Taking math classes in school, even at the graduate level, feels like pattern matching to me. On all tests and most homeworks you're expected to stare at a prob

Taking math classes in school, even at the graduate level, feels like pattern matching to me. On all tests and most homeworks you're expected to stare at a problem long enough until its structure becomes isomorphic to something about which you memorized a theorem. Whether you understand what makes the theorem tick or not is a separate question, but I found a workable test taking strategy in my classes consists of memorizing the theorems that the prof made a big deal about in class, and then just running down the list for each problem. Research math is more open-ended but the idea is the same. The quantity of genius mathematicians who sit down, a la Newton or Gauss, and invent their own mathematics out of thin air is exceedingly small. Most research in math today, even among the "big" papers, is pretty incremental.