What is wrong with von Neumann ’ s theorem on ” no hidden variables ”

It is shown that, although correct mathematically, the celebrated 1932 theorem of von Neumann which is often interpreted as proving the impossibility of the existence of " hidden variables " in Quantum Mechanics , is in fact based on an assumption which is physically not reasonable. Apart from that, the alleged conclusion of von Neumann proving the impossibility of the existence of " hidden variables " was already set aside in 1952 by the counterexample of the possibility of a physical theory, such as given by what is usually called the " Bohmian Mechanics ". Similar arguments apply to other two well known mathematical theorems , namely, of Gleason, and of Kochen and Specker, which have often been seen as equally proving the impossibility of the existence of " hidden variables " in Quantum Mechanics. 1. Hidden variables describing the states of a quantum system The presentation in the sequel follows arguments in Hemmick [1,2], as well as in Manin [pp. 82-95]. The main aim is to highlight the simplicity and clarity both in the mathematical argument, and in the fact that, physically, one of the assumptions in von Neumann's theorem is not reasonable.