Author: Tord Romstad
Date: 16:32:04 12/22/05
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HI Alessandro, How cruel of you to tempt me to write yet another off-topic rant! On December 22, 2005 at 18:41:52, Alessandro Scotti wrote: >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. Most textbooks do indeed suck, but going back to the original sources is rarely a reasonable alternative. After all, the original sources were usually written at a time when the subject was not yet very well understood, which often makes them very tedious to read. When presenting a mathematical subject, there is also an obvious problem of finding the right balance: It is not easy to make everything seem obvious and straightforward while keeping the text compact. I think it should be possible to do a better job than most textbooks, though. > >>It resembles my reaction to Beethoven's music. :-) > >Hmmm... which is "Hey, this is the greatest composer who ever lived!"... >correct?!? :-P Don't be silly. ;-) That award goes to Johann Sebastian Bach. Nobody else are close, but honorable mentions to Scarlatti, Zelenka, Haydn, Mozart and Chopin. Tord
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