math Without Numbers

This book leans toward the simple, and it left me wanting more, but it’s still a well-done attempt to draw people who resist mathematics toward its beauty and elegance. It breaks into four sections — essentially topology, analysis, algebra, and applied mathematics — with an interlude questioning the foundations of mathematics as a discipline. The most interesting was algebra, where most of the book’s complexity (the book’s, not the field’s) lay. The whole project is profoundly Platonic, and I’m not entirely convinced by the “foundations” section, but it’s true that mathematics does seem to work, and that must be worth something. It closes with an argument, via the standard model, that the universe is made of math. It could be — but it also seems so narrowly human to conclude that. Then again, what do I know? I’m just a layman who got curious about math through science fiction and philosophy.