It's because of discussions like these that I wrote this (low-rated) article.

Summary: Mathematical truths can be cashed out as combined claims about 1) the common conception of the rules of how numbers work, and 2) whether the rules imply a particular truth. Together, one's beliefs about mathematical claims AND beliefs about whether real-world systems are ismorphic to their axioms, imply your expectations. If such expectations turn out to be wrong, then either your computation was wrong, or you were wrong that the system's dynamics are isomorphic to that particular axiom system.