I have a problem where I forget the proof of a theorem after some time without reworking it out. However, my teacher said that he was able to prove a theorem even without reworking it out for a long time. This puzzles me: is it I am too incompetent, or my teacher is too smart ?
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5I too find it easy to prove a theorem again after I have proved it a dozen times or more. – André Nicolas Jan 19 '15 at 07:52
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4Keep in mind that a teacher usually proves a theorem many times in front of many different courses while the students only see its proof once. – AlexR Jan 19 '15 at 07:59
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4Do not believe everything what teachers say :) In my opinion it is not bad to forget a proof, the important thing is to remember the theorem correctly and to UNDERSTAND it. Then sometimes remembering a proof you can find some other arguments why the result holds. – Janko Bracic Jan 19 '15 at 08:20
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I concur with everyone else's responses, but I will add this: IMO, the mark of a "smart" mathematician lies in what the mathematician does with the preexisting proven theorems, instead of memorizing them or reproving them a dozen times. We learn to prove certain theorems in school so we get familiar with the topic and area of research; eventually, though, we must use these theorems to explore new areas of math. Otherwise, we're just reinventing that wheel, over and over... – daOnlyBG Jan 19 '15 at 16:59
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Yeah , I know about that . But my teacher said those who can't prove theorem that exist are not able to prove other new theorems – Nothing Jan 19 '15 at 18:17
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Your teacher is probably pretty smart, but that's not why he can prove the theorem and you can't. The difference between you two lies somewhere else:
You only saw the proof once, and you also probably only saw somewhere between several ten and a hundred proofs in your life. Your professor proved the theorem in question once every year for several years, and also probably encountered several thousand other proofs in his life.
