You need to be so smart that you jump the chasm between what school can teach you to what you can teach yourself from undergrad and beyond textbooks. Given the

You need to be so smart that you jump the chasm between what school can teach you to what you can teach yourself from undergrad and beyond textbooks. Given the pressure to pass exams, in addition you need to have enough in the tank that learning more maths doesn’t risk your hoop jumping to get into university. Ironically you need to do well in many things that isn’t maths to be allowed to study maths at an elite university. I am sure it helps alot if your parents are professors!