Why doesn't mathematics collapse, though humans often make mistakes in proofs?
If builders of a huge castle place some stones incorrectly, does it collapse completely?<p>No. Such errors may be discovered soon and taken down, or stand for decades, sometimes with lots of stuff built on top of it, and sometime parts will collapse, but the overall structure of the castle is sound, and, sooner or later, errors will be corrected.<p>And of course, sometimes, somebody decides to start building an entire new wing to the castle using new rules, as, for example, happened when non-Euclidean geometry was discovered/invented.