Math went on because it doesn’t matter. Nobody cares about incompleteness. If you can prove ZFC is inconsistent, do it and we’ll all move to a new system and most of us wouldn’t even notice (since nobody references the axioms outside of set theorists and logicians anyway). If you can prove it’s incomplete, do it and nobody will care since the culprit will be an arcane theorem far outside the realm of non-logic fields of math.
You wouldn’t even notice if some proof is wrong because it relies on an inconsistency that’s the issue. And that’s before you didn’t notice because noone builds anything on axioms but instead uses fragile foundations made of intuition, hand-waving, and mass psychology.
Incomplete is fine that’s exactly what constructive maths is doing.
Math went on because it doesn’t matter. Nobody cares about incompleteness. If you can prove ZFC is inconsistent, do it and we’ll all move to a new system and most of us wouldn’t even notice (since nobody references the axioms outside of set theorists and logicians anyway). If you can prove it’s incomplete, do it and nobody will care since the culprit will be an arcane theorem far outside the realm of non-logic fields of math.
You wouldn’t even notice if some proof is wrong because it relies on an inconsistency that’s the issue. And that’s before you didn’t notice because noone builds anything on axioms but instead uses fragile foundations made of intuition, hand-waving, and mass psychology.
Incomplete is fine that’s exactly what constructive maths is doing.