I whole-heartedly agree with everything you wrote. I competed in Math competitions while in high school but never made it to the IMO. My friends who went to th

I whole-heartedly agree with everything you wrote. I competed in Math competitions while in high school but never made it to the IMO. My friends who went to the IMO were doubtlessly very smart, but they had something else: they had many years of training under their belts. I failed because I was an amateur, they succeeded because they trained like professional athletes. To do Math, intelligence is required, but not sufficient. Tenacity, patience, stubborness, an obsession to figure things out, and the willingness to work very hard are also required. Prof. Terence Tao knows much more than I do on the subject and he explained things clearly: http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths http://terrytao.wordpress.com/career-advice/does-one-have-to... When one is young, one does not mind feeling stupid. Understanding something in Mathematics takes a lot of time and effort. After a certain age, one does not want to feel that stupid anymore. That's why many great mathematicians did their best work before they were 30. It's more psychological than intellectual, I'd say.