I have to disagree with this. Modern (pure) mathematics is abstract and very often completely detached from practical applications because of culture and artist

I have to disagree with this. Modern (pure) mathematics is abstract and very often completely detached from practical applications because of culture and artistic inspiration. There is no "objectivity" driving modern pure mathematics. It exists mostly because people like thinking about it. Any connection to the real world is often a coincidence or someone outside the field noticing that something (really just a tiny-tiny amount) in pure maths could be useful. > forced there by a series of crises where the mathematics that they knew fell apart This can be said to be true of those working in foundations, but the vast majority of mathematicians are completely uninterested in that! In fact, most mathematicians today probably can't cite you the set-theoretic (or any other foundation) axioms that they use every day, if you ask them point-blank.