Mathematical Foundations of Quantum Mechanics

The book Mathematical Foundations of Quantum Mechanics (1932) by John von Neumann is an important early work in the development of quantum theory.

Publication history
The book was originally published in German in 1932 by Julius Springer, under the title Mathematische Grundlagen der Quantenmechanik. An English translation by Robert T. Beyer was published in 1955 by Princeton University Press. A Russian translation, edited by N. Bogolyubov, was published by Nauka in 1964. A new English edition, edited by Nicholas A. Wheeler, was published in 2018 by Princeton University Press.

Significance and Criticism
The book mainly summarizes results that von Neumann had published in earlier papers. Its main significance may be its argument against the idea of hidden variables, on thermodynamic grounds. However, this idea was refuted as early as 1935 by Grete Hermann, but the critique remained unknown until J.S. Bell's rediscovery in 1966.

von Neumann's claim rested on the assumption that any linear combination of Hermitian operators represents an observable and the expectation value of such combined operator follows the combination of the expectation values of the operators themselves. Bell shows that the consequences of that assumption are at odds with results of incompatible measurements, which are not explicitly taken into von Neumann's considerations.