Idea: People hate math because math is not a language, but everybody says it is.
Gallileo said that the “book” of nature “is written in the language of mathematics.” But mathematics isn’t a language. Mathematical signs don’t have meanings like linguistic signs. They have rules that govern how you can move them around and replace them with other signs. Mathematical signs are like pieces on a chessboard, not like words.1
I know, Wittgenstein said that (most) linguistic signs have their meaning based on their use in “language games.” But if by that he meant that linguistic signs function like pieces in a game of chess, he was just wrong. Or, rather, he was confusing linguistic signs with mathematical ones.
The problem is that no one teaches students to think of mathematical signs like pieces in a game. No one teaches kids to play math. So, students get stuck trying to understand or read mathematical problems as if they were learning a foreign language. But math isn’t a language. So, instead of having fun playing mathematical games and solving mathematical puzzles, students end up miserable.
For more on the various types of signs, see my article in The New Yearbook for Phenomenology.