These letters contain some of the first discussions of computational complexity theory, and von Neumann immediately identifies P vs NP as a central problem in the field. The work was unpublished and undeveloped, as von Neumann became ill and died around this time.

Edit: I double-checked my biography of von Neumann and in fact, as the poster below indicated, his responses (if he was able to make any) aren't available. This letter of Goedel has identified an NP problem, and he's asking if it can be solved in polynomial time, so we can't credit von Neumann for identifiying the problem with certainty.