I just want to know, what are the essential elements of being a mathematician? Because I want to decide whether I am better to study physics or mathematics in the University. I knew that a lots of people learn mathematic olympiads and got a good result in the competition, but I am not the people who got good result in the competition. I just want to know is result of those kind of competitions represent the future of being a mathematician? and are those people always got a better result in exams of university?