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I disagree.  I too have a graduate degree in mathematics.  I find it
difficult to believe that all of the mathematicians decided at the same time
that certain symbols would be used for certain words/phrases for the sake of
"elegance".  Like anything, the mathematics language has evolved over time.
I agree that eventually the "elegance" of a proof became involved, but I
equate the "elegance" with shorter proofs (it would get very annoying
writing "which implies" about ten times in a proof).  However, all I have to
do is grab three or four graduate math texts of my shelf and start comparing
theorems and proofs, and I easily find that the math language is still mixed
with the English language, and not in a completely consistent manner.  I
don't know if mathematical historians have examine the notation development
itself, but it would be interesting to know the historical perspective.

BTW:  Did you ever notice that for most word/phrases that have a symbol in
mathematics have one or sometimes two symbols, except for " by
contradiction"?

Craig

Eric Kaljumagi wrote:

> > The funny thing is that this has happened before.  In mathematics much
> of the
> > notation was basically to remove English words from the flow of a
> proof or
> > solution.  Phrases such as "therefore", "there exists", "there exists
> a unique", "is
> > a subset of", "such that", "is an element of", "thus the theorem is
> proved", "by
> > contradiction" etc, all have been given single character symbols in
> mathematics.  Of
> > course it took longer to develop than the IM shorthand.  Fortunately I
> never tried
> > to use any of those symbols in my writing assignments.
>
> Although mathematics certainly has developed shortcuts (e.g.: '3 + 2 =
> 5' for 'Three combined with two is five'), I don't think the intention
> was to remove English words.  Rather, the intention was to remove ALL
> words, thus creating a 'language' that was portable throughout the known
> world.
>
> As a graduate student in mathematics a decade ago, I wrote quite a few
> proofs in English, and I'm quite certain that my professors would not
> have allowed mathematical abbreviations in my writing outside of the
> most basic (e.g.:  '42' for 'forty-two'; 'n -1' for 'one less than
> "n"').  The reason for my confidence is because I attempted to use math
> notation in my writing back then, and I routinely failed to convince my
> professors that such was appropriate.  From what I can tell,
> mathematical abbreviations are always to be used when working problems
> but only used when writing about problems when the alternative would be
> too inelegant.
>
> QED?
>
> Prof. Eric Kaljumagi
> LAC/Math
> Mt. San Antonio College
>
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