are combinatorics-leaning mathematicians very good at mental math?

Question

a common cliché in movies is that mathematicians who specialize in combinatorics are very adept at mental math (arithmetic), is that a real thing? if yes why?

Answer 1

I think the reason for that is that combinatorics is one of the easiest to understand disciplines to a non-mathematician. If people start talking about Galois extensions of splitting fields of whatever, no one knows what's going on. However, combinatorial problems are often easy to understand. That doesn't mean that they are easy to solve, not at all, but the problem can be explained in terms known to a wide audience.

I would guess whenever a movie wants to show a "genius mathematician", they take combinatorics, because there people can actually understand the problem, notice that they have no idea how to solve it, and then maybe even understand part of the solution presented. It has nothing to do with higher intellect in combinatorists.