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Von Neumann and the Mathematics of Göttingen

Part of the Science Networks. Historical Studies book series (SNHS, volume 38)

Abstract

When von Neumann visited Göttingen for the first time, in this small university there was a remarkable, lively nucleus of mathematical research, whose ambitious cultural vision had spread well beyond that of the traditional centre of German mathematics, the University of Berlin. The organization of this nucleus was the result of the personal initiative of the great mathematician Felix Klein, who had obtained the chair at Göttingen in 1885. Göttingen’s mathematical tradition retained at length the orientation given by Klein, although, starting in 1895, it was increasingly subjected to the influence of the different approach introduced by David Hilbert.25 Klein had displayed a deep interest in physics and in the applications of mathematics from the outset, and had collaborated with the mathematicians Julius Plücker and Alfred Clebsch, who, during the second half of the nineteenth century, had represented the opposition to the “purist” tendencies of the Berlin school of mathematics. The “purist” geometry schools — which had sprung up during the century in several European countries, in Germany, France and Italy in particular, — were opposed to studying geometry by the analytical method of Cartesian origin, that is, based on the systematic use of algebra and analysis to represent and study geometric properties. In their view, the theorems, starting from the properties of the geometric entities under investigation, had to be obtained through “synthetic” arguments that were “purely” internal to the geometric discourse, that is, without the help of algebraic calculus. The conflict between the “purist” tendency and the “analytical” approach became very bitter.

Keywords

Quantum Mechanic Mixed Strategy Euclidean Geometry Mathematical Research Axiomatic Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Birkhäuser Verlag AG 2009

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