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Subject: Re: just another reverse bitscan

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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