I’m not sure what it takes to be a great anything, but to be a good mathematician you don’t have to be any of those particular things. You need to be open-minded and be able to think flexibly, and be able to see things from many different points of view at the same time. You need to be able to see connections, which often means being able to ignore certain details about a situation in order to see how it matches up with another when those certain details are ignored. But you also need to be flexible enough to put those details back in, and ignore different ones to see things differently. You need to be able to construct highly rigorous arguments, hold them in your brain, move them around, and fit them together with other highly rigorous arguments. And you need a tolerance, or even a thirst, for the increase in manufactured complexity that this brings with it. This also involves creating ways to deal with that complexity, like creating special eggs and then creating a special egg carton to carry them around in. And then creating a special crate for the special egg cartons, and then perhaps a special truck for those special crates, and so on. Thus it often involves building up gradually bigger and bigger dreams from smaller ones, so it calls for a vivid imagination and ability to bring weird and wonderful ideas to life in your head. There is a myth that math and science are separate from “creative” subjects in the arts, but the line between them is really quite blurry. The myth probably comes from thinking that math is just about step-by-step computations with clear answers. But note that in describing a good mathematician, I did not at any point mention arithmetic, computation, memorization, numbers, or getting the right answers. Some computational parts of math do involve computation, but not all math is computational.