# Mathematics in the Physical Sciences, 1650-2000

### Niccolo Guicciardini

Universita di Siena, Italy### Tinne Hoff Kjeldsen

University of Copenhagen, Denmark### David E. Rowe

Johannes Gutenberg-Universität Mainz, Germany

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## Abstract

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:

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.

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.

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.