Whoo! Now I look at this in some detail in the QM chapter of the book. You may be aware that there's a dispute over that proof that it still going today! Jeffrey Bub and, separately, Dennis Dieks have argued that von Neumann never meant to rule out all possible hidden variables– only a subset of them. They claim what he was actually arguing was that a hidden variables theory couldn't have the same mathematical structure as his own ie they cannot be Hilbert space theories. And that's true: Bohmian mechanics isn't a Hilbert space theory.

To answer your question though...it's complicated (sorry). Von Neumann seems to have been open to the idea of hidden variable theories ie he didn't think they were mathematically suspect. But my gut feeling was that he didn't see the point of them!

However, he wasn't dismissive of Bohm as other physicists were. From my book:

>While Heisenberg and Pauli branded Bohm’s theory as ‘metaphysical’

or ‘ideological’, von Neumann was not dismissive, as Bohm

himself notes with some pride and more than a little relief. ‘It appears

that von Neumann has agreed that my interpretation is logically consistent

and leads to all results of the usual interpretation. (This I am

told by some people.)’ Bohm wrote to Pauli shortly before his theory

was published. ‘Also, he came to a talk of mine and did not raise any

objections.’

Bohm might have hoped for Einstein to embrace his ideas, which

restored both realism (particles exist at all times in Bohmian mechanics)

and determinism. Einstein was, however, less kind than von

Neumann. Disappointed that Bohm had not rid quantum mechanics

of ‘spooky action at a distance’ (which he could not abide) he privately

called Bohm’s theory ‘too cheap’.