Problem regarding mathematical skill of a math lover

Question

I don’t know whether it would be a good idea to seek solution for some personal problem here. But as there’s no harm in asking I’m putting it under the soft tag.

It’s about forming a career in mathematics for an individual like me for whom morning didn’t actually show the day. It not before 14 that I actually got interested in Mathematics when I choose (don’t know why) ‘Mechanics’ as my optional subject. Earlier to it I had a consistent mediocrity in the subject. But everything started to change ever since Mechanics came into my way. I started to realize the scope of the subject & the harder problems started to drive me crazy. I fell in love with Mathematics & my performance started to increase at a consistent level. Ever since I’m with it and today I’m very happy with my decision with a dream of being a mathematician. Right now I’ve completed my master in Mathematics with a high grade with a dream of having a PhD from some reputed institution.

But now as I’m preparing for the competition exams like NET (sample question), NBHM (sample question) or ISI (sample question) for pursuing PhD, I began to feel that I’m slower than I should be. Many a time, the solution of a problem occurred to me much later than others (preparing for the same). Even when I found the trick for a solution I didn’t get why I took so much time to crack it. But I think how fast someone crack problems determine his career in the field. All this things have provoked me to present my questions in the forum:

Does all this happen because of a lack of talent or because of a Mathematicians are designed from the childhood in some other way?

Can my mathematical skill be improved to a Mathematician's level?

Answer 1

I think mathematics is an artificial language that makes possible very profound thinking. As with any other human technique, there will always be people who seem to do everything effortlessly and are always brilliant. These are geniuses and very rare and special human specimens; they are to admire.... but mathematics is not about discovering geniuses, but about a particular way of deep thinking which's only purpose is to enlighten the thinker himself.

But society and people will take every possible excuse to show off how marvelous they are. People will use whatever technique to prove themselves better than everyone else.

I am convinced, that the pleasure a genius feels when he understands some particular mathematical concept and plays with it in his mind, is the same one that you feel when you do it. The pleasure that one can feel by being the best at something has little to do with mathematics. It is the same pleasure a guy can feel by being the one who jumps higher or the one who made some pointless Guiness record. It has nothing to do with the pleasure and satisfaction one can find in mathematics' deep thought.

So keep on studying, love what you study and know that doing what you love is the best thing you can do in life.

To the first question: Some seem to have a special ability to do exams, that's all. In my opinion exams are merely in the way and must be passed so that one can do what is really important, in this case, mathematics.

To the second question: Absolutely, you can train yourself to "mathematician's level" and you will love it.