I've been wondering why von Neumann didn't do much work in the foundations of mathematics. (It seems like something he should have been very interested in.) Your comment made me do some searching. It turns out:

John von Neumann was a vain and brilliant man, well used to putting his stamp on a mathematical subject by sheer force of intellect. He had devoted considerable effort to the problem of the consistency of arithmetic, and in his presentation at the Konigsberg symposium, had even come forward as an advocate for Hilbert's program. Seeing at once the profound implications of Godel's achievement, he had taken it one step further—proving the unprovability of consistency, only to find that Godel had anticipated him. That was enough. Although full of admiration for Godel—he'd even lectured on his work—von Neumann vowed never to have anything more to do with logic. He is said to have boasted that after Godel, he simply never read another paper on logic. Logic had humiliated him, and von Neumann was not used to being humiliated. Even so, the vow proved impossible to keep, for von Neumann's need for powerful computational machinery eventually forced him to return to logic.

ETA: Am I the only one who fantasizes about cloning a few dozen individuals from von Neumann's DNA, teaching them rationality, and setting them to work on FAI? There must be some Everett branches where that is being done, right?