Author: Dann Corbit
Date: 17:15:46 12/22/05
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On December 22, 2005 at 19:32:04, Tord Romstad wrote: >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. CTF material for sure, but my favorite is Holst.
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