I imagine everyone here is familiar with the idea of mathematics as a language. I have a few questions regarding the way people look at equations and math in general, using this analogy. I'm reasonably skilled in math up to basic calculus, and so I kind of understand what "math as a language" is all about. For most simple expressions, if something can be factored out, I see it immediately, et cetera. I was wondering whether this starts to happen with more complicated equations as your mathematical skill increases. For example (and I know this isn't terribly complicated), I can easily figure out the equation for kinetic energy in terms of momentum (as opposed to KE=1/2(mv^2), but it doesn't just show up in my head instantly like some other equations do. I guess my main question is, how would you compare learning mathematics to learning to read? After a while, do the terms just fall into place? Do you find yourself performing substitutions (like in the KE equation, but with more complicated expressions) without thinking? I'm just interested in how everyone else views the process of learning how to do math. Btw, mods, feel free to move this if you feel like it should be in the philosophy section or one of the math sections. I wasn't sure.