Author: Alessandro Scotti
Date: 15:41:52 12/22/05
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On December 22, 2005 at 17:33:12, Tord Romstad wrote: >My mathematical aesthetics are similar. I hate to include >clever and poorly motivated tricks in my proofs, even when >they are simple and logically correct. Everything should be >a progression of small and completely obvious-looking >steps, giving the reader the feeling that she could easily >have done the same work herself. Yet, the opposite is usually true in all textbooks I've ever read. I remember my amazement when studying the proofs of some advanced theorems, although the strongest memory I have is related to Riemann integrals, which are quite basic after all. At any rate, a lot of such proofs consisted in a series of seemingly unrelated corollaries. Then, all of a sudden, they were put together with a few simple steps to form a beautiful theorem! :-O It looked like almost magic at the time, and I would always get the feeling that only the highest minds could conceive such demonstrations. Once dropped outside of the univesity, I started to dig out some old books, trying to get the *original* proofs for those theorems. Whoops! Quite different stuff to be found there! Usually longer and apparently less "brilliant" but at least you could see the reasoning behind! A comforting discover, but seemed to confirm my idea that most textbooks just suck. >It resembles my reaction to Beethoven's music. :-) Hmmm... which is "Hey, this is the greatest composer who ever lived!"... correct?!? :-P
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