People are born with a sense of numbers. Psychologists have confirmed this. Arithmetic is therefore our gateway into mathematics, in the sense that we build o

People are born with a sense of numbers. Psychologists have confirmed this. Arithmetic is therefore our gateway into mathematics, in the sense that we build on the intuition we're born with and obtain greater intuition. This is why it wouldn't surprise me if mental (or at least pencil-and-paper) arithmetic is correlated with understanding complicated mathematics. For one thing: to get to the complicated mathematics, you need algebra. A major part of algebra is arithmetic on polynomials. If I didn't understand arithmetic on integers, what hope have I on a more complicated entity? Okay, forget polynomials. Maybe they're not important. How about logarithms? A good intuition of logarithms is that the log of a number tells you how many digits it has. Paired with a good intuition of multiplication (multiplying a 3-digit by a 2-digit results in at least a 4-digit) makes it feel obvious that log (MN) = log (M) + log (N). Finally, how on earth can you understand calculus at all without realizing that division by a big number gives you a small number? Using calculators certainly is one way to be "good at arithmetic" in the sense of always getting the correct answer without too much thought, but it does not enable arithmetic to be used as a building block for gaining intuition about more complicated things. And arithmetic is one of the best building blocks we have precisely because we're born with the beginnings of it.