Do you know what the mathematical expression is for longing?. . . The negative numbers. The formalization of the feeling that you are missing something.
If we have dwelled on Godel's work at some length, is it because we see it in the mathematical analogy of what we would call the the ultimate paradox of man's existence. Man is ultimately subject and object of his quest. While the question whether the mind can be considered to be anything like a formalized system, as defined in the preceding paragraph, is probably unanswerable, his quest for an understanding of the meaning of his existence is an attempt at formalization.