I have but a naive incomplete conjecture that von Neumann's ability to solve very hard mathematical problems are a direct result of him spending so much time initially at the axiomatic level of mathematical foundations. He must have developed a first-principles level of understanding and intuition about how to tackle mathematical problems, or why their solution would be impossible.

In my own capacity, I've seen solutions to very hard problems as "obvious" or the impossibility of such solutions as "obvious" compared to other engineers who lack a formal training in Computer Science, for example. To use a naive example, what types of problems could be done with regular expressions, and what not, because they are regular languages, and knowing the theory of regular languages. He must have gone so much further down the rabbit hole that things were seemingly obvious, or if a solution was possible at all, it would have to follow from certain first-principles, and could reason his way back to the highest level of abstraction, with immense ease.