I imagine that Ramanujan and many other gifted mathematicians achieved results by derivation, meaning they followed a trail that led to a result, then proved it later if at all. Is this so and if so, why aren't derivations emphasized in education instead of proofs? I find the statement of a theorem without context and without relevance (bearing, concern, objective) and without origin, to be incomprehensible. Is it just me? Do folks who seem to absorb these like sponges have some special facility that I lack? I seem to recall reading that when Newton was criticized for not showing how he came to his conclusions, he said that when his building is finished, he takes down the scaffolding. Doesn't the derivation of a result reveal its bearing? I rarely find that a proof does.
Thank you,