For math, abstraction is both a blessing and a curse. It is a blessing, because the mighty of math comes from abstraction—his ubiquity rests on its transcending specific physical forms of the matter. It is a curse, because abstraction runs against the nature way of human thinking.
Although natural languages are a form of abstraction. Learning them involves trials and errors, the practice, the frustration, and the desire to express ourselves. When practice occurs daily, picking up a natural language comes naturally. For most people, however, that learning process stops once he master the natural language. But , like any other art form, math requires long, boring practice. Just as exercise strengthens one’s muscle, doing math thickens one’s logic fiber. But because practice requires effort(let’s face it, we human are lazy), we won’t do it, if we can get by.
Then there is the misconception. Most people believe, wrongly, math is all about numbers and formulas. This misconception is largely our education’s fault. Indeed, before college, math hardly moves beyond numbers and formulas. But they are just a small part of the big math enterprise. If anything, math is about relations. The trouble is, they are about abstract objects, not sexy ones.
[Point Loma, San Diego, CA, 12/2009]