The GURPS Basic Set which contains rules for the paper and pencil roleplaying game designed by Steve Jackson describes an ability that you can bestow on a character you are creating.
Lightning Calculator – You have the ability to do math in your head, instantly. If you have this talent, then you (the player) may use a calculator at any time, to figure anything you want – even if your character is fleeing for his life at the time!
This description seems to imply that doing math and calculating are the same thing. Do you agree or disagree? Make your case.
Mathematician Laurent Schwartz won the Fields medal in 1950. The following is an excerpt from his autobiography, A Mathematician Grappling With His Century (2001).
I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully. Even when I was the first to answer the teacher’s questions, I knew it was because they happened to be questions to which I already knew the answer. But if a new question arose, usually students who weren’t as good as I was answered before me. Towards the end of the eleventh grade, I secretly thought of myself as stupid. I worried about this for a long time. Not only did I believe I was stupid, but I couldn’t understand the contradiction between this stupidity and my good grades. I never talked about this to anyone, but I always felt convinced that my imposture would someday be revealed: the whole world and myself would finally see that what looked like intelligence was really just an illusion. If this ever happened, apparently no one noticed it, and I’m still just as slow. (…) At the end of the eleventh grade, I took the measure of the situation, and came to the conclusion that rapidity doesn’t have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant. Naturally, it’s helpful to be quick, like it is to have a good memory. But it’s neither necessary nor sufficient for intellectual success.