I do think that it takes years of general dedication towards learning to start tackling such topics, and it takes confidence to know that what one is aiming for is achievable, and it takes the honesty to realize when one truly is and when one truly isn't understanding some topic. I am continually astounded by the insight and intelligence of what some on this board might consider regular folk, and I think that what sets me apart from the masses isn't in hardware (a better brain), but software (beliefs and an outlook more conducive to learning).
From your list of accomplishments, I suspect one of the skills that sets you apart is your time management capabilities. Otherwise commonly known as self-discipline.
Unlike physics say, students have less reason to trust those higher up in this way in a field such as computer science.
"Learn everything from first principles, and when something looks wrong, bring it up."
I barely passed Calculus III; there is no way I could have proven any auxiliary theorems.