Many people believe that one's maths competitions performances are the standard way of judging one's mathematical ability. But how exactly problems like 'determine a prime number p such that 2^p + p^2 is also prime' is related to 'the insolvability of the quintics' or 'Godel's incompleteness theorm'? I love reading books like abstract algebra. (But of course, at the literature level, say like the maths version of "The Elegent Universe", as I believe this book was intended for readers at all levels of education.) I think I will enjoy the 'philosophical side' of mathematics but I am not good at problem solving. I have straight A+ in all high school maths courses but so does everyone else who wants to major maths. So, does university level mathematics (I mean coursework, not the Putnam Competition) heavily involve the kind of thinking or problem solving skills required in writing a maths competition? And between maths and physics, which one involves more philosophical thinking thant problem solving? Regards, A deeply depressed high school senior who want to major in math but has never qualified AIME.