Right, there are game-changing advances in mathematical logic and sea changes in mathematical philosophy. The discovery of non-euclidean geometry did not mean e

Right, there are game-changing advances in mathematical logic and sea changes in mathematical philosophy. The discovery of non-euclidean geometry did not mean euclidean geometry was false, and real analysis is the same whether you found it on sets or categories, by definition. Incompleteness doesn't eliminate the possibility of consistency. Mathematics changes by becoming more expressive and growing outwards and inwards. Sometimes, a theorem is proven to be inconsistent and thrown out. My point was this happens a lot less often with mathematical theorems than it does with scientific facts because facts are based on our inductive study of the universe, whereas mathematics only makes statements about syllogisms. Unlike the real world, math is an area of study where incontrovertible facts are at least possible, because we make everything up, and just have to make sure we're consistent about it. We do not have access to such a priori knowledge about reality.