Where did von Neumann get the idea?
He knew Turing at Princeton in 1937-38 (see this Scrapbook Page.) By 1938 he certainly knew about Turing machines. See these source documents on what von Neumann knew of Turing, 1937-39. Many people have wondered how much this knowledge helped him to see how a general purpose computer should be designed. The logician Martin Davis, who was involved in early computing himself, has written a book The Universal Computer, The Road from Leibniz to Turing. Martin Davis is clear that von Neumann gained a great deal from Turing’s logical theory.