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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,

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Welcome to MSE! Some users here find ALL CAPS speak to be a bit rude, so I recommend editing them out of your question. If you feel they should be emphasized, perhaps use this or this. Also, your name is at the bottom of every post, so it's not necessary for you to sign the end of the post. –  mixedmath May 5 '12 at 4:34
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But they are! Research lectures have derivations, in your sense of the term, not proofs. Much of the content of a good mathematical lecture consists of derivations. Sadly, because of a fashion for conciseness, published papers are more proof-like. –  André Nicolas May 5 '12 at 4:38
    
@George It would help to give some specific examples. –  Bill Dubuque May 5 '12 at 4:51
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