Quote:
Originally Posted by nemo
Oh, I'm terrible. I can "see" a proof almost instantly, but to verbalize it I have to wrestle it out still bloody and kicking and screaming. It can take me weeks to write a proof for something I solved in 2 minutes.
Many of my other friends are much better at it than I am. I figured it was always an ENTP vs. INTx thing.
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I wonder if that is your Ne at work.
I was rather plodding. I would try hard to find counter examples of the theorem I was trying to prove almost immediately. As I kept failing, I tried to notice what was causing that failure and that is usually the crux of the proof I needed. Then I chose a proof strategy that are basic restatements/easy inferences/backward chains form hypotheses and and conclusion. Then I tried to link the "crux" to the two ends of the proof strategy.
If I started having trouble again, I used the source of my trouble to try to construct counter-examples again to what I was trying to prove. If the theorem is true, I would have further trouble constructing counter-examples, and would find another "crux" to the problem and try to link that in (perhaps reconsidering the proof strategy). I could continue like that for hours and hours.
Pretty pedantic huh?
I only immediately "saw" proofs for easy theorems. Of course the more math I know/remember, the easier the inferences/backward chains from the hypothesis/ conclusion was to come up with.
Like in the theorem you mentioned above. The pythogerean generator was a key fact, as was the formula for the in-radius. Those were just things I remembered. I would have been hard-pressed to notice the patterns needed from attempted counter examples to solve that problem through my usual grind.