SPIRITUAL AI

Ákos Császár and Dénes Petz In early autumn of 1926 von Neumann arrived in Gottingen. He immediately learnt quantum theory from Heisenberg's lectures. Von Neumann became an axiomatizer of quantum mechanics on behalf of the so-called Copenhagen school (which did not include Schrodinger.) To Hilbert's delight, von Neumann's mathematical exposition made much use of Hilbert's own concept of Hilbert space. However, it is not sure that axiomatization of the Hilbert space and its linear operators (as a substitute for infinite matrices) by the twenty-three-year-old von Neumann was to Hilbert's delight. Our present concept of Hilbert space, infinite dimensional complex vector space endowed with an inner product whose metric is complete and separable, was formulated by von Neumann. The rigorous quantum mechanics required the use of unbounded operators defined only on a subspace of a Hilbert space. Von Neumann developed several technicalities concerning such operat