# Oberwolfach Reports

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**Volume 2, Issue 4, 2005, pp. 3175–3246**

**DOI: 10.4171/OWR/2005/56**

Published online: 2006-09-30

Mathematics in the Physical Sciences, 1650-2000

Niccolo Guicciardini^{[1]}, Tinne Hoff Kjeldsen

^{[2]}and David E. Rowe

^{[3]}(1) Universita di Siena, Italy

(2) University of Copenhagen, Denmark

(3) Johannes Gutenberg-Universität Mainz, Germany

The workshop was organised by Niccol\`o Guicciardini
(Siena), Tinne Hoff Kjeldsen (Ros\-kil\-de), and David Rowe (Mainz).
During the five days of the conference 25 talks were given and one
special evening lecture was organised.

The organizers developed the idea for this meeting in consultation
with several other colleagues who attended the conference on early
modern mathematics held in Oberwolfach January 5-11, 2003. That
meeting brought together historians with considerable expertise on
developments outside pure mathematics. Afterwards there was a general
consensus among the participants that this format had produced
fruitful interactions and some promising new perspectives. The idea
behind the present workshop called for a similar, open-ended
framework, but covering a broader expanse of time reaching far into
the twentieth century. By focusing on the interplay between
mathematics and the physical sciences the aim was to gain an insight
into developments that had a crucial impact on modern mathematics.

This was achieved by inviting experts on the role of mathematics in
the physical sciences who were able to approach this subject from a
variety of different perspectives. The speakers addressed major
developments relating to the overall theme of the conference which
focused on thematic issues structured around three time periods:
1650-1800, 1800-1920, and 1920 up to recent times. Three particular
topics emerged as central themes of interest:

1) Several of the talks on the period 1650-1800 concerned historical
problems involving the role of mathematics in natural philosophy
during the Scientific Revolution and the Enlightenment, in
particular issues crossing the disciplinary boundaries between
history of mathematics and the so-called mechanical philosophy in
the natural sciences. Such an approach is vital for the historical
understanding of this period in which mechanics, astronomy,
navigation, cartography, hydraulics, etc., constituted an important
stimulus for advances in mathematics.

2) For the period 1800-1920 a number of talks centred on the
problem of probing the geometry of space both mathematically and
empirically after the advent of non-Euclidean geometry. The
Riemannian legacy and Poincar\'e's conventionalism served as two
cornerstones for this topic, a topic that gained new impetus
through Einstein's theory of general relativity and the emergence
of relativistic cosmology in 1917.

3) Throughout the twentieth century, mathematical modelling became an
increasingly important tool in the physical sciences, and with
these developments the modern concept of mathematical models slowly
emerged. Recent research on the history and epistemology of models
indicates that the conception of mathematical models changed in
various disciplines after 1900. This issue was addressed in a
collection of talks, including the case of aerodynamical research
in Germany -- a topic that is part of the larger complex of
issues involving ``mathematics and war'' now receiving widespread
attention. Other problems addressed included mathematical modelling
in meteorology during the second half of the twentieth century, one
of several fields which exerted a strong influence on the modern
conception of mathematical models.

The workshop brought together the core community of historians of
mathematics, many of whom have attended past meetings in Oberwolfach,
along with a number of historians and philosophers of science with
strong interests in mathematical issues. The meeting was characterized
by open discussions which, together with the talks, shed more light on
the interplay between mathematics and the physical sciences and gave
new insights into developments that had a crucial impact on the
development of modern mathematics.

The organizers and participants thank the ``Mathematisches
Forschungsinstitut Oberwolfach'' for making the workshop possible in
the usual comfortable and inspiring setting.

*No keywords available for this article.*

Guicciardini Niccolo, Hoff Kjeldsen Tinne, Rowe David: Mathematics in the Physical Sciences, 1650-2000. *Oberwolfach Rep.* 2 (2005), 3175-3246. doi: 10.4171/OWR/2005/56