Why should we prove already proven mathematical theorems?

Replies

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  durga ch

  I had this friend of mine, who would read theorems statements , and prove with her own derivations in exams, while we were in class8/9.
  since the ability of deriving needs to be developed - proving already proven theorems is OK. Also, while doing so - we end up knowing more than just the theorem.
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  Anoop Kumar

  durga

  we end up knowing more than just the theorem.

  👍
  Knowing how something happen is always better than "what" is something.
  for example Sum of Two Sides of a triangle is greater than third side.
  Its like you know the source code vs just know about UI.
  
  and I love writing at the end of question,
  Hence Proved (It felt me like I am a Physicist.😁)
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  durga ch

  yes! i too loved writing - 'hence proved' 😁
  More than that i loved the 'rough column' we used to make to do rough work
• 

  Anoop Kumar

  Edit: posted twice
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  archlpe

  The_Big_K

  I remember in the geometry class, we were asked to do the QEDs, prove the already proven mathematical and geometrical theorems. Maybe the logic was to make us 'aware' how certain proofs were derived and what was the logic. But all I remember was just remembering (mugging) the steps and writing them down. It all seems like an idiotic exercise to me.
  
  What's your opinion about this?

  at first i would feel the same but as i grew older i could feel that deriving a theorem makes the basics clear. also, in the way you get to know more formulas that could prove helpful in solving problems.
  derivations clears the basics and basics are most important for strong journey
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  Ramani Aswath

  I would repeat what the mountaineer Mallory said in 1924.
  Quote:
  'Because It's There'
  Those famous words were spoken by British climber George Mallory in 1924 when he was asked why he wanted to climb Mount Everest.
  #-Link-Snipped-#
  Endquote
  
  It is funny, but I still do it occasionally, just to keep my hand in.
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  vinod1993

  In my opinion. while we try to prove something which was proven already, we gain creativity(but alas, we just mug it up), i.e. we can use those theorems to prove many other theorems by ourselves and who knows we can end up creating our own theorems as well. We gain a very good understanding that never subsides from our memory. Did you know that Ramanujam proved many theorems which were already proven(he didn't know it was already proved but he managed to prove them, Why? Because he understood it well). We can even create elegant proofs rather than mugging the systematic steps. It increases our "Out of the Box" thinking.!
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  Jeffrey Arulraj

  durga

  yes! i too loved writing - 'hence proved' 😁
  More than that i loved the 'rough column' we used to make to do rough work

  Generally I prefer prove sums than to come to an answer
  
  deduction is always strangely harder in practice