The problem with ideology is if you got an ideology, you already got your mind made up, you know all the answers, and that makes evidence irrelevant and argument a waste of time, so you tend to govern by assertion and attack. The problem with that is that discourages thinking and gives you bad results.
Kurt Gödel
The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules. . . One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.
