Any given mathematical statement (eg, 11 is a prime number) must either be true or false, right?The "primeness" of "11" is no more in doubt than any other proven theorem in Mathematics. The author is very misleading in his presentation of the example, though he then correctly states the reality in the subsequent paragraph, though he leaves out an important caveat: Gödel showed that there will exist some statements derivable in a mathematical system which can't be decided based on the axioms of that system. There is nothing, however, to prevent you from proving the statement true by appealing to axioms outside of the system you are working in.Wrong! Godel showed that however elaborate mathematics becomes, there will always exist some statements (not the above ones though) that can never be proved true or false.
But the point remains: any statement which is proveable by standard Mathematical proof techniques is NOT a "Gödel statement" and hence is NOT undecideable. That some statements are undecideable cast no doubt on the ones we can, and do eventually prove. There is no evidence that reality will turn out to be based on Gödelian statements, so it may not even be an issue for physicists.
There is an important assumption that is often overlooked: the methods of proof in the system must be "finitistic." IOW if you allow something like transfinite induction then you can prove completeness and consistency.
Of course then the question is, is a method like transfinite induction intuitively obvious?
Perfect. This article is pure nonsense. You have nailed it.