The culture of research mathematics in 1860s Prussia

Adolph Mayer and the theory of the second variation in the calculus of variations

Craig Fraser

pp. 121-140

in: Maria Zack, Dirk Schlimm (eds), Research in history and philosophy of mathematics, Basel, Birkhäuser, 2018

Abstract

The paper examines the intellectual culture of higher mathematics in Prussia and more broadly in Germany in the middle of the nineteenth century. There was at this time a strong ethos of pure mathematics in which the subject was pursued more for its intrinsic interest than for its utility or practical applications. This outlook was reflective of the prominence of neohumanism in German culture of the period. In the case of mathematics, it led to a higher degree of logical sophistication in the elaboration of theories. The work of Adolph Mayer in the calculus of variations at Prussia's University of Königsberg is presented as a case study that illustrates the outlook and underlying values of German higher mathematics in the second half of the century. The self-consciously theoretical character of this mathematics distinguished it in a qualitative way from the style and mentality of the Enlightenment masters of analysis a century earlier. Our study provides evidence for the basic historicity of the development of analysis from 1750 to 1870.