I think the answer is both yes and no. I think the conventional way certain subjects are taught can preclude someone, regardless of how good they are at a subject from ever fully understanding it. It simply does not make sense to the person and no amount of diligent study will change that. I do think, though, that a different approach to then entire subject (though perhaps so different that no one has yet thought of how to actually accomplish this approach) may open it right up.
Using myself as an example, I really excel at academics. Math included. But something about calculus made absolutely no damn sense to me. I spent hours in class, i went to student tutors. I finally hired a private tutor and he exasperatedly told me that I "just do not get it" and that I cannot comprehend calculus and its something that you cant memorize as numbers change each time.
what I eventually did was go back to the calculus proofs. Those giganto page long proofs where 18 things cancel each other out and finally become smaller mathematical facts once simplified. I understood (to some degree) those monster proofs. I understood the logic of them and I could manipulate them. But I could not mentally handle the smaller condensed versions. So i created a method of approximation of the correct answer (ironic given calculus is math of approximation and im approximating the calculus answer) from the giganto proofs. It took me ages to do a problem, but I went from a student with a <50 average to a B+ student from the half way point of the class. I probably got 95 or better on every test from the second half on.
Of course the issue was that regardless of how well my approximation worked in getting the right answer and making lotsof hard to decipher math work to confuse my professor... i still didn't know calculus. Because of this physics was rendered impossible. Physics, at least at my institution, is 10% algebra and 90% calculus based. The amount of time it would take to do multuple calculus problems per physics question rendered the class effectively impossible. No matter how much I understood physics.... and i really did. I could explain everything theoretically perfectly. I could not do the math of it because i could not wrap my head around how calculus works.
I still cant. I've tried to reapproach basic calculus in some time off between college and medical school. with 2 semesters of physics and the MCAT behind me, I still couldn't make head from tail on the most simple of calculus problems from my introductory calculus class. Yet I can write out a page full of math and approximate the right answer even if I dont know why and it takes 10x longer for me to do it rather than everyone else.
It's just not interesting to me.
