Recently I have been perplexed by a non-mathematical problem.
One of my Indian student-friend is preparing for the next year's IMO exam but he says that he doesn't like simply doing hard and challenging problems. To him it is kind of boring to only solve problems. For example he likes to read the Logical Foundations of Geometry rather than solving geometry problems. He has recently appeared for a number of M. C. Q. exams but did not qualify in any of them.
He couldn't answer even the half of the questions because he didn't want to answer any question which he couldn't prove. I don't think in this way he can crack the IMO exam because in IMO the skill of problem solving is acquired by solving harder and harder problems and its the thing that is required most.
The only thing that he has to his credit is that he has given an elementary proof of Sylvester-Gallai Theorem (a modification of my wrong proof that I asked for verification in Mathematics Stack Exchange), some theorems on Elementary Number Theory (among which one deals with a non-trial method of finding the order of an integer modulo some integer) which are perhaps new (I don't know precisely because I am not an expert in this field). He wants to be judged by his works, not by passing any exam (even the IMO!). He even tried to send his works to some journal and to some mathematicians also but either it was rejected or he got no reply from the corresponding mathematicians.
Basing upon the incidents, I think that the best way to motivate him would be to have recommendation for his work from some renowned mathematician of his interested fields which are only Number Theory, Logic and Euclidean Geometry but I don't think that it will be logical for any mathematician to waste time on his work without knowing that it is something significant. I can tell this to him but probably it will do much harm to him rather than doing good.
Is there any other way to tell him the truth or is there some other way to motivate him to do mathematics rather than trying to seek its logical consistency?