Social History and Philosophy of Mathematics 1919 – 1960, a Young Conservative Revolution in Science?
After Thomas Kuhn’s famous book, scientific revolutions were for a while at the centre of the history of science, and expressions like paradigm change even entered everyday speech. To what extent Kuhn’s categories – geared in particular towards the history of physics – also apply to the history of mathematics, is still a complicated question. Meanwhile, the foundational crisis of mathematics – as the actors themselves called it after WW I – of the early twentieth century has been studied by historians and philosophers from various points of view; it has, for instance, been interpreted as an expression of modernism.
My interest concerns the time between the wars – or rather, the long period of the World Wars, extended all the way to the end of the 1950s. During this time, several traditional mathematical theories were transformed in ways that were as fundamentally new as they were retrograde, as ontologically liberal as they were conservative with respect to problems. I am studying the historical process of that period via two specific examples of mathematical subdisciplines, each of which illustrates in its own way the distinctiveness of post crisis modernity: probability calculus (including the theory of random processes, and in comparison to applied mathematical statistics) on the one hand, and Algebraic Geometry on the other, which was entirely rewritten as of the 1930s.
It turns out that the radical rewriting of these subdisciplines took place in the triangle between history of science, philosophy, and politics; geopolitical aspects are particularly important for an adequate description of this part of the history of mathematics. As a consequence, this subject, which at first sight appears to be extremely specialized and confined to the history of mathematics, actually generates questions of much more general interest about the first half of the twentieth century – and makes us think anew about the term of conservative revolution, which for various good reasons is controversial among historians and politically engaged persons.
Schappacher, N. 2010. «Rewriting Points.» (Invited talk, History of Mathematics section). in: Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010, pp. 3258-3291.
Oehler-Klein, S. / Schappacher, N. 2007. «Siegfried Koller und die neuen Herausforderungen der Statistik im Nationalsozialismus» in S. Oehler-Klein (ed.): Die Medizinische Fakultät der Universität Gießen im Nationalsozialismus und in der Nachkriegszeit: Personen und Institutionen, Umbrüche und Kontinuitäten. Stuttgart: Franz Steiner Verlag, pp. 247-262.
Schappacher, N. 2008. How to describe the transition towards a new mathematical practice : the example of Algebraic Geometry. Oberwolfach Reports 24.
Schappacher, N. 2007. «A historical sketch of B.L. van der Waerden’s work on Algebraic Geometry 1926-1946» in J. J. Gray & K. H. Parshall (eds.): Episodes in the History of Modern Algebra (1800-1950). History of mathematics series, vol. 32. Providence, RI: American Mathematical Soc. [u.a.], pp. 245-283.
Goldstein, C. / Schappacher, N. / Schwermer, J. (eds.). 2007. The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae. Berlin (u. a.): Springer Verlag.