WMY2000 NewsLetter 3
LETTERS TO THE EDITORS
MATHEMATICS 1900-1950-...
In spite of the scientific value and the historical interest of
Hilbert's
famous Twenty-Three
Problems enounced in 1900, one must agree that mathematics have
developed
in unforeseen
directions throughout the XXth century.
In 1992, a symposium held in Luxembourg addressed the
comprehension of
that evolution
during the first half of the present century. One issue was the
publication of the volume
"Development of Mathematics 1900-1950" (Birkhäuser, Basel, 1994,
3-7643-2821-5, 0-8176-
2821-5)" with articles by J. Dieudonné, J.L. Doob, G.
Fichera, M.
Guillaume, W. Hayman, C.
Houzel, J.-P. Kahane, A. Lichnerowicz, J. Mawhin, L. Nirenberg,
J.-P.
Pier, W. Schwarz. The
book presents a chronological list of major results obtained
during the
period under study (P.
Dugac, B. Eckmann, J. Mawhin, J.-P. Pier); it also contains a
list, drawn
up by P. Dugac, of
original and reference sources.
Whereas it is already hazardous to undertake this investigation
of
evolution up to 1950, a
still more ambitious task would consist in tracing these
movements during
the later period, as
former classifications and structures do not seem to apply any
more. A
group of persons has
started on this historical and thematic study in view of World
Mathematical Year 2000. They
should appeal to specialists for contributions covering a wide
spectrum
of themes which would
ultimately be linked by logical connections.
Liaison address : Jean-Paul Pier, Mathématiques
Centre universitaire de Luxembourg
162 A, Avenue de la Faïencerie,
L-1511 Luxembourg (Luxembourg)
Fax : (352) 46.66.44.237.
e-mail : pier@crpcu.lu
MUSIC AND MATHEMATICS : DREAM OR REALITY ?
Some years ago, I used to be irritated by the commonplace
saying
that mathematicians had
a privileged relationship with music. However, for some time now,
a
number of contacts with
people whose intellectual life was devoted to these two poles,
and my own
experience as
musician and mathematician, have led me to rethink this view. In
the
Middle Ages, the
Quadrivium included the four basic sciences which were
arithmetic,
geometry, astronomy and
music. And Leibniz still spoke about the "secret calculation".
Could this
close tie between the
two subjects over many years account for the symbiosis which we
seem to
note today? This
question leads to another : although the medieval learning
mentioned
earlier derived from the
Greek system, it was widely dominated by the Western European
schools.
Did this give rise to
a qualitative or a quantitative difference in the relatedness of
the two
subjects in Western
Europe and in countries with a completely different culture like
China or
India for instance?
These are questions we would like to attempt to answer in the
context of
a study for the
World Mathematical Year 2000. A questionnaire was proposed to the
members
of the Société
Mathématique de France (SMF) with a view to collecting
statistical
data that will allow us to
confirm or to infirm this music-mathematics relationship. We are
planning
to carry out a
counter-test in another scientific area (possibly chemistry) to
see if
differences emerge.
This operation has already been successful among members of the
SMF. We
would now
very much like to submit it to a wider sample. The questionnaire
is now
available in English on
the web :
Questionnaire Mathematics and Music .
In advance we wish to
thank all
those who agree to
spare a little of their time (not more than fifteen minutes) to
fill in
the questionnaire.
Also, as I am new in the field, I am slowly discovering that many
people
have already
delved into this issue from a historical, psychological or
philosophical
point of view. So I do
hope that the people I have not yet had a chance to get in touch
with
will kindly let me have
their opinion (and a bibliography, if they wish) in order to give
more
weight to the project.
Liaison address Laurent Mazliak
Laboratoire de Probabilités
Université Pierre et Marie Curie
Tour 56 3ème étage
4, Place Jussieu
F-75252 Paris Cedex 05
France
Back to summary