Maybe I am reviving an old thread (one year old, in fact)...  But I would
like to add a small personal contribution to this!

I do not mean to add myself to a glorious list including Lutoslawski and
others, but as I would probably be acccurately defined as a musician and
mathematician, I have often come across this comparison.  (To set the
background image, I studied the violin at the Paris Superior Conservatory
of Music, played in several major Parisian halls in my early 10s, was
chosen as a 1988 laureate of the Y.Menuhin Foundation by a jury presided by
Menuhin.  Later I graduated from one of France's two or three major Schools
(colleges of University level) for science and engineering and I am
currently completing a PhD in geometry.) The point is that I often hear
comments such as "oh yes, music and mathematics are closely related, aren't
they? " Sometimes people suggest that I should turn to computerized
composition.  Of course, this common belief comes from Pythagorician scales
and the like, and also from the idea that both mathematics and music demand
a lot of rigour.  But from my own modest experience, I would say that
whereas similarities are factually numerous, the deepest reasons why one
devotes himself/herself to each of both fields are vastly unrelated.  An
instance of essential differences existing between them is the following:
mathematical theories try to set theoretical patterns which are as general
as possible, but they form a universe which is self-contained to some
extent and cannot pretend to encompassing or reflecting all aspects of life
(at least, it should not, and those mathematicians who assert the contrary
often turn out to be a bit dull out of their field...).  In particular,
maths are not Art, even if they can be found as a powerful tool in many
artistic masterworks.  Music, while often being much less perfect and
almost never achieved, does reflect (in its own ever-changing language)
elements of life which are basically non-musical, and gives birth to new
musical cells which are mysteriously reminiscent of their unspok!  en
source.  This also gives music much of its subtle healing power.  There is
a genuine similarity, though:  the fact that both fields keep in touch with
the elementary at every moment.  It is truly part of their strength.  In
particular, neither a mathematician nor a musician should mistake
complication for complexity, confusion for density...  although many do.
Socially speaking, apart from a common feature (many professional
mathematicians know nothing out of their particular field, and the same
goes with many instrumentalists, apart from the truly great musicians), I
could say that both worlds are quite ignorant of each other.  Well, quite
a few scientists enjoy music, they are devoted music-lovers and like to
show their skills on a piano -- often in "effective" pieces, such as Liszt,
within a kind of untold "best amateur" competition -- and they can also be
sharp music critics who can describe a concert down to the second, while
nothing will be said about inspiration or creative process.  However, many
scientists simply find classical music boring, except maybe those Bach
fugues which, they were told, are worth 30 simultaneous chess matches.
What is sure is that (at least in France) most professional musicians
totally lack any interest in mathematics!  They often are most defiant of
formal analysis, anyway, as though it were a mortal threat against genuine
artistic expression.  That it could open new paths to approach their "inner
truth" is something they would never acknowledge.  On a side note, I would
say that whereas some scientific methods definitely can help as a working
tool, mathematical theories used by some composers as their "flags" often
are rather basic and/or not fully comprehended by them from a scientific
point of view.  I would not be too sure about this, but statingthat
Stockhausen would win over all astrophysicians might well be a gross
overstatement...  Poetry using fashionable scientific concepts can lend an
interesting colour to a piece of music, but it rarely brings major advance
in fundamental science.

Well, those are only hints, bits and pieces.  Right now, I would not write
an essay about this (my PhD is calling me back to work!)

Happy New Year to all,

Thanh-Tam Le