On one hand, from my point of view at least there is a general understanding, even perhaps a correct sense of logic that one acquires while studying math and the physical sciences. since I am convinced, and I believe that studies have now shown that all of that math homework actually makes us "smarter", I have long been a stong defender the study of math in particular at all levels. But at the same time, as I grow older and dumber, I have noticed how much of mathematics is memorized. I know this since I have noticed how much I have forgotten. Use it or lose it. But buried in this is a more fundamental issue. I can remember that as I did my homework, many of those wrong answers made sense for a time. Then, as if someone hits a switch, in the midst of doing all of those problems, the correct way of thinking becomes perfectly clear. And what once seemed logical makes no sense at all. So what exactly has happened here? My sense is that the operations are forgotten but the logic somehow remains - as if something was permanently hard wired in the brain. But, AFAIK there is no such hard wiring in the brain. So, is logic [math] really just a matter of memorization, or if not, what exactly is the distinction in this context between learning, and memorizing?