I think the thing is both NTPs can agree one can formalize in different ways -- the question is which does one view as more interesting and fundamental? Keeping the fuzzy intuition in the mind's eye, or not not missing ways one can actually build a coherent framework? I find Ti-doms have a bit quicker of an eye for the latter.
Godel is an interesting case. I'm not sure if he was more an N or a T type actually. While his results symbolize a more T approach, it's interesting to consider that the man may have been more N-ish in his motivations. May! I'm not quite sure of that. It's a good question you raise. He seemed to have certain grandiose intuitions for what logic/mathematics is all about and might have viewed his theorems as the outcome of a passion to capture those. I find it interesting that he was led to argue against materialism and so on. Sounds like he could've been pretty N-ish to me!
But
just going off of the incompleteness theorems, that's very T stuff.
It's important to note I can't arrive at stuff by pure Ne, and another can't by pure Ti, it's definitely a mix; one can't conclude anything from an intuition held only in the mind without making it explicit in some way...really the question tends to be where all the energy going to the brain is spent