Abstract
This chapter discusses the von Neumann's claim of impossibility of hidden-variables theories. The work of von Neumann was mainly concerned with the axiomatization of the mathematical methods of quantum theory. His side remarks on hidden variables were merely an unfortunate step away from the main line of his reasoning. The public recognition that somehow von Neumann's formulation of hidden-variables theory was not a fortunate one and could not have the generality and exhaustiveness which von Neumann suggested, goes back at least to Bohm. With von Neumann and with Gleason and with all other quantum theorists there do not exist any pure quantum-mechanical states. As a reason for the nonexistence of hidden variables, von Neumann alludes to the impossibility of a relation like and to the validity of inequalities like in hidden variables theory, which he considers to be in conflict with the relations of quantum theory.
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