“Thinking carefully” is necessary but not sufficient for “math things”.
a better model for a successful mathematician is someone who is past a certain innate ability threshold who has the drive to keep going and the morale to not give up
I don’t know about that—there are opportunity costs. Let’s say you’re smart, and conscientious, and have good analytical skills, etc., but not particularly good at math. Yes, you can probably make a passable mathematician if you persevere and sink a lot of time and effort into learning math. But since math is not your strong point, you probably would have made a better X (social scientist, hedge manager, biologist, etc.) with a lot less effort and frustration. Thus going for math would be a losing move.
“Thinking carefully” is necessary but not sufficient for “math things”.
I don’t know about that—there are opportunity costs. Let’s say you’re smart, and conscientious, and have good analytical skills, etc., but not particularly good at math. Yes, you can probably make a passable mathematician if you persevere and sink a lot of time and effort into learning math. But since math is not your strong point, you probably would have made a better X (social scientist, hedge manager, biologist, etc.) with a lot less effort and frustration. Thus going for math would be a losing move.
And, of course, this.