The simple reason is that what you think is math is actually not math at all. When I started studying theoretical math, on my first day, I was told to complete

The simple reason is that what you think is math is actually not math at all. When I started studying theoretical math, on my first day, I was told to completely forget what I have learned in school because "it is not math". And then when we talked with our professors about them giving lectures for other students (studying electrical engineering or physics, etc.) we would hear from them something like "Yeah, these guys think math is hard but they don't actually study math". In short -- adding or multiplying things, applying numbers to formulae -- isn't math. Actual mathematicians do not need to calculate a lot of stuff in their heads (though estimating things is sometimes helpful) and don't need to remember formulae (although if you spend any time doing actual math you will learn a lot of formulae). And if they need to they are just as likely to pull out a calculator or Google as any other person. And funny thing is -- before I went to study math I have attended trade school. There, besides a lot of useful topics like economics, accounting, law, touchtyping, etc., we had one semester of actual arithmetic. Which was actually about calculating stuff in your head, fast. We would spend ENTIRE time learning tricks to calculate things faster. And the exams would consist solely of sheets of paper with columns of things to calculate (multiply these three six-digit numbers, etc.) which we had to do in memory.