Nature of talent
So I have a theory about mathematical talent or any other talent. I say that in humans there is a neural mechanism behind generating proofs, but rather than generating a sequence of steps, brain generate a higher level sequence of goals subconsciously. The steps in between these higher level goals require conscious logical reductions, but the goals themselves are just practically magic coming from subconscious. People with talent for a particular field is better at the higher level goals and that is not something they can ever learn from books, its just something they are born with. For example, Einstein out of no where assumed that mass curve space time and spent 10 years proving it, he had a feeling for what is possible and what is not. There were tons of smart people, but no one had a higher level intuition like that. Similarly, Mathematics Olympiad questions can only be solved by people who get these higher level goals by magic. The in between steps are just logical reductions. What do you think from your experience?
People that become good mathematicians or anything else have a magical feeling about what works and what doesn't. So they don't get stucked in tying out all unnecessary combinations. When they have figured out the higher level goals, they fill the gaps by logical reductions. But its all in the neural network, just not all in consciousness.