I don't think knowing any specific mathematics is necessary for CS, but having the capacity to learn mathematics is, and most people who have that capacity end up with a degree somewhere in the science umbrella. You don't need calculus specifically, but you need the ability to abstract, to form rules and express precisely where they apply and where they do not.

Maybe the question is then whether someone has that curiosity about maths?

True curiosity and then follow through to be able to learn. Which I would argue is aptitude.